Consider the function below. (If an answer does not exist, enter DNE.) f(x) = x3 − 27x + 3 (a) Find the interval of increase. (Enter your answer using interval notation.)
Answer:
(-∞,-3) and (3,∞)
Step-by-step explanation:
f(x) = x³ − 27x + 3
1. Find the critical points
(a) Calculate the first derivative of the function.
f'(x) = 3x² -27
(b) Factor the first derivative
f'(x)= 3(x² - 9) = 3(x + 3) (x - 3)
(c) Find the zeros
3(x + 3) (x - 3) = 0
x + 3 = 0 x - 3 = 0
x = -3 x = 3
The critical points are at x = -3 and x = 3.
2. Find the local extrema
(a) x = -3
f(x) = x³ − 27x + 3 = (-3)³ - 27(-3) + 3 = -27 +81 + 3 = 57
(b) x = 3
f(x) = x³ − 27x + 3 = 3³ - 27(3) + 3 = 27 - 81 + 3 = -51
The local extrema are at (-3,57) and (3,-51).
3, Identify the local extrema as maxima or minima
Test the first derivative (the slope) over the intervals (-∞, -3), (-3,3), (3,∞)
f'(-4) = 3x² -27 = 3(4)² - 27 = 21
f'(0) = 3(0)² -27 = -27
f'(4) = 3(4)² - 27 = 51
The function is increasing on the intervals (-∞,-3) and (3,∞).
The graph below shows the critical points of your function.
According to psychologists, IQs are normally distributed, with a mean of 100 and a standard deviation of 15 . a. What percentage of the population has IQs between 85 and 100 ?
Partition the circle into 4 equal sections. What unit fraction of the circle’s area does each section represent?
Answer:
1/4
Step-by-step explanation:
If the 4 sections have equal areas, then each section has 1/4 of the original circle's area.
F
13
5
H
12
G
se
Find mZH to the nearest degree.
67
O 18
O 45
O 23
Answer:
∠ H ≈ 23°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan H = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{FG}{HG}[/tex] = [tex]\frac{5}{12}[/tex] , thus
∠ H = [tex]tan^{-1}[/tex] ( [tex]\frac{5}{12}[/tex] ) ≈ 23° ( to the nearest degree )
List the angles in order from the largest to the smallest for ABC.
AB= 14, AC = 15, BC = 16
Answer:
B. ∠A, ∠B, ∠C
Step-by-step explanation:
1. Draw a model with AB as the shortest line and BC as the longest line.
∠A connects the two shortest lines, making it the largest angle.
∠B connects the shortest and the longest lines, making it the second largest angle.
∠C connects the two longest lines, making it the smallest angle.
Answer:
A > B > C
Step-by-step explanation:
Ypu probably wouldn't think about it unless someone pointed it out, but if you look at a triangle of any type you can see that the sizes of the sides are directly related to the sizes of the angles opposed to them.
By this I mean, the largest side will have the largest angle across from it and the smallest side will have the smallest angle.
Based off of my drawing, it looks like the order is angle A, then B, then, and then C.
please help me in these question ????
A school bag contains 12 pens of which 5 are red and the other are black. 4 pens are selected from the bag.
(a) How many different samples of size 4 pens are possible?
(b) How many samples have 3 red pens and 1 black pen?
(c) How many samples of size 4 contain at least two red pens?
(d) How many samples of size 4 contain
If the average yield of cucumber acre is 800 kg, with a variance 1600 kg, and that the amount of the cucumber follows the normal distribution.
1- What percentage of a cucumber give the crop amount between and 834 kg?
2- What the probability of cucumber give the crop exceed 900 kg ?
Answer:
Step-by-step explanation:
A school bag contains 12 pens of which 5 are red and the other are black. 4 pens are selected from the bag.
(a) How many different samples of size 4 pens are possible?
12C4=12!/(4!*8!)=495
(b) How many samples have 3 red pens and 1 black pen?
5C3*7C1
5C3=5!/(3!*2!)=10
7C1=7!/(1!*6!)=7
=>5C3*7C1=10*7=70
(c) How many samples of size 4 contain at least two red pens?
(5C2*7C2)+(5C3*7C1)+(5C4*7C0)
5C2=5!/(2!*3!)=10
7C2=7!/(2!*5!)=21
5C3=5!/(3!*2!)=10
7C1=7!/(1!*6!)=7
5C4=5!/(4!*1!)=5
7C0=7!/(0!*7!)=1
=>(5C2*7C2)+(5C3*7C1)+(5C4*7C0)=285
(d) How many samples of size 4 contain at most one black pen?
