[tex]\displaystyle\lim_{h\to0}\frac{f(9+h)-f(9)}h = \lim_{h\to0}\frac{(9+h)^4-9^4}h[/tex]
Carry out the binomial expansion in the numerator:
[tex](9+h)^4 = 9^4+4\times9^3h+6\times9^2h^2+4\times9h^3+h^4[/tex]
Then the 9⁴ terms cancel each other, so in the limit we have
[tex]\displaystyle \lim_{h\to0}\frac{4\times9^3h+6\times9^2h^2+4\times9h^3+h^4}h[/tex]
Since h is approaching 0, that means h ≠ 0, so we can cancel the common factor of h in both numerator and denominator:
[tex]\displaystyle \lim_{h\to0}(4\times9^3+6\times9^2h+4\times9h^2+h^3)[/tex]
Then when h converges to 0, each remaining term containing h goes to 0, leaving you with
[tex]\displaystyle\lim_{h\to0}\frac{f(9+h)-f(9)}h = 4\times9^3 = \boxed{2916}[/tex]
or choice C.
Alternatively, you can recognize the given limit as the derivative of f(x) at x = 9:
[tex]f'(x) = \displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h \implies f'(9) = \lim_{h\to0}\frac{f(9+h)-f(9)}h[/tex]
We have f(x) = x ⁴, so f '(x) = 4x ³, and evaluating this at x = 9 gives the same result, 2916.
HELP PLEASE PICTURE ABOVE. NO LINKS JUST HOW TO SOLVE STEP BY STEP AND THE ANSWER PLEASE
9514 1404 393
Answer:
4) -ln(2)/3
5) x = 9
6) x = 2
7) x = -6
Step-by-step explanation:
4) e^(-3x) = 2 . . . . given
-3x = ln(2) . . . . . take the natural log
x = -ln(2)/3 . . . . divide by the coefficient of x
__
5) ln(3x -5) = ln(11) +ln(2)
3x -5 = 11·2 . . . . . take antilogs
3x = 27 . . . . . . . . add 5
x = 9 . . . . . . . . . . divide by 3
__
6) log4(x -1) +log4(x +2) = 1
(x -1)(x +2) = 4 . . . . . take antilogs
x^2 +x -2 = 4 . . . . . . eliminate parentheses
x^2 +x +1/4 = 6 1/4 . . . add 2 1/4 to complete the square
(x +0.5)^2 = 6.25 . . . . write as a square
x +0.5 = ±2.5 . . . . . . . take the square root
x = -0.5 ± 2.5 = {-3, +2} . . . . . . x = -3 is an extraneous solution
x = 2
__
7) 8^x = 4^(x -3)
2^(3x) = 2^(2(x -3)) . . . . write using a common base of 2
3x = 2(x -3) . . . . . . . . . . take logarithms base 2
x = -6 . . . . . . . . . . . . . . .subtract 2x
Evaluate g(2) given. Help
Answer:
[tex]g(2) = 3[/tex]
Step-by-step explanation:
Given
See attachment
Required
[tex]g(2)[/tex]
To solve this, we make use of:
[tex]g(x) = |7 - x^2|[/tex]
Because [tex]x \le 2[/tex]
i.e. [tex]2 \le 2[/tex]
So, we have:
[tex]g(2) = |7 - 2^2|[/tex]
[tex]g(2) = |7 - 4|[/tex]
[tex]g(2) = |3|[/tex]
Remove absolute brackets
[tex]g(2) = 3[/tex]
PLEASE HELP!
THE QUESTION IS IN THE PHOTO!
For What value of x is ABC~DEF?
Answer:
x=12
Step-by-step explanation:
Since the triangles are congruent, you can use either B or D to solve for x.
7x+10=94
7x=94-10
7x=84
x=84÷7
x=12
Keiko bought 3 POUNDS of fruit salad. How many OUNCES of fruit salad did Keiko buy?
Answer:
48 ounces.
Step-by-step explanation:
:) have a good rest of your day.
The table shows the test scores of students who studied for a teat as a group (group a) and students who studied individually (group b).
Which would be the best measures of center and variation to use to compare the data?
Answer:
https://rr.noordstar.me/83819a0f
Answer: B
Step-by-step explanation:
I didn't waste time looking at if the data was Symmetric or skewed, because A, C and D are all false statements:
A - If it's skewed Mean wouldn't be used
C - If it's Symmetric IQR wouldn't be used
D - If it's skewed Standard Deviation wouldn't be used
Simplify 150 -(0.4 x 150)+15
Carlos, Brad, and Rick earned $221.88 raking leaves and cleaning yards last week. If they split their earnings equally, how much will each of them get?
Answer:
Step-by-step explanation:
Chanclas
Answer:
$110.94
Step-by-step explanation:
221.88 divided by 2 is 110.94
You are making a pyramid-shaped trophy.
