Answers
The value of h'(2) = 50.
What do you mean by function?
A relation between a collection of inputs and outputs is known as a function. In other word, it is a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
here we are given a function h(x)
here h(x) = - 5f(g(x)) ------(i)
and we are given the value of
g(2) =3 ; f(2) = 1 ; g'(2) = -2
f(3) = 4 ; f'(3) = 5 ; f'(2) = 6.
and we need to find the value of h'(2).
here f(x), g(x) and h(x) are the function of x and f'(x), g'(x) and h'(x) denotes the derivative of f(x), g(x) and h(x) respectively.
so we are given ,
h(x) = - 5f(g(x))
differentiating with respect to x both side
h'(x) = -5 f'(g(x).g'(x).
at x =2,
h'(2) = [tex]-5*f'(g(2))*g'(2)[/tex]
and we know g(2) = 3 and g'(2) = -2.
so,
h'(2) = [tex]-5*f'(3)*-2[/tex]
h'(2) = [tex]-5*5*-2\\[/tex] ( as f'(3) = 5 )
h'(2) = 50
so Option C is correct, the value of h'(2) = 50.
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Related Questions
Multiply using the distributive property
D) Simplify the expression:
8(1 + 7d) =
Answers
Answer:
8 + 56d
Step-by-step explanation:
We will open the parentheses, multiplying the stuff outside by the stuff inside. So, we get:
8*1 + 8*7d
Then, we can simplify by giving us:
8 + 56d
Hope this helped!
How many centimeters are equal to 0.6 inches? Enter your answer as a decimal and round to the nearest hundredth.
Answers
Answer:
1.52cm rounded
1.524 exact
Step-by-step explanation:
For this, we use the basic conversion of 1 inch is 2.54 cm.
We can do:
2.54 cm x 0.6 inch = 1.52 cm rounded.
Write the equation for a parabola with a focus at (0,5) and a directrix at x = -7
Answers
Answer:
(y-5)^2=14(x+7/2)
Step-by-step explanation:
The equation for a parabola with a focus at (0,5) and a directrix at x = -7 is (y - 5)² = 14 (x + 3.5).
What is Parabola?A parabola is a two dimensional figure on a plane which is U shaped and any point on the parabola is at an equal distance from a fixed point called focus and a fixed line called directrix.
Given,
Focus of the parabola at (0, 5).
Directrix is x = -7.
The parabola is horizontal parabola since the directrix is a vertical line.
Equation of the parabola is of the form,
(y - k)² = 4p (x - h)
Here (h, k) is the vertex.
Vertex of the parabola is the mid point of focus (0, 5) and the point (-7, 5).
(h, k) = ([tex]\frac{0 + -7}{2}[/tex], 5) = (-7/2, 5)
Now, p is the distance from vertex to focus.
p = 0 - -7/2 = 7/2 = 3.5
So the equation is,
(y - 5)² = 4× 3.5 (x - -3.5)
(y - 5)² = 14 (x + 3.5)
Hence the equation is (y - 5)² = 14 (x + 3.5).
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HELP!!!!!!
Maya plans to watch 3 movies each month. Write an equation to represent the total number of movies n that she will
watch in m months.
Answers
Answer:
m=3n
Step-by-step explanation:
3 movies per month. So 3 n per m.
Answer:
n=3m
Step-by-step explanation:
n is number of movies
3 is the 3 movies per month
m is each month
so it's n=3m
How many liters are in 4.78 gallons? *
Answers
Answer:
around 18.094 liters
Step-by-step explanation:
Answer:
Around 18.0942683 Liters
A farmer decides to sell 25% of his 500 cows. How many cows does he
sells?
Answers
Please help!
The supplement of an angle has a measure that is 20° more than twice the measure of the angle, x°. Write an equation that can be used to find the value of x?
Answers
Answer:
20 + 2x = 180
Step-by-step explanation:
20 + 2x = 180
2x = 160
x = 80
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answers
Given:
The quadratic equation is:
[tex]12a^2+9a+7=0[/tex]
To find:
The solution of the given equation in simplest form by using the quadratic formula.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the quadratic formula is:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have,
[tex]12a^2+9a+7=0[/tex]
Here, [tex]a=12,b=9,c=7[/tex]. Using the quadratic formula, we get
[tex]x=\dfrac{-(9)\pm \sqrt{(9)^2-4(12)(7)}}{2(12)}[/tex]
[tex]x=\dfrac{-9\pm \sqrt{81-336}}{24}[/tex]
[tex]x=\dfrac{-9\pm \sqrt{-255}}{24}[/tex]
[tex]x=\dfrac{-9\pm i\sqrt{255}}{24}[/tex] [tex][\because \sqrt{-a}=i\sqrt{a}][/tex]
The solutions of the given equations are [tex]x=\dfrac{-9-i\sqrt{255}}{24}[/tex] and [tex]x=\dfrac{-9+i\sqrt{255}}{24}[/tex].
