The average student complete after 12 lessons is 57.74 entries per minute.
To find s(x), we need to integrate ds/dx with respect to x:
ds/dx = 9(x + 4)^(-1/2)
Integrating both sides, we get:
s(x) = 18(x + 4)^(1/2) + C
To find the value of C, we use the initial condition that the average student can complete 36 entries per minute with no lessons (x = 0):
s(0) = 18(0 + 4)^(1/2) + C = 36
C = 36 - 18(4)^(1/2)
Therefore, s(x) = 18(x + 4)^(1/2) + 36 - 18(4)^(1/2)
To find how many entries per minute the average student can complete after 12 lessons, we simply plug in x = 12:
s(12) = 18(12 + 4)^(1/2) + 36 - 18(4)^(1/2)
s(12) ≈ 57.74 entries per minute
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The average student can complete 72 entries per minute after 12 lessons.
To find the data entry speed as a function of the number of lessons, we need to integrate the rate of change equation with respect to x.
Given: ds/dx = 9(x + 4)^(-1/2)
Integrating both sides with respect to x, we have:
∫ ds = ∫ 9(x + 4)^(-1/2) dx
Integrating the right side gives us:
s = 18(x + 4)^(1/2) + C
Since we know that when x = 0, s = 36 (no lessons), we can substitute these values into the equation to find the value of the constant C:
36 = 18(0 + 4)^(1/2) + C
36 = 18(4)^(1/2) + C
36 = 18(2) + C
36 = 36 + C
C = 0
Now we can substitute the value of C back into the equation:
s = 18(x + 4)^(1/2)
This gives us the data entry speed as a function of the number of lessons, s(x).
To find the data entry speed after 12 lessons (x = 12), we can substitute this value into the equation:
s(12) = 18(12 + 4)^(1/2)
s(12) = 18(16)^(1/2)
s(12) = 18(4)
s(12) = 72
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Select the correct answer,
What is the value of x?
log3 x = 4
A.27
В.7
С.12
D. 81
Answer:
D. 81
Step-by-step explanation:
Raise
3
to the power of
4
.
81
=
x
Rewrite the equation as
x
=
81
.
x
=
81
Find the area of the circle. Use 3.14 or 22/7 for pi. Round your answer to the nearest hundredth, if necessary.
Step-by-step explanation:
Given
diameter (d) = 9 ft
radius (r) = 9/2 = 4.5 ft
Area of the circle
= πr²
= 3.14 * ( 4.5) ²
= 3.14 * 20.25
= 63.585
= 63.59 ft
Hope it will help :)
Micah has 294 songs stored in his phone,which is 70% of the songs that Jorge in his phone.How many songs are stored on Jorge'S phone ?
Answer:
206
Step-by-step explanation:
70% of 294
70/100 × 294/1
205.8
round it off to 206
Scientists have found fewer fossils of plants than of animal bones. Why do you think this is?(You may state your opinion!)
Prism A is similar to Prism B. The volume of Prism A is 540 cm.
What is the volume of Prism B? (determine scale factor first)
Answer:
1080
Step-by-step explanation:
540x2/ or 540 + 540
can you guys help me out
Answer:
a. S = 3n + 2
b. There while be 62 squares.
Step-by-step explanation:
We know the first term of this sequence is 5. To figure out the equation, subtract the following term from the previous. Do you see a common difference?
8 - 5 = 3
11 - 8 = 3
14 - 11 = 3
We're seeing a constant difference of 3 (which makes this an arithmetic sequence), but the first term is 5. That mean something is being added to make the first term 5. Subtract 3 from 5 to get 2. This means 2 is being added to every multiple of 3, which leads us to the equation: S = 3n + 2.
To find the 20th term of this sequence, substitute n for 20 and do the operations.
S = 3(20) + 2
Multiply 3 by 20, then add 2.
S = 62
The 20th term will have 62 squares.
2.) Find the value of n in the equation 1/2(n+4) = 6 *
Answer:
2
Step-by-step explanation:
Evaluate the expression when a=−15 and b=−5.
hat would -
A divided by b = ?
be?
Answer:
3Step-by-step explanation:
Given the following values a=−15 and b=−5.
We are to find a/b
a/b = -15/-5
a/b = 15/3
a/b = 5*3/5*1
a/b = 5/5 * 3
a/b = 1*3
a/b = 3
Hence a divided b will be 3
What is the rate of change of
the function when x=-1 and
x = 1?
A
A. 2
B. 4
C. -2
D. -4
0.
Answer:
c!!!!!!!!!!!!!!!!!!!
whats 667453x765678-543
Answer:
511054077591
Step-by-step explanation:
Answer:
511,054,077,591
Step-by-step explanation:
Is this an actual question tho?
1 4/5 as a decimal thank you (will be giving brainliest to first answer that is correct) : D
Answer:
yes its decimal
Step-by-step explanation:
The given fraction into percent and decimal are; 2.8 and 280%
How to convert percent to fraction and decimal?Percent counts the number compared to 100.