The trophy has a square base with side lengths of 9 inches and a slant height of 11 inches.
The paint needed costs $0.15 per square inch.
How much will it cost to paint the faces of the trophy?
Show your work
Answer: [tex]\$29.7[/tex]
Step-by-step explanation:
Given
The trophy has a side of [tex]a=9\ in.[/tex]
Slant height [tex]l=11\ in.[/tex]
Rate of painting [tex]r=\$\ 0.15/in.^2[/tex]
Lateral surface area of square pyramid is [tex]2al[/tex]
Insert the values
[tex]\Rightarrow 2\times 9\times 11\\\Rightarrow 198\ in.^2[/tex]
Cost of painting
[tex]\Rightarrow 198\times 0.15=\$29.7[/tex]
Before a high-school football game the footballs were inflated to p = 13 psi (pounds per square inch). After the game the mean inflation was 12.5 psi.
Select the null hypothesis H0.
Group of answer choices
0=13
0=12.5
0<13
0>12.5
Answer:
The null hypothesis is [tex]H_0: \mu = 13[/tex]
Step-by-step explanation:
Before a high-school football game the footballs were inflated to p = 13 psi (pounds per square inch).
This means that, as we are going to test the inflation levels before and after the game, we test at the null hypothesis that it is of 13 psi, that is:
[tex]H_0: \mu = 13[/tex]
Find the surface area of a square pyramid with side length 4 mi and slant height 5 mi.
Answer:
SA = 56 sq mi
Step-by-step explanation:
SA = area of base + 1/2(perimeter of base)(slant height)
SA = 16 + 1/2(16)(5)
SA = 16 + 8(5)
SA = 16 + 40
HELP ILL GIVE YOU BRAINLIEST AND A FOLLOW
what does x=?
Answer:
#1: x=8, #2: x=21, #3: x=9
Step-by-step explanation:
So, to solve each of these x's, we need to do two things:
Find the scale factor
Then scale for x.
So lets start off with the first one.
We have a side value fo 3.
In the scaled version, we have the same side with a value of 6.
To find the scale, divide the 6 by 3:
6/3
=
2
So our scale is 2.
Next, lets look at our value on the traingle we know, and solve for the unkown x. We know that on the orginal traingle, its 4. For the version thats 2 times bigger, its x
So to solve this, multiply the 4 by 2:
4*2
=
8
This is your x value for the first question.
Next we have the side value 12 for the trapezoid. For the one next to it, the trapezoid has the same side with a value of 18.
To find the scale, lets divide 18 by 12.
18/12
=
1.5
That is our scale factor.
In these trapezoids, the bottom value is orginally 14.
In the scaled version, which we know is 1.5 times bigger, we have x.
To solve for x, lets multiply the 14 by 1,5:
14*1.5
=
21
So we know our x is 21 for the second answer.
Finally we have the third question.
This one is opposite to the last ones, where the smaller value has the missing x value.
Here our top side value is 20.
On the scaled version it is 15.
Lets divide 15 by 20, instead of what we normally do. Which would have been 20 by 15:
15/20
=
.75
Now, with this scale factor, our x will be smaller than the known value. Looking at the side length, the orginal value is 12.
On the scaled side length that is 0.75 times as big, its x
So lets multiply 12 by 0.75:
12*0.75
=
9
So this is your last x value, for your third answer!
This might seem long and tedious, but its actually a simple way of thinking about it, and you may find that you can quickly do this in your head, instead of a shorter, more complex way.
Hope this helps!
help me please help. ........................
Answer: the third option (3/6 > 5/12)
Step-by-step explanation:
process of elimination:
option one is incorrect because 1/2 = 3/6 (not 1/2 > 3/6)
option two is incorrect because again, 1/2 = 3/6
option four is incorrect because 3/6 > 5/12
ava goes to lunch with 3 of her friends. The cost of their meals are $8, $4, $7, and $5. if they split the bill evenly. how much should each person pay? ANSWER NOW
Answer:
Each person should pay $6.00
Step-by-step explanation:
First, add everyone's cost
8 + 4 + 7 + 5 = 24
Then, divide by 4
24 ÷ 4 = 6
Lastly, have a great day! :)
solve system of equations
y= 8x + 1
y = 6x + 3
(2,4)
(0,1)
(1,9)
or (4,14)
Find all exact solutions of the equation on the interval [0, 2π).
cosxtanx=cosx
Answer:
[tex]\displaystyle x=\left\{\frac{\pi}{4}, \frac{5\pi}{4}\right\}[/tex]
Step-by-step explanation:
We want to solve the equation:
[tex]\cos(x)\tan(x)=\cos(x)[/tex]
On the interval [0, 2π).