Therefore, the correct option is B.
Cameron worked as a salesperson at an electronics store and sells phones and phone accessories. Cameron earns a $11 commission for every phone he sells and a $2. 50 commission for every accessory he sells. On a given day Cameron made a total of $361 in commission from selling a total of 56 phones and accessories sold.
Answers
The number of phones sold is 26 and the number of accessories sold is 30.
What is a Linear equation:An equation is said to be linear if the maximum power of the variable is usually 1. A linear equation with one variable has the standard form Ax + B = 0. In this case, x is the variable and A is the coefficient of x, and B is a constant.
In mathematical problems, 'x' stands for unknown value or quantity. Here we use the Linear equation concept to solve the problem.
Given that
Cameron earns an $11 commission for every phone he sells and a $2. 50 commission for every accessory he sells.
On a given day Cameron made a total of $361 in commission from selling a total of 56 phones and accessories sold.
Let x and y be the number of phones and accessories
Given that
Cameron made a total of $361 in commission
=> 11x + 2.5y = 361 ----- (1)
Total number of phones and accessories sold
=> x + y = 56
Multiply by 11
=> 11x + 11y = 616 ----- (2)
Do (2) - (1)
=> 11x + 11y - ( 11x + 2.5y) = 616 - 361
=> 11x + 11y - 11x - 2.5y = 255
=> 8.5y = 255
=> y = 255/8.5
=> y = 30
Substitute y = 30 in x + y = 56
=> x + 30 = 56
=> x = 26
Therefore,
The number of phones sold is 26 and the number of accessories sold is 30.
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Select the correct answer
Which function has the same graph as x+y= 11
OA X=-y+11
OB fx= -x+11
OC (X) = x-11
OD. x) = y-11
Answers
The scores on the last math quiz are summarized in the following frequency table:
Score
10 9
8
7
6
4 3 2 1 0
7
5
3 2
1
0
0
10
0
Frequency 6
The information is then put into the following histogram:
Frequency
5
4
3
210
1 2 3 4 5 6 7 8 9 10
5
1
Score
Answers
Therefore , the answer to the above problem is 5.75 for the mean and 9 for the median.
What is mean?Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the amount of values present in the dataset by its total number of values in the data. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the integers in a data set and dividing the total by the total number of numbers. For example, in the data below
Here,
Spread it all out here first:
4, 5, 6, 7, 7, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10
The mean is calculated by dividing total total by the total number of scores. Add up each number.
There are 16 numbers total, and they add up to 92. 92 / 16 = 5.75
To get the median, identify the middle number among all the other numbers.
Sadly, there is no "center number" given that there are 16.
Add the ninth and eighth numbers together, then divide by to find the middle.
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A group of hikers starts at an elevation of 2.53 kilometers. When they stop for lunch, their elevation has increased by 1.24 kilometers. When they stop to camp, their elevation has decreased by 0.53 kilometer compared to their lunch stop. Which expressions represent the elevation, in kilometers, of the group’s campsite?
Answers
So, the elevation of the group's campsite can be represented by the following expression:
(2.53 + 1.24) - 0.53 = 3.77 - 0.53 = 3.24
Alternatively, you could also write the expression as:
2.53 + (1.24 - 0.53) = 2.53 + 0.71 = 3.24
Both expressions represent the elevation, in kilometers, of the group's campsite.
Can someone please help me on this & I’ll reward you afterwards
Answers
Answer: 4y (4y^2-2y-5)
Step-by-step explanation:
P=-3w+9 solve for w
Pls help
Answers
Isolating for a variable: rearranging an equation so that a variable is on its own. This is done by performing inverse operations until a variable is isolated.
[tex]P-9=-3w+9-9[/tex]
[tex]p-9=-3w[/tex]
[tex]\frac{p-9}{-3}=\frac{-3w}{-3}[/tex]
[tex]-\frac{P-9}{3} =w[/tex]
What is a plot point example?
Answers
A plot point example contains a point in a story that defines the turning point in the story.
What is a plot point?A story's plot point is a crucial turning moment that occurs during the narrative. The tale and the characters may be developed and advanced using these ideas.
Why are plot points necessary in stories?Plot points offer your tale movement by advancing the plot and dragging the reader along. 'A particularly crucial portion of a storyline of a work of fiction,' according to the definition of a plot point. Never undervalue the significance of your framework, even if your book is contemplative or literary.
