Answer:
26 kangaroos on the farm
32 goats on the farm
Step-by-step explanation:
To find the number of goats and kangaroos on the farm, we need to determine the number of legs each animal has. Let's say that there are 'g' goats and 'k' kangaroos.
Since each goat has 4 legs, the total number of legs for all the goats is 4g. Similarly, since each kangaroo has 2 legs, the total number of legs for all the kangaroos is 2k.
Adding these two quantities, we have:
4g + 2k = 180
Since each goat has 1 head, the total number of heads for all the goats is g. Similarly, since each kangaroo has 1 head, the total number of heads for all the kangaroos is k.
Adding these two quantities, we have:
g + k = 58
Now, we have two equations and two unknowns. To solve for 'g' and 'k', we can use substitution or elimination method.
Let's use substitution method:
From the second equation, we can find g:
g = 58 - k
Substituting this in the first equation, we get:
4(58 - k) + 2k = 180
Expanding and solving, we get:
232 - 4k + 2k = 180
232 - 2k = 180
-2k = -52
k = 26
So, there are 26 kangaroos on the farm. To find the number of goats, we can use the first equation:
g = 58 - k = 58 - 26 = 32
Therefore, there are 32 goats on the farm.
a rectangular sheet of dimensions 44cm *14cm is rolled along its length and a cylinder is fromed find the surface area of the cylider
The total surface area of cylinder formed is 924 cm²
We are given a rectangular sheet of paper of dimensions 44 cm* 14 cm is rolled along its length
So, height of formed cylinder = Length of rectangular sheet = 14 cm
Circumference of base of cylinder = Breadth = 44 cm
Circumference of circle = 2πr
So,
2 × (22/7) × r =44
r = (44×7)/(22×2)
Radius of cylinder is 7 cm
Height = 14 cm
Total surface area of cylinder = 2πr(h+r)
= 2 × 22/7 × 7 (14 +7 )
= 924 cm²
Hence the total surface area of cylinder formed is 924 cm² .
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Which of the following points lie in the solution to the following system of inequalities y less than or equal to x -5 and y greater than or equal to -x-4
(-5,2)
(5,-2)
(-5,-2)
(5,2)
The point that lies in the solution to the system of inequalities is (5,-2). The correct answer would be an option (B).
What is inequality?An Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The system of inequalities is given in the question, as follows:
y ≤ x -5 and y ≥ -x-4
Since the required point is to satisfy the system of inequalities.
Then the graph attached below represents a solution to the system of inequalities.
Point A (-5,2) does not lie in the solution to the system of inequalities.
Point B (5,-2) lies in the solution to the system of inequalities.
Point C (-5,-2) does not lie in the solution to the system of inequalities.
Point D (5,2) does not lie in the solution to the system of inequalities.
Therefore, the point that lies in the solution to the system of inequalities is (5,-2).
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Give the most specific name for the quadrilateral.
O parallelogram
rectangle
O trapezoid
O isosceles trapezoid
Explain your reasoning.
B I U
E T² T₂
The most specific name for the quadrilateral is trapezoid, the correct option is C.
What are quadrilateral?A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. There are two main types: concave and convex. There are also various subcategories of convex quadrilaterals, such as trapezoids, parallelograms, rectangles, rhombi, and squares.
Given;
The figure with 4 sides and two opposite are equal
Now,
In the figure two opposite sides are equal in length
But they all are not parallel only on pair of opposite sides are parallel.
Also, the figure the adjacent angle are equal.
Therefore, the quadrilateral will be trapezoid.
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Suppose that the functions q and r are defined as follows
Suppose that the functions q and r are defined as q(x) = 2x+2 and r(x) = x² +1, the function (r * q)(4) =(q * r)(4) and they are equal to 170.
Which is the commutative law?
commutative law, in mathematics, is either of two laws relating to number operations of addition and multiplication that are stated symbolically as a + b = b + a and ab = ba. From these laws, it follows that any finite sum or product is unaltered by reordering its terms or factors.