First, we can subtract cos(x) from both sides:
[tex]\cos(x)\tan(x)-\cos(x)=0[/tex]
Factor:
[tex]\cos(x)\left(\tan(x)-1\right)=0[/tex]
Zero Product Property:
[tex]\cos(x)=0\text{ or } \tan(x)-1=0[/tex]
Solve for each case:
[tex]\cos(x)=0\text{ or }\tan(x)=1[/tex]
Using the unit circle:
[tex]\displaystyle x=\left\{\frac{\pi}{4}, \frac{\pi}{2}, \frac{5\pi}{4}, \frac{3\pi}{2}\right\}[/tex]
However, since tangent isn't defined for π/2 and 3π/2, we remove them from our solutions. Hence:
[tex]\displaystyle x=\left\{\frac{\pi}{4}, \frac{5\pi}{4}\right\}[/tex]
In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. Downtown StoreNorth Mall Store Sample size2520 Sample mean$12$6 Sample standard deviation$3$1 The point estimate for the difference between the two population means is 6. Find a 95% interval estimate for the difference between the two population means. 0.654 to 2.615 3.958 to 8.042 4.692 to 7.308 5.699 to 8.301
Answer:
4.692 to 7.308
Step-by-step explanation:
Given :
n1 = 25 ; n2 = 20 ;
Mean x1 = $12 ; mean x2 = $6
Standard deviation, s1 = 3 ; s2 = 1
Confidence interval :
(x1 - x2) ± t*√(s1²/n1) + (s2²/n2)
x1 - x2 = (12 - 6) = 6
√(s1²/n1) + (s2²/n2) = √(3²/25) + (1²/20) = 0.640
Degree of freedom :
((s1²/n1) + (s2²/n2))² / (s1²/n1)²/n1-1 + (s2²/n2)²/n2-1
Numerator = 0.1681
Denominator = 0.0054 + 0.0001315 = 0.0055315
Degree of freedom = 0.1681 / 0.0055315 = 30.38 = 30
Tcritical at 0.05, df = 30 = 2.042272
Hence ;
6 ± 2.042272(0.640)
6 ± 1.30705408
Lower boundary = 6 - 1.30705408 = 4.69294592
Upper boundary = 6 + 1.30705408 = 7.30705408
(4.693 ; 7.307)
A billboard is 5.0 m by 2.5 m. A scale diagram of the billboard is 0.25 m by
0.125 m.
a.
1:
Calculate the scale.
b. Calculate the scale factor (k).
c.
Is this a reduction or enlargement? Justify your thinking.
Pls help
Answer:
A the answer is a because i was just working on that rn
Step-by-step explanation:
When you sunbathe nine feet from the swimming pool, your distance to a point of
tangency with the pool is twelve feet. Find the radius of the pool.
Answer:
[tex]9.5 \sqrt{?} [/tex]
When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object
with mass 9 kg, the acceleration of the object is 5 m/s². When the same force acts upon another object, its acceleration Is 3 m/s? What is the mass of this
object?
Answer:
Constant Force F= ?
A= 5m/s²
M=9kg
According to the Question
A
[tex] \alpha [/tex]
1/m
A=F/m
So F=ma
F=5×9
F=45N
we look for m using the formula A=F/m
m=F/A
where A=3
F=45
M=?
So M=45/3
M=15kg
URGENT NEED HELP CLICK TO SEE
Answer: 2*5^2-12
5 to the 2nd power is 25
2*25-12
2*25=50
50-12=38
the answer is C 38
hope this helps
Find the value of x UREGENT HELP PLEASE
Answer:
15.3
Step-by-step explanation:
Cos 32 = x/18
Cos 32 = 0.848048096
x/18 = 0.848048096
x = 15.3 (rounded)
Henry is looking for the best deal on a tablet that regularly costs $829. Help him compare the price of the tablet at a stre
with the price on the store's website by completing the following.
(a)
The store's website is offering the tablet at a 80% discount off the regular price. Ignoring tax and shipping, how
much would he pay for the tablet on the store's website?
(b)
The store is having a sale, offering a 70% discount off the regular price of the tablet. Henry also has an
in-store-only coupon for an additional 10% off the sale price. Ignoring tax, how much would he pay for the tablet at
the store?
(c)
Select the true statement.
Henry would pay less for the tablet on the website.
Henry would pay less for the tablet at the store.
O Henry would pay the same amount at the store and on the website.
X
$
Answer:
$165.8 ;
$223.83 ;
Henry would pay less for the tablet on the website.
Step-by-step explanation:
Given :
Regular price = $829
On website :
80% discount off the regular price :
(100 - 80)% * regular price
20% * 829
0.2 * $829 = $165.8
At store :
70% off regular price :
(100 - 70)% * 829
0.3 * 829
= $248.7
10% off sale price :
(100 - 10)% * $248.7
0.9 * 248.7
= $223.83
Henry would pay less for the tablet on the website.