There is a fraction, containing numerator(upper value) and denominator(lower value).
So, if we have a%, that means for each 100, there are 'a' parts. If we divide each of them with 100, we get,
For each 1, there are a/100 parts.
Thus, 50% = 50/100 = 0.50 (in decimal)
There is a fraction, containing numerator(upper value) and denominator(lower value).
The mixed fraction contains a sum of whole number and a proper fraction.
WE have been given a fraction as;
14/5
Then Fraction Decimal Percentage
2.8 and 280%
The given fraction into percent and decimal are; 2.8 and 280%
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Write an equivalent expression by distributing the "
−−" sign outside the parentheses:
−(3h−2.3k)−7
Answer:
= -3h + 2.3k -7
Step-by-step explanation:
you want to distribute your negative to each value in parentheses
remember that negative x negative = positive
remember that negative x positive = negative
How do I know if it is sss, sad, asa, or aas?
i have attached a image which may help u <3
Which scenario best matches the inequality x greater than 3 ?
Answer:
d
Step-by-step explanation:
i got an 100 on the test :)
Plz help on BOTH of the questions
Answer:
4.30000x(1+3%)x10%=$3090
5. 20x1.5x2.1=63
Step-by-step explanation:
Parallel or perpendicular
HELP! WILL GIVE BRAINLY!!! Find the volume of a cylinder with height = 10ft and the diameter of the base circle is 12ft.
Answer:
About 1,130.4 Cubic Feet
(My previous answer was a mistake. It has now been corrected)
Step-by-step explanation:
The Volume of a cylinder = Height * Pi * Radius^2
The radius is half the diameter, so 12 ÷ 2 = 6
Pi rounded to the hundredth place is 3.14.
Volume = 10 * 3.14 * 6^2 = 1,130.4
Therefore the Volume is about 1,130.4 cubic feet.
Answer:
Exact Volume = 360pi cubic feet
Approximate Volume = 1130.4 cubic feet
The approximate volume is found when you use pi = 3.14; use more decimal digits of pi to get a more accurate value.
===========================================================
Explanation:
The volume of a cylinder is found by the formula
V = pi*r^2*h
where,
pi = 3.14 approximatelyr = radius = 6 ft, since the radius is half the diameter.h = height = 10 ftSo,
V = pi*r^2*h
V = pi*6^2*10
V = pi*36*10
V = pi*360
V = 360pi ........... exact volume in terms of pi
V = 360*3.14
V = 1130.4 ......... approximate volume if you use pi = 3.14
The units of the volume are in "cubic feet" which we can abbreviate to "ft^3". Think of a 1 ft by 1 ft by 1 ft cube. The volume would be 1*1*1 = 1 cubic foot. So basically having a volume of roughly 1130 cubic feet means we need this many cubic blocks to form the cylinder (some of the blocks will be cut up to be able to fit).
Which point is the intersection of RS and VT?
Answer:
point U
Step-by-step explanation:
I learned this before
Hope this helps
A cylinder has radius 3.8 meters. Its volume is 159 cubic meters. Find its
height to the nearest tenth of a meter.
Answer:
Step-by-step explanation:
In The autumn 40% of the leaves on a tree are yellow and 24% of them are green the remaining 72 leaves are half yellow how many leaves are on the tree
Percentage of yellow leaves on a tree during Autumn = 40%
Percentage of green leaves on a tree during Autumn = 24%
Percentage of half yellow leaves on the tree during Autumn :
[tex] = \tt100 - 40 + 24[/tex]
[tex] = \tt 100 - 64[/tex]
[tex] = \tt 36 \%[/tex]Thus, the percentage of half yellow leaves on the tree during Autumn = 36%
Number of half yellow leaves on the tree = 36%
Let the total number of leaves on the tree be x.
Which means :
[tex] = \tt36 \% \: of \: x = 72[/tex]
[tex] = \tt \frac{36}{100} \times x = 72[/tex]
[tex] = \tt \frac{36 \times x}{100} = 72[/tex]
[tex] = \tt \frac{36x}{100} = 72[/tex]
[tex] = \tt 36x = 72 \times 100[/tex]
[tex] = \tt36x = 7200[/tex]
[tex] = \tt x = \frac{7200}{36} [/tex]
[tex] \color{plum} = \tt \: x = 200[/tex]
Thus, total number of leaves on the tree = 200
Number of yellow leaves on the tree :
[tex] = \tt40 \% \: \: of \: \: 200[/tex]
[tex] = \tt \frac{40}{100} \times 200[/tex]
[tex] = \tt \frac{40 \times 200}{100} [/tex]
[tex] = \tt \frac{8000}{100} [/tex]
[tex] \color{plum} \tt = 80 \: yellow \: \: leaves[/tex]
Thus, total number of yellow leaves on the tree = 80
Number of green trees on the tree :
[tex] = \tt24 \% \: \: of \: \: 200[/tex]
[tex] = \tt \frac{24}{100} \times 200 [/tex]
[tex] = \tt \frac{24 \times 200}{100} [/tex]
[tex] = \tt \frac{4800}{100} [/tex]
[tex] \color{plum} = \tt 48 \: green \: \: leaves[/tex]
Thus, the total number of green leaves on the tree = 48
Since the sum of all types of leaves form 200[80+48+72=200], we can conclude that we have found out the correct number of each type of leaf.
