To solve the given derivative we need to apply the chain rule.
Given that, [ln(g(x))]².
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
The chain rule is a formula that expresses the derivative of the composition of two differentiable functions [tex]f[/tex] and [tex]g[/tex] in terms of the derivatives of [tex]f[/tex] and [tex]g[/tex].
Find the derivative using the chain and power rules.
ln(g²x²)/x
Therefore, to solve the given derivative we need to apply the chain rule.
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The mean height of 12 men is 1.70 m, and the mean height of 8 women is 1.60 m. Find:the total height of the 12 men
Answer:
20.4 m
Step-by-step explanation:
mean is calculated as
mean = [tex]\frac{total}{count}[/tex]
given mean height of 12 men is 1.70 m , then
[tex]\frac{total}{12}[/tex] = 1.7 ( multiply both sides by 12 to clear the fraction )
total height = 12 × 1.7 = 20.4 m
If the original function is f(x)
What would be the function notation when the function was
Shifted Right 6
The function notation when the function was shifted right 6 is f(x-6).
Given that, the function was shifted right 6 units.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Rule: In function notation, to shift a function left, add inside the function's argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x - b) shifts f(x) b units to the right.
So, the transformation from the original function to new function is
f(x-6)
Therefore, the function notation when the function was shifted right 6 is f(x-6).
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The greatest temperature ever recorded in the United States occurred at an elevation of 178 feet below sea level. The greatest temperature ever recorded in Africa occurred at an elevation of 545 feet greater than in the United States. At what elevation, in feet, did the greatest temperature in Africa occur?
The greatest temperature in Africa occur is 367 feet.
What are integers?The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion.
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
The greatest temperature ever recorded in the United States occurred at an elevation of 178 feet below sea level.
Using integers we represent it as (-178) feet.
and, greatest temperature ever recorded in Africa 545 feet greater than in the United States
= -178 + 545
= 367 feet.
Hence, The greatest temperature in Africa occur is 367 feet.
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2, 5, 4, 10, 8, 20 [Hint: It is a combined series: two geometric series. Find common ratio for each by dividing.]
The two combined geometric series is separated and the common ratios are shown
2, 4, 8, - common ratio = 25, 10, 20 - common ratio = 2What is geometric series?The total of a geometric sequence's finite or infinite terms is known as a geometric series.
The ratios of every two successive terms in the series (sum of terms) are equal. this means that
4/2 = 8/4 = 210/5 = 20/10 = 2The common ratio is calculated by dividing the succeeding term (eg 2nd term) by the preceding term (eg 1st term)
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21. An artist created a piece of art with 675 round glass beads. There were
also 179 beads in the shape of a heart. Write a number sentence to
find about how many more round beads there were.
By using subtraction, it can be calculated that there were 496 round beads more than heart shaped beads
What is subtraction?
Suppose, there are two numbers and it is required to find out how much one number is bigger than the other. The operation used for this is subtraction.
The larger number is called minuend and the smaller number is called subtrehend.
Here, subtraction will be used
Number of round glass beads = 675
Number of beads in the shape of heart = 179
Number of more round beads there were = 675 - 179
= 496
There were 496 round beads more than glass beads
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The steps that Patel could he use to solve the quadratic equation include:
8(x² + 2x) = –3
8(x² + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
How to illustrate tye information?It is preferred to solve quadratic equations without the use of the known quadratic formula solver. This can be completing squares and solving for x.
The equation given is:
8x² + 16x + 3 = 0
8(x² + 2x) = -3
Completing squares in the brackets and balancing the equation:
8(x² + 2x + 1) = -3 + 8
Factoring the perfect square will give 8(x + 1)² = 5.
This is illustrated in the options picked for the step.
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Write these as normal numbers.
b)
9.6 × 10⁹
Answer:
9600000000
Step-by-step explanation:
9.6 x (10^9)
First, write 10^9 as 1000000000
Multiply by 9.6
= 9600000000.
For a field trip 9 students rode in cars and
the rest filled eight buses. How many
students were in each bus if 265 students
were on the trip?
Answer:
32 students were on each bus.
Step-by-step explanation:
First deduct 9 students from the total number: 265 - 9 = 256
Then divide the students among the total number of buses, which is 8: 256/8 = 32
So there are 32 students on each bus.
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3.201 x 10^9 and 4.85 x 10^3
(3.201 x 10^9) * (4.85 x 10^3) =
15524850000000
in scientifc notation
1.552485 x 10^13
Radius of the base of a cylinder is 38 mm and its height is 51 mm. Find the surface area of the cylinder, in terms of pi
The surface area of the cylinder in term of π is 6764πmm^2
What is surface area of a cylinder?A cylinder is a three-dimensional solid that contains two parallel bases connected by a curved surface. The bases are usually circular in shape. The perpendicular distance between the bases is denoted as the height “h” of the cylinder and “r” is the radius of the cylinder.