Carl worked in the grocery store 24.25 hours last week. This week he worked 30.5 hours.
How many more hours did he work this week than last?
Answer:
6.25 hours
Step-by-step explanation:
30.5 - 24.25 = 6.25 hrs.
please help me i dont understand thank you!!
Answer:
32 units squared
Step-by-step explanation:
Split up the figure into easy to find area parts. So, theres 2 triangles, and in the middle of those, you can make a square. And that would make the top part a large triangle! Now find the area of these
Large triangle: 1/2 (4)(10) = 20
Smallest triangle: 1/2(2)(2) = 2
Medium triangle: 1/2(6)(2) = 6
Square: 2*2 = 4
Now add them all up! 20+2+6+4 = 32 units squared!
Justin has a 2pound bag of Lima beans that he want to divide between 3families.how many pound of Lima beans should each family's receives? A. 3/2 pound b.2/3 c.2 1/3 pound d.3 1/3 pounds
Answer:
2/3 pounds of lima beans
Step-by-step explanation:
2 divided by 3 = 2/3 = 2/3
Hope this helps!
Answer:
2/3 pounds (Option B)
Step-by-step explanation:
Using unitary method ,
3 families will receive = 2 pounds of lima beans.
(Dividing both the sides by 3)
⇒ [tex]\frac{3}{3}[/tex] family will receive = [tex]\frac{2}{3}[/tex] pounds of lima beans
⇒ 1 family will receive = [tex]\frac{2}{3}[/tex] pounds of lima beans.
∴ Each family will receive 2/3 pounds of lima beans.
Answer the question.
11. Sarah's mom buys a basket that contains 8 bottles of lotion. Half of
the bottles each contain 150 milliliters of lotion. The other bottles
each contain 175 milliliters of lotion.
How many liters of lotion does Sarah's mom buy?
Answer:
1.3 liters
Step-by-step explanation:
4 x 150 is 600
4 x 175 is 700
700 + 600 = 1300 milliliters
1300 milliliters = 1.3 liters
Answer:
1.3 liters
Step-by-step explanation:
So first off, lets find the amount of milileters of lotion there is.
To do this, take 8, and divide it in half:
8/2 = 4. So we know that 4 bottles of lotion each contain 150 militers of lotion.
We know that the other 4 bottles each contain 175 milileters of lotion.
Next, lets multiply the 150 and 175 by the four bottles:
150x4
=
600
175x4
=
700
Now lets add these two values together, to find the total amount of lotion:
700+600
=
1300
Remember, this problem asked for liters of lotion, not milileters. Lets recall that 1000 milileters are equivelent to 1 liter:
1300/1000
=
1.3
This is your answer!
Hope this helps! :)
The FBI wants to determine the effectiveness of their 1010 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. Step 1 of 2: Suppose a sample of 517517 suspected criminals is drawn. Of these people, 211211 were captured. Using the data, estimate the proportion of people who were caught after being on the 1010 Most Wanted list. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Answer:
The proportion of people who were caught after being on the 1010 Most Wanted list would be 40.81%.
Step-by-step explanation:
Since the FBI wants to determine the effectiveness of their 1010 Most Wanted list, and to do so, they need to find out the fraction of people who appear on the list that are actually caught, supposing a sample of 517517 suspected criminals is drawn, and of these people, 211211 were captured, to estimate the proportion of people who were caught after being on the 1010 Most Wanted list using this data, the following calculation must be performed:
517,517 = 100
211,211 = X
211,211 x 100 / 517,517 = X
21,121,100 / 517,517 = X
40.81 = X
Therefore, the proportion of people who were caught after being on the 1010 Most Wanted list would be 40.81%.
How many 1/7 cup servings are in 9 cups of pecans (in fraction form)
HELP!! 5) Which number is IRRATIONAL?
A) V9
B) V27
C) V36
D) V81
Describe the overall shape of this distribution. Explain your answer in complete sentences.
Answer: The histogram is skewered to the right (right-skewered)
Step-by-step explanation:
The peak veers to the left and the tail is towards the right.
The histogram given is right-skewed.
What is a histogram?
A histogram is a representation of the distribution of data with intervals.
We have,
Right-skewed and left-skewed are terms used to describe the shape of a data distribution.
A right-skewed (or positively skewed) distribution is one in which the tail on the right-hand side of the graph is longer or fatter than the tail on the left-hand side.
A left-skewed (or negatively skewed) distribution is the opposite of a right-skewed distribution.
In this case, the tail on the left-hand side of the graph is longer or fatter than the tail on the right-hand side.
Now,
We see that the histogram given is right-skewed because the tail on the right-hand side of the graph is longer or fatter than the tail on the left-hand side.
Thus,
The histogram given is right-skewed.
Learn more about histograms here:
https://brainly.com/question/16819077
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