Given the following functions:
q(x) = 2x+2
r(x) = x² +1
Taking the product
q(x)*r(x) = (2x + 2)(x² +1)
Note that according to the communatative law, (r * q)(x) = (q * r)(x)
(r * q)(4) =(q * r)(4) = (2(4)+2)((4)² +1)
(r * q)(4) =(q * r)(4) = (10)(16+1)
(r * q)(4) =(q * r)(4)= 10(17)
(r * q)(4) =(q * r)(4) = 170
Hence, the function (r * q)(4) =(q * r)(4) and they are equal to 170.
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2. The area of a garden plot can be represented by
the expression 85.2z - 58.8. The garden will be
divided into six sections for planting six different
vegetables. The sections will be equal in area.
Write an expression that represents the area of
each section.
The expression that represents the area of each section is 14z-9
How to find the expression?The expression to denote the area of each section would be: 14z -9
Given that,
The expression for the area of plot area 84z -54
The number of equal sections in which it is divided 6
To find,
The expression for each section = ?
The area of each section = (total area of the garden(/number of equal sections
= (84x-54)/6
= 6(14z-9)/6
=14z - 9
Thus, is the expression that would represent every section's area.
Jean bought a $1,980 snow thrower on an installment plan. The installment agreement included a 10% down payment and 18 monthly payments of $116 each.
Jean purchased a snow thrower for $1,980 using an installment plan that required a 10% down payment of $198 and 18 monthly payments of $116. This allowed Jean to spread out the cost of the snow thrower over time, avoiding a large upfront cost.
Jean recently purchased a snow thrower for $1,980 using an installment plan. To start, Jean had to make a down payment of 10% of the total purchase price, which was $198. This down payment allowed Jean to spread the remaining cost of the snow thrower across 18 monthly payments of $116 each. After making all 18 payments, Jean will have paid the full purchase price of $1,980. This installment plan option is an excellent way for Jean to get the snow thrower he needs while avoiding a large upfront cost and spreading the payments out over a period of time. With this installment plan, Jean can pay off the purchase of the snow thrower while still having money left over each month to cover other expenses.
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PLEASE HELP ASAP IF YOUHELP QUICK I WILL
GIVE BRANLIST In a repeated experiment, Kim rolled a fair die twice. The theoretical probability of both rolls equaling a sum greater than 10 is Predict how many times
36
the rolls will result in a sum greater than 10 if the experiment is repeated 108 times
OPTIONS
3
9
10
1&
The theoretical probability that a sum greater than 10 is obtained is given as follows:
p = 1/12.
Out of 108 trials, the expected number of trials with a sum greater than 10 is given as follows:
9.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The 36 total outcomes for the pair of dices is given as follows:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)Out of these outcomes, three of them, (5,6), (6,5) and (6,6) have a sum greater than 10, hence the probability is given as follows:
p = 3/36
p = 1/12.
Then the expected number is given as follows:
E(X) = 108 x 1/12
E(X) = 9.
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Answer:
9
Step-by-step explanation:
experiment, Kim rolled a fair die twice. The theoretical probability of both rolls equaling a sum greater than 10 is Predict how many times.
Therefore the experement is 9
Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 70 miles per hour, with a standard deviation of 3 miles per hour. Estimate the percent of vehicles whose speeds are between 64 miles per hour and 76 miles per hour.
Answer:
The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.
In this case, the mean speed is 70 mph and the standard deviation is 3 mph. So, we can estimate the percent of vehicles whose speeds are between 64 mph and 76 mph as follows:
64 mph = 70 mph - 3 mph * 1
76 mph = 70 mph + 3 mph * 1
Since the speeds are within one standard deviation of the mean, we can use the Empirical Rule to estimate that approximately 68% of the vehicles have speeds between 64 mph and 76 mph.