The total surface area of a cylinder is 2πr(r+h)
Where r is the radius and h is the height of the cylinder
therefore T.S.A= 2×38π(38+51)
T.S.A=76π×89
The total surface area(T.S.A) of the cylinder =6764πmm^2
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If P= (2, 7) and Q= (2, -3), which could be the coordinates of R if triangle PQR is isosceles?
If P= (2, 7) and Q= (2, -3), then for triangle to be isosceles coordinate of R must be 2
Let coordinates
P = (2, 7) and Q = (2, -3)
PR = QR
(X-2)^2 +(Y-7)^2 = (X-2)^2 + {Y-(-3)}^2
(Y-7) = {Y - (-3)}^2. or y - 7 = ±(Y
or Y^2 - 14Y + 49 = Y^2 + 6Y + 9
20Y = 40
Y=2
coordinates of R if triangle PQR is isosceles ;
Hence any point R on the line Y = 2 will make PQR a isosceles triangle
with PR = QR.
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4. Enrique collected 152 recyclable bottles, and
Latasha collected brecyclable bottles. Write
an expression for the number of bottles they
collected altogether.
The required expression is Total = 152+x .
What is expression ?
Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. The four different types of mathematical operators are addition, subtraction, multiplication, and division. For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.
Here,
The number of bottles Enrique collected = 152
Let us take number of bottles collected by Latasha as x. Then,
Total number of bottles collected by the is ,
=> Total = Number of bottles collected + Number of bottle collected
by Enrique By Latasha.
=> Total = 152+x
Hence the required expression is Total = 152+x.
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Write the expression in words 2x + 2
Answer:
two times x plus two
Step-by-step explanation:
What is the reason for each step in the solution of the equation?
−6x=−2(x+12)
Drag and drop the reasons into the boxes to correctly complete the table.
Answer:
Given
Distributive Property
Addition Property of Equality
Division Property of Equality
Step-by-step explanation:
Frist you distribute the -2 by multiplying it to everything in the parentheses. Next, you add 2x to both sides of the equation and lastly you divide both sides of the equation by -4
What is 3/4 written in 12 of denominator
Answer: The correct answer in 9/12
Step-by-step explanation:
For 3/4, the numerator is 3 and the denominator is 4
To change the denominator to 12, you must multiply by 3 (12/4=3)
3/4 * 3/3
= (3*3)/(4*3)
= 9/12
Bella fills Her gas tank with 13 1/2 gallons of gas. After driving the car she has 11 4/5 gallons left. How much gas did Bella use?
Answer:
1.7 gallons
Step-by-step explanation:
You would chand the 1/2 and 4/5 into tenths by multiplying 1/2 by 5 getting 5/10 then multiplying 4/5 by 2 to get 8/10 so you would have 13 5/10- 11 8/10 to get 1.7 gallons left.
Determine which integer will make the inequality 12 > 2x + 4 true.
Answer: Integers less than 4 will make the inequality true.
Step-by-step explanation:
1) subtract both sides by 4 to isolate 2x so we are now left with 8 > 2x.
2) divide both sides by 2 so we are left with just x, leaving us now with 4 > x.
Integers must be less than 4 because if you substitute x as 4, we have 12 > 12, which is not true. But, if we substitute x as 3, we are left with 12 > 10, which makes the inequality true.
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Which lists the distances between towns in order from greatest to least?
(picture of problem below)
Answer:
Step-by-step explanation:
the side opposite to greater angle is greater.
72>60>48
AB>AC>BC
A=Afton
B=Badeton
C=Capeton
A company that most adults would erase all of their personal data online if they could. In order to test this claim, a GFI Software Survey of 565 randomly selected adults showed that 59% of them would erase all of their personal information online if they could.
A. State the null and alternative hypotheses (in symbols).
B. Explain what a Type 1 and a Type 2 error would be in this case.
C. State the conclusion if the null hypothesis is rejected.
D. State the conclusion if the null hypothesis is not rejected.
a) The null and alternative hypothesis are given as follows:
Null: [tex]H_0: p \leq 0.5[/tex]Alternative: [tex]H_1: p > 0.5[/tex]b) The errors are given as follows:
Type I: A sample which gives enough evidence that most people would erase the data, if in reality they wouldn't.Type II: A sample in which the proportion of people that would erase their data isn't significantly above 50%, when in fact it is.c) The conclusion of a rejected null hypothesis is: There is enough evidence that most adults would erase their data if they could.
d) The conclusion of a not rejected null hypothesis is: There is not enough evidence that most adults would erase their data if they could.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that most adults would erase all of their personal data online if they could, that is, if the proportion is not greater than 50%, hence:
[tex]H_0: p \leq 0.5[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that they would erase the information, that is, if the proportion is greater than 50%, hence:
[tex]H_1: p > 0.5[/tex]
A rejected null hypothesis means that the alternative hypothesis is accepted, that is, there is enough evidence that most adults would erase their data if they could.