▪︎Therefore, the total number of leaves on the tree = 200
The number of leaves is on the tree is 200.
Given that,
There is 40% of the leaves that should be yellow.24% of them should be green.And, the remaining should be 72 leaves that represent half yellow.Now as per the above explanation:
The percentage of half yellow trees should be= 100 - 40 + 24
= 100 - 64
= 36
Here we assume the number of leaves on the tree be x
So,
36% of x = 72
x = 200
Therefore we can conclude that the number of leaves is on the tree is 200.
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40 is 8% of what number?
Answer:
500
Step-by-step explanation:
40×100÷8=500
Number 40 is 8 percent of 500.
What is the percentage?The percentage refers to a number that is out of 100. When describing components of a whole in mathematics, percentages are employed similarly to fractions and decimals. When employing percentages, the idea is that there are 100 equal pieces that make up the whole. In addition to the shorthand "pct," which is used less frequently, the symbol "%" is used to indicate that a number is a percentage.
Let the unknown number be "x" whose 8% is 40.
Hence,
8% of x = 40
1% of x = 40/8 = 5
Thus, the value of x = 500
Therefore, 8 percent of 500 if 40.
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How do you find the original price from a coupon or discount?
Answer: ,GJHGFHJGJH HJGLHGLKG HKLGKL G LKJKJLGKJGKGKJKKJ K
Step-by-step explanation:
Distance=7cm/1yrx1000yr=
9514 1404 393
Answer:
70 m
Step-by-step explanation:
Perhaps you want to evaluate the expression:
[tex]\dfrac{7\text{ cm}}{1\text{ yr}}\cdot 1000\text{ yr}=7000\text{ cm}=70\text{ m}[/tex]
__
There are 100 cm in 1 m. The units of yr cancel.
Please I need help does anyone know a hack for khan academy
Answer:
Answer:
0.3643
Step-by-step explanation:
Standard Form and Scientific Notation
What is standard form of numbers?
Standard form is the normal way of writing numbers no matter how big or small the number is.
Examples:
15,000,000
0.0000000678
What is scientific notation?
Scientific notation is a different way of expressing numbers. It is a short way of expressing very big numbers or very small numbers. It is also known as exponential form. Scientific notation is written as the product of a number and a power of 10.
Examples:
1.3 × 10⁶
34.5 × 10^⁻9
Going back to the question above, we need to convert the given scientific notation to its standard form.
Converting of Scientific Notation to Standard Form
To convert a number from scientific notation to standard form, move the decimal point.
The exponent tells the direction and the number of times we need to move the decimal point.
The positive exponent indicates a large number so we need to move the decimal point to the right.
The negative exponent indicates a small number so we need to move the decimal point to the left.
Do not write the power of 10 anymore.
Solution:
Now, let us convert 3.643 x 10^-1 in standard form.
The exponent is negative 1 so we will move the decimal point to the left once.
3.643 = 0.3643
olve for x: 3(x + 1) = −2(x − 1) + 6.
3. Plot the points and then answer the questions:
(1, -3) (-3, 9) (2,-6)
a. Is this a proportional relationship?
b. What is the constant of proportionality?
Please help !!
Answer:
a. yes there is a proportional relationship
b. I believe the constant is -3
8123 divided by 7 please help!
4. I NEED HELP ASAP!! PLEASE PUT AND ANSWER AND STEP BY STEP EQUATION!! IF YOU DON'T KNOW THE ANSWER DON'T PUT ANYTHING!!
Write a rule for the linear function shown in the graph.
A. y = 2x - 2
B. y = -2x + 2
C. y = 1/2x - 2
D. y = -x + 2
Answer:
The answer is A (y = 2x - 2)
Step-by-step explanation:
B and D aren't correct because the y-intercept is a positive 2 instead of negative 2 like the graph shown. We're now left with A and C. Go on one point of the graph and count up or down to go on the same y value as the other point. Go left or right and count until you go to the same point. Remember that the slope equation is rise/run. Rise meaning up or down. Run meaning left or right.
Answer:
y = -x+2
Step-by-step explanation:
For first one
I need the answer as soon as possible
Answer:
Reflection on the Y axis.
Step-by-step explanation:
(I cannot see the rest of the answers but I am assuming reflection is one of them). The shape reflects perfectly on the Y axis.
List the possible rational roots of the equation. 0 = 22x4 - x2 + 121
Answer:
22×4=88÷2=44+121=165
Answer:
±1
±1/2
±1/11
±1/22
±11
±11/2
±121
±121/2