So, the answer is approximately 68%.
write a number or expression in each empty box to create a true equation 15 + 10 = _____ (3 + 2)
Answer:
5(3-2)
Step-by-step explanation:
15-10
5×3-5×2
Some candles are in the shape of a right circular cylinder. For one such candle, the radius is 9 cm and the height is 26.5 cm. Find the volume of the candle. Round your answer to the nearest whole number. Do not type the units in the space below. (Be sure to use the pi button on your calculator to do the calculation.)
The volume of the candle is 6740 cubic cm
How to find the volume of the candle.From the question, we have the following parameters that can be used in our computation:
Radius, r = 9 cm
Height, h = 26.5 cm
The volume of a cylinder is calculated as
Volume = πr²h
substitute the known values in the above equation, so, we have the following representation
Volume = 3.14 * 9² * 26.5
Evaluate the products and exponents
Volume = 6740 cubic cm
HEnce, the volume is 6740 cubic cm
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The function f(x) = x³ +9 is one-to-one.
a. Find an equation for f1, the inverse function.
b. Verify that your equation is correct by showing that f(f(x)) = x and f¹(f(x)) = x.
a. Select the correct choice below and fill in the answer box(es) to complete your choice.
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
OA. f¹(x)=, for all x
O B. f¹(x)=, for x ≥
O c. f¹(x)=, for x‡|
x#
OD. f¹(x)=, for xs
Since f(f1(y)) = y and f1(f(x)) = x, we can conclude that f1 is the correct inverse function for f.
What is functio ?
Function can be defined in which it relates an input to output.
Given function ,
The function f(x) = x³ +9 is one-to-one.
To find the inverse function f1, we need to switch the roles of x and y in the equation for f(x). So, we have:
y = x³ + 9
Next, we need to solve for x in terms of y:
x³ + 9 = y
x³ = y - 9
x = (y - 9[tex])^{(1/3)}[/tex]
So, the inverse function is:
f1(y) = (y - 9[tex])^{(1/3)}[/tex]
To verify that f1 is the correct inverse function, we need to show that f(f1(y)) = y and f1(f(x)) = x:
f(f1(y)) = f((y - 9[tex])^{(1/3)}[/tex] = (y - 9[tex])^{(1/3)}^3[/tex] + 9 = y - 9 + 9 = y
And:
f1(f(x)) = f1(x³ + 9) = (x³ + 9 - 9[tex])^{(1/3)}[/tex] = [tex]\mathrm{ x^3^{(1/3)}}[/tex] = x
Therefore, Since f(f1(y)) = y and f1(f(x)) = x, we can conclude that f1 is the correct inverse function for f.
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Shen is riding in a bike race that goes through a valley and a nearby mountain range.
The table gives the altitude (in feet above sea level) for the five checkpoints in the race.
Use the table to answer the questions.
Checkpoint Altitude
(feet above sea level)
1 3,459
2 1,499
3 668
4 -202
5 -99
(a) The top of a hill rises 66 feet above Checkpoint 4.
What is the altitude of the top of the hill?
(b) How much higher is Checkpoint 1 than Checkpoint 5?
1) Note that the altitude of the top of the hill is -136 feet above sea level.
2) Note that Checkpoint 1 is 3,558 feet higher than Checkpoint 5.
What is the rationale for the above response?Altitude or height is a distance measurement between a reference datum and a point or object, generally in the vertical or "up" direction. The precise definition and reference datum vary depending on the circumstance.
1) Checkpoint 4 has an altitude of -202 feet above sea level. The top of the hill rises 66 feet above Checkpoint 4. Therefore, the altitude of the top of the hill is:
-202 + 66 = -136 feet
So, the altitude of the top of the hill is -136 feet above sea level.
2) To find the difference in altitude between Checkpoint 1 and Checkpoint 5, we need to subtract the altitude of Checkpoint 5 from the altitude of Checkpoint 1.