An example of plot point is :
In a story about a young girl who is trying to save her village from an impending monster attack, the plot point may occur when the girl discovers an ancient artifact that gives her the power to defeat the monster. This event marks a significant turning point in the story, as it sets the stage for the girl to take on the monster and potentially save her village.
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what is 2.38 correct to 2 significant figures
Answers
Answer: 2.4
Step-by-step explanation:
we start from the right most digit, that is 8. Since 8 is greater than 5, we add 1 in the number before 8, that is 3. When we add 3 and 1 we get 4. This way, we get our answer 2.4 , which is correct to 2 significant figures.
hope that helps...
As drug A gets absorbed into the body, less and less of it remains. A scatterplot of data showed a curved relationship between hours since drug A was administered (x) and the number of milligrams of drug A remaining in the body (y). Taking the logarithm of the milligrams of drug A remaining obtains a linear pattern on a scatterplot, and creates the following printout from a statistical software package:
Predictor Coef SE Coef t-ratio P
Constant 3. 00 0. 401 7. 481 0. 000
Time -0. 0737 0. 005 -14. 74 0. 000
s= 0. 014 R-sq= 98. 5% R-Sq(Adj)= 99. 0%
Required:
Write down the correct equation that follows from this output?
Answers
The equation is
log ( milligrams of drug A ) =3 - 0.0737 ( Time)
As per the details stated above,
Curved relationship between the number of milligrams of drug A is (x) still in the body and the number of hours since drug A was delivered (y)
The co-efficient of the constant is 3.00
the co-efficient of the time is -0.0737
the SE co-efficient of the constant is 0.4017
the SE co-efficient of the time is 0.005
the t-ratio of the constant is 7.481
the t-ratio of the time is -14.74
now the equation formed is
logarithm of drug A in milligrams is (The co-efficient of the constant - the co-efficient of the time )
that is log ( milligrams of drug A ) =3 - 0.0737 ( Time).
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How do you find the horizontal asymptote and Y intercept?
Answers
The process of finding the horizontal asymptote and y intercept is explained below.
In order to find the steps, we must know that what is meant by asymptote and intercept.
The process of finding the asymptote is defined as the horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.
If the degree of numerator is less than degree of denominator then horizontal asymptote at y = 0
Where as if the degree of numerator is greater than degree of denominator by one then there is no horizontal asymptote
Finally if the degree of numerator is equal to degree of denominator then the horizontal asymptote at ratio of leading coefficients.
As per the definition of intercept we have identified that the point that will intersect at the y axis is referred as the y intercept.
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54. Suppose the population of a country is currently 8,100,000. Studies show this
country's population is increasing 2% each year.
a. What exponential function would be a good model for this country's
population?
b. Using the equation you found in part (a), how many years will it take for the
country's population to reach 9 million? Round your answer to the nearest
hundredth.
Answers
a. The exponential function that is good model for the country population is:
Pₙ = 8100000(1.02)ⁿ ,
b. It will take 5.27 years to reach 9 million.
What is exponential function?An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
Exponential Function Formula
An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent.
a. Given, initial population P₀ = 8100000, Rate of increase R = 2%.
If a constant rate of growth be R% per annum,
then function for population after n years
Pₙ = P₀ x (1+R/100)ⁿ
Population Pₙ = 8100000 × (1+2/100)ⁿ
Pₙ = 8100000(1.02)ⁿ
b. Let after x years population will be 9 million.
then,
9000000 = 8100000 (1 + 2/100)ˣ
(1 + 2/100)ˣ = 9000000/8100000
(1.02)ˣ = 90/81
(1.02)ˣ = 1.11
Taking log on both sides
ln (1.02)ˣ = ln (1.11)
ln(a)ⁿ = n ln(a)
x ln(1.02) = ln (1.11)
x = ln(1.11)/ln(1.02)
x = 5.27 years
Hence, the population will reach 9 million in 5.27 years.
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Solve x to the nearest tenth
Answers
Answer:
12.5
Step-by-step explanation:
We see in the other triangle that the ratios is 2:5 (4 to 10).
Therefore, assuming they are similar, we can assume the ratio is the same for the missing triangle.
So,
10/4 = 2.5
5(given) x2.5 = 12.5
Answer:
7.7
Step-by-step explanation:
10² - 4² = 84
√84 = 9.16 so 9.2
now we now have the hypotenuse of the other triangle
9.2² - 5² =59.64
√ 59.64 = 7.72 so 7.7
A company makes chocolate candies in the shape of a solid sphere. Each piece of candy has a diameter of 6cm. If a box contains 15 pieces of candy, how much chocolate does the box contain? Use 3. 14 for π, and do not round your answer
Answers
The total amount of solid sphere chocolate in the box is 1695.6 cubic centimeters.