A not rejected null hypothesis, conversely, means that there is not enough evidence that most adults would erase their data if they could.
What are type I and type II errors?Type I errors are when a true null hypothesis is rejected. Hence, the context of this problem, it would mean a sample which gives enough evidence that most people would erase the data, if in reality they wouldn't.
Type II errors are when a false null hypothesis is not rejected. Hence, the context of this problem, it would mean a sample in which the proportion of people that would erase their data isn't significantly above 50%, when in fact it is.
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Solve.
log3 (2x + 5) = 3
Enter your answer in the box.
X = ?
Answer:
x = 11
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
given
[tex]log_{3}[/tex] (2x + 5) = 3 , then
2x + 5 = 3³ = 27 ( subtract 5 from both sides )
2x = 22 ( divide both sides by 2 )
x = 11
Which of the graphs below shows correctly plotted points for the following line? y=2x+3
Answer: The image is for an idea of what you should look for
Step-by-step explanation:
Emmett prepared 10 kilograms of dough after working 2 hours. How much dough did Emmett prepare if he worked for 4 hours? Assume the relationship is directly proportional.
The kilograms of dough that Emmett prepare if he worked for 4 hours is 20 kilograms.
What is a proportional relationship?A proportional relationship simply means the relationship that has an equivalent ratio as well as a constant.
In this case, Emmett prepared 10 kilograms of dough after working 2 hours. The kilograms per hour will be:
= 10/2
= 5 kilograms per hour
Therefore, in 4 hours, the kilograms will be:
= Number of hours × 5 kilograms
= 4 × 5
= 20 kilograms
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Marco opened a savings account 10years ago. The account earns 5% interest,compounded annually. If the current balance is $400, how much did he deposit initially? Round your answer to the nearest cent.
Answer:
245.57
Step-by-step explanation:
[tex]P\left(1+0.05)^{10}=400 \\ \\ P=\frac{400}{(1.05)^{10}} \\ \\ P \approx 245.57[/tex]
the cost of 2kg carrots is £7 work out the cost of 5kg carrots.
How would I solve this?
Answer:
y=2x-22
Step-by-step explanation:
lets make the equation into slope intercept form
-2x+y=-8 let's move the -2x to the other side we get
y=2x-8
now let's create our equation with the points given
to create the equation you want to make it point slope form with the point given
y-0=2(x-11) distribute the 2 and we can remove the 0
y=2x-22
a vegetable seller purchased 1 quintal of potatoes at rs 35 per kg and sold at a loss of rs 350. find his rate of selling price and loss percent
Answer:
Selling price = RS 3150
Loss percent = 10%
Step-by-step explanation:
1 quintal = 100kg
Cost price = 35*100
= RS 3500
Loss = RS 350
Selling price = RS 3500-350
Selling price = RS 3500-350 =RS 3150
Loss percent = Loss *100%
Cost Price
= 0.1 *100
= 10%
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7 candy bars cost $6.65. At this rate, how much do 9 candy bars cost?
Answer: $8.55
because 6.65 divided by 7 is 0.95 and 0.95 multiplied by 9 is 8.55
so the answer is $8.55
One year, the population of a city was 181,000. Several years later it was 150,230. Find the percent decrease.
The percentage decrease in population is 17%
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply it by 100. percentage . The word per cent means per 100. It is represented by the symbol “%”.
percentage decrease in population= (0riginal population- new population)÷ original population × 100
%decrease in population = (181000 - 150230) ÷ 181000× 100
=( 307770×100)/181000
= 17%
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17%
Step-by-step explanation:
i tried it it worked
Determine which integer will make the inequality 4x + 6 < 2x + 12 false.
Answer:
x>=3 make the inequality false
Step-by-step explanation:
4x-2x<12-6
2x<6
x<3
Answer:
Any number higher than 3
Ex. 4, 5, 6, 7, 8, 9, 10, etc
Step-by-step explanation:
4x + 6 < 2x + 12
-2x -2x
---------------------
2x + 6 < 12
-6 -6
------------------
2x < 6
÷2 ÷2
-----------
x < 3
Since x is less than 3, any number higher than 3 will make the inequality false. For Ex. 4
4(4) + 6 < 2(4) + 12
16 + 6 < 8 + 12
22 < 20 (false)
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A coin (5 grams), a small parachute (21 grams), and a hammer (710 grams) are all dropped from a height of 10 meters. The coin and the hammer take
about the same amount of time to fall. Which statement describes the time it takes for the parachute to fall? (1 point)
O It takes less time to fall because it has the most surface area.
O It takes the same amount of time to fall because the effect of gravity is the same.
O It takes less time to fall because it has the least mass
O It takes longer to fall because it experiences greater air resistance.
Answer:
the last one= It takes longer to fall because it experiences greater air resistance.
also the reason is the air resistance provides an upthrust to the parachute which takes longer time to fall
Answer: It takes longer to fall because it experiences greater air resistance.