Answers
If the function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex] then by differentiating the equation with respect to x, we get sin (2)(18[tex]$$x^8[/tex] + 5[tex]$$x^4[/tex]).
What is meant by differentiation?Differentiation is a process that is applied to a function to determine the rate of change of the function in comparison to the rate of change of the independent variable. The result of differentiating a function is known as its derivative. It gives the slope of the function's graph at each point.Differentiation refers to tailoring instruction to meet the needs of each individual. Whether teachers differentiate content, process, products, or the learning environment, the use of continuous assessment and flexible grouping makes this a successful instructional approach.Let the given function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex]
Differentiating with respect to x, we get
d/dx((2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex])
= sin (2) (d/dx(2[tex]$$x^4[/tex] + 1) [tex]$$x^5[/tex] + d/dx ([tex]$$x^5[/tex]) (2[tex]$$x^4[/tex] + 1)
d/dx (2[tex]$$x^4[/tex] + 1) = 8x³
d/dx ([tex]$$x^5[/tex]) = 5[tex]$$x^4[/tex]
= sin (2) (8x³ + 5[tex]$$x^4[/tex] ( (2[tex]$$x^4[/tex] + 1)
Simplify
= sin (2) (8x³ + 5[tex]$$x^4[/tex] ( (2[tex]$$x^4[/tex] + 1)
= sin (2) (18[tex]$$x^8[/tex] + 5[tex]$$x^4[/tex]
Therefore, the function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex] then by differentiating the equation with respect to x, we get sin (2)(18[tex]$$x^8[/tex] + 5[tex]$$x^4[/tex]).
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Related Questions
In the following expression, n is a rational number: Which expression below is equivalent to this expression?
Answers
Answer:
none of them
Step-by-step explanation:
f(x)=(-3x^2-1)/3x^3 does f have an inverse function?
Answers
Answer: Yes, Probably
Solve the equation in the image below correct to 2 decimal places. in Logarithm Terms
Answers
The solution to the given equation is 5.630.
What is a logarithmic equation?
An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.
Here, we have
2^(x+1) = 3^(2x-5)
Taking logarithms on both sides, we get
(x+1)log2 = (2x - 5)log3
xlog2 + log2 = 2xlog3 - 5log3
log2 + log3⁵ = 2xlog3 - xlog2
log 2* 243 = x(log6 - log2)
log486 = x(log6/2)
log486 = xlog3
x = log486/log3
x = 5.630
Hence, the solution to the given logarithmic equation is 5.630.
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A 6-foot-tall woman walks at 8ft/s toward a streetlight that is 30 ft above the ground. At what rate is the tip of her shadow moving? I got nothing on this bit the picture, and don't know where to start. does anyone know how to solve this one?
Answers
The rate at which the tip of the woman's shadow is moving, found by making use of the relationships between similar triangle and differentiation is 10 ft/s
What are similar triangles?Similar triangles are triangle in which all three sides of one proportional to three sides of the other triangle
Height of the woman = 6 ft.
The speed with which the woman walks towards the streetlight = 8 ft/s
The length of the shadow of the woman
Height of the street light = 30 ft.
Let a represent the horizontal distance from the woman to the street light, and let b represent the horizontal distance from the woman to the tip of her shadow, from the similar triangles formed by the shadow, we have;
[tex]\dfrac{30}{x+y} =\dfrac{6}{y}[/tex]
Which gives;
[tex]y = \dfrac{x}{4}[/tex]
The length of the tip of the woman's shadow to the street light, l, in terms of x is therefore;
[tex]l =x + y = x + \dfrac{x}{4} = \dfrac{5\cdot x}{4}[/tex]
[tex]\dfrac{dx}{dt} = 8[/tex]
Therefore, dx = 8·dt
x(t) = 8·t
Writing the function for the l in terms of time t gives;
[tex]l = \dfrac{5\cdot x}{4}[/tex]
[tex]l = \dfrac{5\times 8\cdot t}{4} = \dfrac{40\cdot t}{4} = 10\cdot t[/tex]
The speed at which the tip of the shadow is moving,
[tex]\dfrac{dl}{dt} = \dfrac{d}{dt} \left (10\cdot t ) = 10[/tex]
The speed of the shadow dl/dx = 10 ft./s
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For a 14-person team, how does the actual weekly labor cost compare to the target?
$15 over target $300 over target $600 over target
$1,800 over target
$6,000 over target
Answers
The actual weekly labor cost compared to the target is 240 hours
What are Time and Work?
According to fundamental mathematical concepts, time may be described as the amount of time that a specific activity occurs, whereas work can be described as the collection of actions carried out in order to attain a specific activity or outcome. It should go without saying that time is needed to accomplish a task. It implies that time and work have a certain relationship.
The task completed is calculated as the sum of the number of people participating in the work and the number of days it took to finish. The fundamental time and work equation is W = N X D.
Target costing is a system under which a company plans in advance for the price points, product costs, and margins that it wants to achieve for a new product.
Given
Regular Rate $15.00/hr
Overtime Rate $22.50/hr
Targeted Labour Cost $12,000/wk
Labour Hours Needed 800/wk
According to the question:
Overtime means each employee can work beyond the input of 40 hrs. Per week.