What is volume?The space occupied within an object's borders in three dimensions is referred to as its volume.
What is the volume of sphere?The volume or the space inside the borders of the sphere is given by the formula:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Given that the diameter is 6cm, the radius r = 3cm.
Substituting the value of radius in volume we have:
[tex]V = \frac{4 (3.14)(3)^3}{3}[/tex]
[tex]V= 113.04[/tex]
The box contains 15 candies hence the total volume will be:
V = 15 * 113.04
V = 1695.6 cubic centimeters.
Hence the total amount of chocolate in the box is 1695.6 [tex]cm^3[/tex].
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who can help me for 13 points
Answers
Answer:
slope is zero
Step-by-step explanation:
slope is the difference of the y-values over the difference of the x-values
(-3-(-3)) ÷ (5-2)
0/3
Under which condition is the sample proportion, , a point estimate of the population proportion?
A.
The sample size, n, is small enough.
B.
The sample represents a proportion of the population.
C.
The sample proportion is unbiased.
D.
The sample proportion is never a point estimate of the population proportion.
Answers
Answer:
c. the sample portion is unbaised
Step-by-step explanation:
plato
If the sales tax in your city is 12% and your item cost $97, how much tax would you pay on that item?
Answers
Answer:
Step-by-step explanation:
11.64
What is undecidable language?
Answers
Therefore , the solution of the given problem of algorithm comes out to be when the language L of all yes cases to a decision problem P cannot be decided, the problem is said to be "undecidable."
Describe an algorithm.Algorithms exist to identify, solve, and frequently automate a solution to a particular problem; regardless of the situation, they are essentially problem solvers of expression.
In area of beginning textbooks, algorithms are typically introduced as "a set of phases to solve a problem."
Here,
Alternatively, a Turing computer that halts for all inputs cannot recognize a language for whose membership cannot be determined by an algorithm.
It is known as undecidable language.
There is no Turing Machine for an undecidable language that accepts the language and decides on each input string (TM can make decision for some input string though).
When the language L of all yes cases to a decision problem P cannot be decided, the problem is said to be "undecidable."
Therefore , the solution of the given problem of algorithm comes out to be when the language L of all yes cases to a decision problem P cannot be decided, the problem is said to be "undecidable."
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What is the volume of the solid hemisphere?
Answers
Answer:
volume of the hemisphere
[tex] \frac{1}{2} \times \frac{4}{3} \times \pi \times {3}^{3} \\ \frac{2}{3} \times 27 \times \pi \\ 18\pi {cm}^{3} [/tex]
5/6 - 1/4 please answer needed quick
Answers
Answer:
7/12
Step-by-step explanation:
write all numerators above the least common denominator 12
10-3/12
subtract
10-3=7
Answer 7/12
Answer:
I already said it in the comments 5 min ago but 7/12
Step-by-step explanation:
Help no links or files pls help
Answers
Answer:
2. one angle is 108, and other is 72
3. x is 12
Step-by-step explanation:
the ratio is 3:2.
3x + 2x = 180
5x = 180
x = 36
36 x 3 = 108
36x 2 = 72
so that is why the two angles re 108and 72.
for the last question, 37 plus 41 plus x = 90
37 plus 41 is 78
90 - 78 = 12
so that is why x is 12.
Write and solve an equation to find the value of x.
Answers
Answer:
x = 60
Step-by-step explanation:
Let the two opposite angles be equal and let's call them y.
Because of the theory of angles on a straight line 120 +y = 180
y = 60
Because of the theory of angles on a straight line 2x + y = 180
2x + 60 = 180
2x = 120
x = 60
Alternatively. (also a lot easier)
120 and 2x are opposite angles so they are equal and so;
2x = 120
x = 60
Please mark as brainliest if this answer is helpful.
please answer! it's more complicated than it looks!
Answers
Answer:
1. 360
2. Yes because in a regular hexagon all angles are congruent so the exterior angles are as well
3. (i) 60 (ii) 120
4.
(i) 1. 360 2. Yes because in a regular octagon all angles are congruent so the exterior angles are as well 3. (i) 45 (ii) 135
(ii) 1. 360 2. Yes because in a regular 20-gon all angles are congruent so the exterior angles are as well 3. (i) 18 (ii) 162
Step-by-step explanation:
Works for each polygon
1. First take the number of sides and subtract it by 2 then multibly that by 180
6-2=4x180=720
Then divide by the number of angles and subrtact that number by 180 to find the measure of one exterior angle
720/6=120
180-120=60
Then multiply by the number of exterior angles
60x6=360
2. Regular polygons always have equal angles so the exterior angles are as well
3. Put in your numbers from earlier
(i) 60 (ii)120
Hope this helps! :)
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