Altitude difference = Altitude of Checkpoint 1 - Altitude of Checkpoint 5
Substituting the values given in the table, we get:
Altitude difference (AD) = 3,459 - (-99)
AD = 3,459 + 99
Thus, AD = 3,558
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Write out all functions ????:{1,2,3,4}→{????,????} (using two-line notation). How many functions are there? How many are surjective? How many are injective? How many are bijective?
Since the domain has 4 elements and the range has 2 elements, each element in the domain can be mapped to one of the two elements in the range. Thus, there are a total of [tex]$2^4 = 16$[/tex] functions from the domain to the range.
What is functions ?
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the codomain or range) with the property that each input is related to exactly one output. Functions can be represented in many ways, including algebraic expressions, graphs, tables, or verbal descriptions.
Functions are widely used in various fields of mathematics, science, and engineering to model and analyse real-world phenomena, and to make predictions or decisions based on data.
There are 4 elements in the domain and an empty set in the codomain.
Using two-line notation, the functions are:
{1→∅, 2→∅, 3→∅, 4→∅}{1→∅, 2→∅, 3→∅, 4→∅}{1→∅, 2→∅, 3→∅, 4→∅}{1→∅, 2→∅, 3→∅, 4→∅}There is only one possible image for each element in the domain, which means that there is only one function.
Since there is only one function, it is both surjective and injective. Therefore, there is only one bijective function.
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The sixth-graders at Liam's school got to visit either the science museum or the history museum. 10 students picked the science museum and 39 students picked the history museum. What is the ratio of the number of sixth-graders who visited the science museum to the number of sixth-graders who visited the history museum?
The ratio of the number of sixth-graders who visited the science museum to the number of sixth-graders who visited the history museum is
10:39.
What is meant by the ratio of two quantities?
A ratio displays the multiplicity of two numbers. Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent." In general, a: b, which can be interpreted as "a is to b," is used to denote a ratio between two quantities, let's say "a" and "b."
Given,
Number of students who picked the science museum = 10
Number of students who picked the history museum = 39
The ratio of students who visited the science museum to students who visited the history museum = 10:39.
Therefore the ratio of the number of sixth-graders who visited the science museum to the number of sixth-graders who visited the history museum is 10:39.
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I need the answer NO LINKS URGENT NO LINKS URGENTS
Answer: See the attached image below for the proof table.
Explanation:
We start with what we're given. Simply repeat the given information word for word. This is statement 1 of the proof.
Statement 2 mentions AB is parallel to CD. This is valid due to the definition of a parallelogram. The name means "two sets of opposite parallel sides. Statement 3 is a similar situation.
Statement 4 relies on statement 2. The red angles in the diagram are congruent alternate interior angles. They are only congruent because of AB parallel to CD.
Statement 5 relies on statement 3 for similar reasoning as the previous paragraph. Focus on the blue angles.
Statement 6 is hopefully self explanatory so there's not much for me to mention here.
Statement 7 has us connect statements 4, 5, and 6 to prove triangle ADB is congruent to triangle CBD. We use the ASA (angle side angle) theorem here.
Statements 8 and 9 finish up the proof. CPCTC stands for "Corresponding parts of congruent triangles are congruent". If two triangles are congruent, then their corresponding pieces must be congruent as well. It would be like saying two houses are identical if and only if their front doors are identical.
the perimeter of a pentagon is 60 in. The five sides are repersented by consecutive integers. Find the lengths of the sides.
The lengths of the sides of the pentagon are;
12 Inches
13 inches
14 inches
15 inches
16 inches
How to determine the valueThe formula for the perimeter of a pentagon is expressed with the formula;
P = 5a
Given that the parameter are;
P is the perimeter of the pentagona is the length of its sideSince the sides are consecutive integers, then;
60 = 5(a)
expand the bracket
60= 5a
Make 'a' the subject
a = 12In
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Solve for x with the given measures
Graph the following conditions. Click on the graphic to choose the correct answer. [(x, y): x + y = 5) 4 -3 -2 -1 YA 6 5 4 3 2 + T -2 -3 A 5 19 - K 2 3 4 5 6 X
A graph of the equation under this condition {(x, y): x + y = 5)} is shown in the image attached below.