(7C1*5C3)+(7C0*5C4)
7C1=7!/(1!*6!)=7
7C0=7!/(0!*7!)=1
5C3=5!/(3!*2!)=10
5C4=5!/(4!*1!)=5
=>(7C1*5C3)+(7C0*5C4)=(7*10)+(1*5)=75
There are 25,400,000 nanometers in an inch. What is this number written in scientific notation?
Answer:
254 x 10^5
Step-by-step explanation:
Hope this helps :)
If anything is misunderstood plz comment and I will change to the answer which you give me thank you very much :)
Answer:
2.54 x 10^5
hope this answer helps u ._.
What number is halfway between 250 and 300
Answer:
the number that is halfway between 250 and 300 is 275
Step-by-step explanation:
250+300= 550/2= 275
The number i,e halfway is 275.
Important information:The two numbers is 250 and 300.calculation:[tex]= (250 + 300) \div 2\\\\= 550 \div 2[/tex]
= 275
Find out more information about the Number here : https://brainly.com/question/17429689?referrer=searchResults
Alex wants to sew a pillow in the shape below. How many square yards of fabric are needed to sew the pillow? Fabric is only sold in increments of ¼ yard.
The shape is missing, so i have attached it.
Answer:
2.6
Step-by-step explanation:
From the image attached, the diameter of the inner semi - circle is 0.5 yards while the length of each side of the pillow is 0.2 yards.
Thus, for us to find the length of the seam which is along the edges of the pillow, we will calculate the perimeter of the outer semicircle, then add the perimeter of the inner semicircle and also add the sides too.
Now, due to the fact that the length of the sides of the pillow are 0.2 yards each, the diameter of the outer circle would be;
0.5 + 0.2 + 0.2 = 0.9 yards. So, the perimeter of the outer semicircle is,
P0 = πd/2 = π × 0.9/2 =0.45π yds
The perimeter of the inner semicircle would be given as;
PI = πd/2 = π × 0.5/2 =0.25π yds.
Thus, we can calculate the total perimeter of the pillow as;
PT = P0 + PI + 0.2 + 0.2
PT = 0.45π + 0.25π + 0.2 + 0.2
PT ≈ 2.6 yards
Alex will need 2.6 yds
Answer:
0.5
Step-by-step explanation:
At a local high school, the student population is growing at 12% a year. If the original population was 242 students, how long will it take the population to reach 300 students? Round to the nearest tenth of a year.
Answer: 2 years
Step-by-step explanation:
The exponential growth function is given by :-
[tex]y=A(1+r)^x[/tex] (i)
, where A = initial value , r = rate of growth and x= time period.
As per given ,
A= 242
r= 12% = 0.12
To find : t when y= 300.
Put all the values in (i)
[tex]300=242(1+0.12)^x\\\\\Rightarrow\ \dfrac{300}{242}=(1.12)^x\\\\\Rightarrow\ 1.23967=(1.12)^x[/tex]
Taking log on both sides , we get
[tex]\log (1.2396) = t \log (1.12)\\\\\Rightarrow\ 0.09328=t(0.049218)\\\\\Rightarrow t=\dfrac{0.09328}{0.049218}=\approx2[/tex]
hence, it will take 2 years.
When a dummy variable is included in a multiple regression model, the interpretation of the estimated slope coefficient does not make any sense anymore.
a. True
b. False
Answer: b. False
Step-by-step explanation:
A dummy variable is a numerical variable used in regression analysis to represent values for categorical data by using value 0 (shows absence of particular category) or 1 (shows presence of particular category) .We cannot use categorical data to evaluate the slope coefficient (numerical value) until we convert them into dummies.Hence, the given statement is absolutely false.
What’s the next number is this series 31,29,24,22,17,
Answer:
15
Step-by-step explanation:
Just find out the pattern. It is decreasing, so let's find out how much it is decreasing by.
31-29= -2
29-24= -5
24-22= -2
22-17= -5
The pattern is -2, -5, -2, -5... So the next one should be -2 again! 17-2=15.
Remember, a pattern doesn't always have to be subtracting, adding, dividing, or multiplying at a constant number! It can switch between two, like this problem!
can someone simplify 4x-3y please!!