Labor requirement = 800 hrs.
14 men labor capacity = 14× 40 = 560 hrs.
So overtime hours required = 800-560=240 hrs
Hence,
The actual weekly labor cost compared to the target is 240
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Mara solved an exponential equation by using logarithms. This is her work.
Latex: 7 \cdot 3^x=189
7
⋅
3
x
=
189
7
⋅
3
x
=
189
Latex: 3^x=27
3
x
=
27
3
x
=
27
Latex: \log _3\!(3^x)= \log _3\!27
log
3
(
3
x
)
=
log
3
27
log
3
(
3
x
)
=
log
3
27
Latex: x \log _3\!3=9
x
log
3
3
=
9
x
log
3
3
=
9
Latex: x \cdot 1=9
x
⋅
1
=
9
x
⋅
1
=
9
Latex: x=9
x
=
9
x
=
9
Review Mara's work in steps 3 and 4. (Hint: There is one mistake in those steps.)
a. Be sure to explain what she did and why it was correct or incorrect for Step 3.
b. Be sure to explain what she did and why it was correct or incorrect for Step 4.
c. Provide Mara with feedback on what the mistake was and how to fix it.
Answers
a) The mistake that mara made in step 3 is that; she didn't apply the basic rule of logarithm which should have given the expression log 3^x = x log 3
b) The mistake that mara made in step 4 is that; you must eradicate the log at the same time and as such it should be x log 3 = 3log 3
c) The mistake she made throughout is not applying the basic rule of logarithm.
How to solve Exponential Equations using logarithm?
She is trying to solve the exponential function 7 x 3^x = 189 with the following steps;
Step 1. 7 x 3^x = 189
Step; 2. 3^x = 27; This step is correct because she got it by using division property of equality to divide both sides by 7.
Step 3; log^3 (^3) = log^27; This step is incorrect because from basic rules of logarithm, we know that; log 3^x = x log 3
Step 4. xlog^33=9; This is incorrect because you cannot remove the log on one side of the equation without doing the same on the second side. Thus, what she she should have had here is;
x log 3 = 3log 3
Step 5. x * 1 = 9; This is wrong because dividing both sides by log 4 gives; x = 3
Step 6. x = 9; This is wrong because x = 3
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Complete question is;
Mara solved an exponential equation by using logarithms. This is her work.
1. 7 x 3^x = 189
2. 3^x = 27
3. log^3 (^3) = log^27
4. xlog^33=9
5. x * 1 = 9
6. x = 9
Review Mara's work in steps 3 and 4. (Hint: There is one mistake in those steps.)
a. Be sure to explain what she did and why it was correct or incorrect for Step 3.
b. Be sure to explain what she did and why it was correct or incorrect for Step 4.
c. Provide Mara with feedback on what the mistake was and how to fix it.
Sebastian bought x gallons of gas at a price of $2.91 per gallon at his local gas station. When he paid for the gas, Sebastian also paid $11.40 for granola bars and a box of tissues.
If Sebastian filled 10 gallons of gas, how much did he spend in all at the gas station?
A. $3.92
B. $24.71
C. $40.50
D. $116.91
Answers
If Sebastian filled 10 gallons of gas, the total amount he spent at the gas station was C. $40.50.
How is the total amount determined?Using the mathematical operations of multiplication and addition, we can compute the total amount that Sebastian spent at the gas station.
We first determine the total cost of gas that Sebastian bought by multiplying the unit cost by the quantity.
Secondly, we add the above total cost to the total cost of other items he bought at the station to arrive at the total amount spent.
The cost of gas per gallon = $2.91
The number of gallons of gas bought = 10
The total cost of gas = $29.10 ($2.91 x 10)
The total cost of granola bars and tissues = $11.40
The total amount spent = $40.50 ($29.10 + $11.40)
Thus, mathematically, Sebastian spent C. $40.50 at the gas station.
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The data from a simple random sample with 25 observations was used to construct the plots given below. The normal probability plot that was constructed has a correlation coefficient of 0.975. Judge whether a t-interval could be constructed using the data in the sample.
Answers
It could be said that the normal probability plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.
If the data from a simple random sample with 25 observations was used to construct the plots given below. The normal probability plot that was constructed has a correlation coefficient of 0.975., on analysing
The normal plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.
Therefore, It could be said that the normal plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.
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I need help with an orthocenter of a triangle question. Brainly is having a problem uploading my picture so here is the question: Find the coordinates of the orthocenter of the triangle with the given vertices: P(-1,2), Q(5,2), R(2,1). My Textbook has horrible step by step instructions and I really want to understand this process. Thanks!