What is an ordered pair?In Mathematics, an ordered pair simply refers to a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
Next, we would determine the ordered pairs that satisfies the given linear function in standard form.
When the value of x = 1, the output value of this linear function is given by;
y = 5 - x
y = 5 - 1
y = 4 ⇒ (1, 4)
When the value of x = 0, the output value of this linear function is given by;
y = 5 - x
y = 5 - 0
y = 5 ⇒ (0, 5).
When the value of x = 2, the output value of this linear function is given by;
y = 5 - x
y = 5 - 2
y = 0 ⇒ (2, 3).
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To encourage bulk buying, a company reduces the list price of $2,000 per unit by nine cents times the number of units bought. Write a function statement for the company's revenue (R) from a particular distributor that buys x units
The company’s revenue (R) from a particular distributor that buys x units is R(x) = 8999.93x
What is algebra?Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
Given:
original price = $9000 per unit.
let the number units bought be x
then amount= 9000x.
If the price reduces the list price by seven cents times the number of units bought .
7cents= 0.07 dollar
Then,
R(x) = 9000x - 0.07x
R(x) = 8999.93x
Hence, R(x) = 8999.93x.
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Factorise: 16x4 - y4
Answer:
= (4x^2 + y^2)(2x + y)(2x - y).
Step-by-step explanation:
16x^4 - y^4
= (4x2)^2 - (y^2)^2
= (4x^2 +y^2)(4x^2 - y^2)
=(4x^2 + y^2)( (2x)^2 -y^2)
= (4x^2 + y^2)(2x + y)(2x - y).
Answer:
Step-by-step explanation: [tex]16x^{4} -4y^{4} = (4x^{2} )^{2} -(2y^{2} )^{2}= (4x^{2} + 2y^{2} )(4x^{2} - 2y^{2})[/tex]
identity used =
[tex](a^{2} -b^{2} ) = (a+b)(a-b)[/tex]
Rafael and Lucy, married taxpayers, each contribute $2,850 to their respective § 401(k) plans offered through their employers. The AGI reported on the couple's joint return is $40,500. Determine their credit for retirement plan contributions (the Saver’s Credit).
Answer:
Rafael and Lucy's credit for retirement plan contributions is $570.
Step-by-step explanation:
The Saver's Credit is a tax credit for low and moderate-income taxpayers who make contributions to a retirement plan. The credit is worth between 10% and 50% of the taxpayer's contributions, up to a maximum credit of $1,000 ($2,000 for married taxpayers filing jointly).
To determine the credit amount, we need to calculate the taxpayers' adjusted gross income (AGI) and their credit rate.
For the tax year in question, the AGI is $40,500 and the contribution limit is $2,850 per person. The total contribution amount is $2,850 x 2 = $5,700.
The credit rate is determined by the taxpayer's AGI and filing status, as follows:
For AGI up to $19,750 for married taxpayers filing jointly, the credit rate is 50%.
For AGI between $19,750 and $32,000 for married taxpayers filing jointly, the credit rate is 20%.
For AGI between $32,000 and $40,000 for married taxpayers filing jointly, the credit rate is 10%.
For AGI above $40,000 for married taxpayers filing jointly, the credit is not available.
Since the taxpayers' AGI is $40,500, the credit rate is 10%. The credit amount is calculated as follows:
Credit amount = Credit rate x Contribution amount
Credit amount = 10% x $5,700 = $570
So, Rafael and Lucy's credit for retirement plan contributions is $570.
Draw a rectangular fraction model to explain your thinking. 1/2 of 2/3 = 1/2 of_ third(s) =_ third(s)
A rectangle that has been divided into equal parts is referred to as a rectangular fraction. Depending on how many equal pieces you divide the whole into, the equal parts may be divided into halves, thirds, fourths, and so on.