Answer:
I think you should change it to 4x + 3y
Step-by-step explanation:
hope this helps
Apply the square root property of equality.
x + =
Answer:
Step-by-step explanation:
Answer:
+ 1/16 = +- 2/3
A pharmacy has purchased 550 products over a period of 3 months. If their average inventory was 235 products in a 3 month period what was their inventory turnover rate for this period
Answer:
2.34
Step-by-step explanation:
A pharmacy purchased 550 products over a period of 3 months
The average inventory was 235 products during the period of 3 months
Therefore, the inventory turnover rate for this period can be calculated as follows
= 550/235
= 2.34
Hence the inventory turnover rate for this period is 2.34
Find the value of x.
Answer:
x=3
Step-by-step explanation:
I guessed and checked which x value would make ABC proportional to DBE. If x=3, than DB=8 which is double BE. If x=3, than AB=14 which is double BC. Since it is proportional, It should be correct. I don't remember the actual way you solve this with a formula but this makes sense to me.
Answer:
x=3
Step-by-step explanation:
We can use ratios to solve since the triangles are similar
x+5 4
------------ = ---------------
x+5 +2x 4+3
Simplifying
x+5 4
------------ = ---------------
3x+5 7
Using cross products
7(x+5) = 4(3x+5)
Distribute
7x+35 = 12x+20
Subtract 7x from each side
35 = 5x+20
Subtract 20 from each side
15 = 5x
Divide by 5
3 =x
Fill in the missing values to make the equations true .
Answer:
a) 15
b) 9
c) 2
Step-by-step explanation:
im try it by using trial and error by calculator
A sample of 255 observations is selected from a normal population with a population standard deviation of 27. The sample mean is 20. Determine the standard error of the mean.
Answer:
1.691
Step-by-step explanation:
Standard error of the mean is expressed as SEM = S/√n
S is the population standard deviation
n is the sample size (number of observation)
Given S = 27 and n = 255
SEM = 27/√255
SEM = 27/15.97
SEM = 1.691
Hence the standard error of the mean is 1.691
In order to study the mean blood pressure of people in his town, Richard samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group. Which type of sampling is used?
a. Convenience sampling
b. Cluster sampling
c. Stratified sampling
d. Systematic sampling
Answer:
C Stratified sampling
Step-by-step explanation:
Stratified sampling : Stratified sampling is a type of sampling technique in which the total population is divided into smaller groups or strata to complete the sampling process. The strata is formed based on some common characteristics in the data of the population.
One of the advantage of stratified random sampling is that it covers important population characteristics in the sample.
Solve 2(x - 1) + 3 = x - 3(x + 1) (make sure to type the number only)
Answer:
x = -1
Step-by-step explanation:
2(x - 1) + 3 = x - 3(x + 1)
Distribute
2x -2+3 = x -3x-3
Combine like terms
2x +1 = -2x-3
Add 2x to each side
2x+1 +2x = -2x-3+2x
4x+1 = -3
Subtract 1 from each side
4x+1-1 = -3-1
4x= -4
Divide by 4
4x/4 = -4/4
x = -1
If the area of the square is A(s) = s², find the formula for the area as a function of time, and then determine A(s(3)).
A(t) = 100t^2 + 500t + 625
3,025 square pixels
Answer:
A(t) equals 100t²+ 500t + 625.
The area of the square image after 3 seconds is 3,025 square pixels.
i will give brainliest and 5 stars if you help ASAP
Answer:
£39.20
Step-by-step explanation:
→ Identify which ratio goes to each person
2 : 1 : 5
2 = Paul
1 = Colin
5 = Brian
→ Divide the total tip by the total sum of the ratio's
£78.40 ÷ ( 2 + 1 + 5 ) ⇔ £78.40 ÷ 8 = £9.80
→ Now we know one part is equal to £9.80 we multiply this number by each of the associated ratio's
Paul = £9.80 × 2 ⇔ £19.60
Colin = £9.80 × 1 ⇔ £9.80
Brian = £9.80 × 5 ⇔ £49
→ Minus Brian's tip against Colin's tip
£49 - £9.80 = £39.20
Plz answer quick will give good rate and thanksss
h(x) = (x - 3)^2 determine which x-value whether it is in the domain of h or not
In domain not in domain
0
3
4
Answer:
Hey there!
All of the values: 0, 3, and 4 are in the domain.
This is because h(x) = (x - 3)^2 is a parabola, or a quadratic. By definition, the domain, or the possible x values of a parabola are infinite.
Hope this helps :)
Find the Vertical asymptotes of the graph of f
[tex]f(x) = \frac{x + 2}{ {x}^{2} - 4}[/tex]
Answer:
x = 2 and x = -2
Step-by-step explanation:
To find the vertical asymptotes, set the denominator equal to zero and solve for x:
vertical asymptotes are x = 2 and x = -2
A ladder leans against a vertical at angle of 60° to the wall of the foot of the ladder is 5m away from the wall calculate the length of the ladder
Answer:
Your question indicates the ladder is at an angle of 60° to the wall, meaning the angle between the wall and the ladder is 60° and the angle between the ladder and the ground must be 30°. Not a very efficient way to set up a ladder.
5.7735 meters. The top of the ladder is 2.8868 meters off the ground.
Now, if you meant the ladder is 60° from the ground, that’s a different story.
Then, the ladder is 10 meters long and reaches 8.6603 meters from the ground.
A 30–60–90 right triangle is half of an equalateral triangle. Therefore the hypotenuse is double the length of the short leg, and by the Pythagorean theorum, we can determine that the other leg is the length of the short leg times the square root of 3.
All lengths in this answer are rounded to the nearest tenth of a millimeter.
Step-by-step explanation:
If 6x +3= 2x+ 19, then x =
Answer:
x = 4
Step-by-step explanation:
6x + 3 = 2x + 19 ------ subtract 3 both sides
6x + 3 - 3 = 2x + 19 - 3 simplify
6x = 2x + 16 ------ subtract 2x both sides
6x - 2x = 2x + 16 - 2x simplify
4x = 16
x = 16 / 4
x = 4
Answer: x = 4
Step-by-step explanation: If the variable appears on both sides of the equation, we put the variables together on one side of the equation and the numbers together on the other side of the equation.
So let's put our variables on the left side by first subtracting
2x from both sides of the equation to get 4x + 3 = 19.
Next, we subtract 3 from both sides to get 4x = 16.
Finally, we divide both sides by 4 to get x = 4.
what is area of this tile?
The area of the triangle is 5.88 square centimeters.what is the length of the base.the heights is 2.1
Answer:
base = 5.6 cm
Step-by-step explanation:
area of a triangle = 1/2 * base * height
area = 5.88 cm²
height = 2.1 cm
5.88 = 1/2 * base * 2.1
5.88 = 1.05 base
5.88 / 1.05 = base
base = 5.6 cm
the area of triangle is 5.25 sq cm what is length of base
Jayden, who burns 345 calories in 45 min
while hiking is preparing for a 6 hour hike.
He uses a special supplement beverage
pack that provides water, needed
electrolytes, and 310 calories. The goal is to
replace roughly 1/3 of the calories burned
while carrying as light a load as possible.
How many packs should he take?
This question is solved using proportions.
First, we find how many calories he will burn in the hike.Then, we find how many calories he will need to replace, and the number of packs needed.Doing this, we get that he should take 3 packs.
How many calories he burns in the hike?
In 45 minutes, he burns 345 calories. How many calories in 6*60 = 360 minutes?
45 minutes - 345 calories
360 minutes - x calories
Applying cross multiplication:
[tex]45x = 345*360[/tex]
[tex]x = \frac{345*360}{45}[/tex]
[tex]x = 2760[/tex]
He burns 2760 calories in the hike.
How many calories he wants to replace?
Roughly 1/3, so he have to find one third of 2760, that is:
[tex]\frac{2760}{3} = 920[/tex]
How many packs?
One pack recovers 310 calories, how many packs for 920 calories?
1 pack - 310 calories
x packs - 920 calories
Applying cross multiplication:
[tex]310x = 920[/tex]
[tex]x = \frac{920}{310}[/tex]
[tex]x = 2.97[/tex]
Rounding up, he should take 3 packs.
A similar question is found at https://brainly.com/question/14426926
PLEASE HELP MEEEEEEEEEEEEEEE
Answer:
x=16.1
Step-by-step explanation:
open the brackets
-4.5= -0.5x-3.55
Take 3.55 to the other side.
-4.5-3.55 = -8.05
5/10x= -805/100
0.5x= - 8.05 = 16.1