1/2 of 2/3 is equal to 1/3
What is the equation?
The equation is defined as a mathematical statement with at least two terms that contain variables or values that are equal.
To represent the multiplication of 1/2 and 2/3, we can draw a rectangle and divide it into equal parts.
1) First, we draw a rectangle.
2) Then, we divide it into 2 equal parts horizontally.
3) Next, we divide each half vertically into 3 equal parts.
4) Now we can see that each small rectangle represents 1/6 of the whole rectangle.
So, 1/2 of 2/3 is equal to 1/2 of 1/3.
Therefore, 1/2 of 2/3 is equal to 1/3.
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Find the perimeter of the triangle as both a decimal and in simplest
radical form
Add the sides' lengths to find a triangle's perimeter. As an illustration, the perimeter of a triangle with sides a, b, and c is given by P = a + b + c.
What is meant by perimeter?The radius of a shape's edge is known as the perimeter. Discover how to calculate a shape's perimeter by multiplying its side lengths.It is measured from the object's edge to its perimeter. Like the yard that is fenced in at your home. The distance around anything is called its perimeter. The fence is 200 feet long for a yard that is 50 feet by 50 feet.The measurement of a shape's perimeter is its length. It takes adding the lengths of all four sides to determine a rectangle's or square's perimeter.The length of a two-dimensional shape's perimeter is referred to as its perimeter. The total length of all the sides of the thing is also a definition for it.To learn more about perimeter refer to:
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12 (long division) 924
The solution is, 12 (long division) 924 = 77.
What is division?Division is the process of splitting a number or an amount into equal parts.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
given that,
12 (long division) 924
so, we get,
12 | 924 | 77
84
----------------
84
84
-----------------
0
Hence, The solution is, 12 (long division) 924 = 77.
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Whats the correct answer answer asap for brainlist
The sentence that uses the word "obstinancy" incorrectly is: if we eat out too often, its result in obstinancy and poor health. The Option C is correct.
Definition of the word "obstinancy", its uses and example:Obstinancy is a noun that refers to the quality of being stubborn or resolutely unyielding. It describes a person's refusal to change their views, opinions, or actions, even in the face of compelling evidence or persuasive arguments. Example of its use: despite the pleas of his family, the man's obstinancy led him to continue his dangerous lifestyle.
We often use the word "obstinancy" for the followings:
to describe someone's persistence in pursuing a particular course of action despite obstacles or challenges.to describe someone's reluctance to change their opinion or attitude in light of new evidence.to describe someone's refusal to give in to the demands or requests of others.Read more about Obstinancy
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If the diameter of the pie is ten inches, the approximate arc length of one slice of pie is.
Answer:
It depends on the amount of slices.
Step-by-step explanation:
The diameter of the pie is 10 inches. Multiply this by π and we get approximately 31.4. Basically just divide it by the number of slices. For example, if there were six slices, 31.4/6=5.23, so that's the arc length of one slice.
You can earn a maximum profit of $
by investing $
in stock A, $
in stock B, and $
in stock C.
The solution that gives the maximum profit for the linear optimization question is presented as follows;
A maximum profit of $840 can be earned by investing;
$3,000 in stock A
$6,000 in stock B
$7,000 in stock C
What is linear programming?Linear programming is a optimization technique that helps in determining the maximizing or minimizing parameters of linear functions.
The parameters in the question, obtained from a similar question obtained online includes;
The amount available to be invested = $16,000
The expected returns for stock A = 4%
The expected return for stock B = 5%
Expected returns for stock C = 6%
Amount to be invested in each stock ≥ $1,000
Amount to be invested in stock C ≤ $7,000
Amount invested in C ≤ 4 × Amount invested in stock A
Amount invested in stock B ≤ 2 × Amount invested in stock A
Let x represent the amount invested in stock A, let y represent the amount invested in stock B therefore;
The amount invested in stock C = 16,000 - x - y
x ≥ 1000y ≥ 1000y ≤ 2·x16,000 - x - y ≥ 1000...(1)
16,000 - x - y ≤ 7000...(2)
16,000 - x - y ≤ 4·x...(3)
Therefore, we get;
- y ≥ 1000 - 16,000 = -15000 + x
-y ≥ -15000 + x
y ≤ 15000 - x16,000 - x - y ≤ 7000
y ≥ 9,000 - x16,000 - x - y ≤ 4·x
-y ≤ 4·x + x = 5·x - 16,000
-y ≤ 5·x - 16,000
y ≥ 16,000 - 5·xThe vertices of the feasible regions on the graph of the inequalities are;
(5,000, 10,000), (3,000, 6,000), (8,000, 1,000), and (14,000, 1,000)
The profit function is;
Profit = 0.04·x + 0.05·y + 0.06·(16000 - x - y)
Plugging in the value of the vertices of the feasible region in the profit function, we get;
Point (5,000, 10,000)
Profit = 0.04 × 5000 + 0.05 × 10000 + 0.06 × (16000 - 5000 - 10000) = 760
Point (3,000, 6,000)
Profit = 0.04 × 3000 + 0.05 × 6000 + 0.06 × (16000 - 3000 - 6000) = 840
Point (8,000, 1,000)
Profit = 0.04 × 8000 + 0.05 × 1000 + 0.06 × (16000 - 8000 - 1000) = 790
(14,000, 1,000)
Profit = 0.04 × 14000 + 0.05 × 1000 + 0.06 × (16000 - 14000 - 1000) = 670
Therefore, the maximum profit of $840 is earned by investing $3,000 in stock A and $6,000 in stock B which indicates that the investment in stock C is $16,000 - $3,000 - $6,000 = $7,000
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differentiate (1+2x²)⁴
Answer:
16x(1+2x^2)^3
Step-by-step explanation:
f(x)=(1+2x^2)^4
Use chain rule
4(1+2x^2)^3(4x)
PLEASEE HELPPP!!! 3 QUESTIONS
Consider the function below.
f(x)=8/x−6
What would be the output if the input is 8?
responses:
-1/4
-4
-8/14
-8/6
What is the average rate of change of the function f(x)=3x^2−5 over the interval [2, 6]?
responses:
-3
-48
-12
-24
The average mass of a certain type of microorganism is 2.4×10^−6
grams. What is the approximate total mass of 5,000 of these microorganisms?
responses:
-0.00012 g
-0.0012 g
-0.012 g
-0.12 g
A. The value of the function at x = 8 will be 4. Then the correct option is B.
B. The average rate of change of the function in the interval of [2, 6] will be 24. Then the correct option is D.
C. The total mass of 5,000 of these microorganisms will be 0.012 g. Then the correct option is C.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
A. The function is f(x) = 8 / (x - 6), then the value of the function at x = 8 is given as,
f(8) = 8 / (8 - 6)
f(8) = 4
Then the correct option is B.
B. The function is f(x) = 3x² - 5, then the average rate of change of the function in the interval of [2, 6] is given as,
Average rate = [3(6² - 4²)] / (6 - 2)
Average rate = 24
Thus, the correct option is D.
C. The average mass of a certain type of microorganism is 2.4 × 10⁻⁶ grams. Then the total mass of 5,000 of these microorganisms is given as,
⇒ 2.4 × 10⁻⁶ × 5,000
⇒ 0.012 grams
Thus, the correct option is C.
More about the function link is given below.
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Franka's annual salary is $79600. About 25% of her salary is deducted for taxes. Estimate the amount deducted from Franka's pay each year
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 79600}}{\left( \cfrac{25}{100} \right)79600}\implies \text{\LARGE 19900}[/tex]