Answers
The orthocenter of the triangle with vertices P(-1,2), Q(5,2), R(2,1) is
(2, 5)How to find orthocenterOrthocenter is calculated by
finding the slope of a side and the slope of the line perpendicular to the side finding the equation of the perpendicular line passing through the third side of the trianglerepeat step 1 and 2 for another sideWith two equations, solve for the two unknowns (x, y)this gives the coordinate of the orthocenterformula for slope is
m = (y₂ - y₁) / (x₂ - x₁)
slope of the perpendicular = -1/m
Using side PR P(-1,2) R(2,1) ,
m = (1 - 2) / (2 - -1)
m = 1 / 3
slope of the perpendicular = -1/m = - 1 / (1/3) = -3
using point-slope formula for equation of line passing through Q (5, 2)
point slope formula
(y - y₁) = m (x - x₁)
(y - 5) = -3 (x - 2)
y - 5 = -3x + 6
y = -3x + 6 + 5
y = 11 - 3x
Using side PQ P(-1, 2), Q(5, 2)
m = (2 - 2) / (5 - -1)
m = 0
slope of horizontal line is zero for horizontal line the perpendicular is a vertical line
using point-slope formula for vertical line passing through R (2, 1)
point slope formula
(y - y₁) = m (x - x₁)
0 = (x - 2)
x = 2
The two equations are
y = 11 - 3x
x = 2
solving both equations with x already known
y = 11 - 3 * 2
y = 11 - 6
y = 5
Therefore the orthocenter is (2, 5)
The triangle is attached
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Given: 5(2x-4)=10
Prove: x=3
Drag the correct reason to the box.
Answers
After simplifying an equation the value of x is x = 3.
What is solving an equation?
Unifying Principle for Equation Solving
By deleting parenthesis and grouping like terms, each side of the equation can be made simpler.
The variable term on one side of the equation can be separated using addition or subtraction.
To find the variable, use multiplication or division.
Consider, the given equation
5(2x - 4) = 10
10x - 20 = 10 Removing parenthesis
10x -20 + 20 = 10 + 20 Adding 20 on both sides
10x = 30 Simplifying
x = 3 Dividing both sides by 10
Hence, the value of x is, x = 3.
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the side length of a square is √8 find the area.
is the number rational or irrational?
Answers
The area of a square with a side length √8 represents a rational number, which is equal to 8 square units.
Is the number behind the area of the square a rational number?
Rational numbers are real numbers of the form m / n, where m and n are integers, where n ≠ 0. The rest of real numbers are irrational (i.e. π, √5, ∛7, e) Besides, the area of the square is determined by the following formula:
A = l²
Where l is the side length of the square.
First, substitute the side length of the square in the area formula:
A = (√8)²
Second, use algebraic properties to simplify the expression and find the corresponding result:
A = ([tex]8^{\frac{1}{2} }[/tex])²
A = 8
This number represents a rational number as 8 is equivalent to the rational number 8 / 1.
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Factor: 64x³ + 125y³
Answers
64x³+125y³
= (4x+5y)( 16x²-20xy+25y²)
a³ + b³ = ( a + b )( a² - ab + b² )
64x³ + 125y³
= ( 4x )³ + ( 5y )³
= ( 4x+5y )[ (4x)²- (4x)(5y)+(5y)²]
= (4x+5y)( 16x²-20xy+25y² )
Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 4% each year. In other words, if you have $1 this year, next year it will only buy you $0.96 worth of stuff. How much will $100 buy you in 20 years?
Answers
The amount that $100 will be able to buy in 20 years, given an inflation rate of 4% is $44.20
How to find the value of money?When given the inflation rate, know that this rate is the rate at which the value of money decreases per year.
If given a rate of 4% as inflation, then the value of a dollar would decrease by 4% a year.
In 20 years therefore, the value of $100 would be:
Value in 20 years = Value today x (1 - inflation rate) ^ number of years
= 100 x (1 - 4%) ²⁰
= $44.20
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Mark earns a salary of £28000 per annum. At the end of the on increase first year he is given he is of 3%.. At end of the second given an increase of 2.5%. Work out Mark's salary at the end of the two years.
Answers
Answer:
£27839
Step-by-step explanation:
O×M=N (original x multiplier = original value)
£28000×0.97%=£27160< 1st year decrease
£27160x1.025=£27839<2nd year increase
Name the points. I give you brainiac or whatever.
Answers
Answer:
B: (4, 2)
D: (-4, -1)
E: (3, -3)
F: (0, 4)
Step-by-step explanation:
(x-coordinate, y-coordinate)
Answer:
B: (4, 2)
D: (-4, -1)
E: (3, -3)
F: (0, 4)
Step-by-step explanation:
(x-coordinate, y-coordinate)
Lenny and Lashae are shopping for new guitar strings in a music store. Lenny buys 2 packs of strings. Lashae buys 2 packs of strings and
a music book. The book cost $16. Their total cost is $72. How much is 1 pack of strings?
Answers
Answer:
Strings packs cost $14 each
Step-by-step explanation:
Lenny and Lashae are shopping for new guitar strings in a music store. Lenny buys 2 packs of strings. Lashae buys 2 packs of strings and a music book. The book cost $16. Their total cost is $72. How much is 1 pack of strings?
Lenny: 2s
Lashae: 2s + b
when b = $16 then these equations are:
Lenny: 2s
Lashae: 2s + 16
together they spent $72 so:
lenny + Lashae = $72 or:
2s + 2s + 16 = 72
subtract 26 from both sides:
2s + 2s + 16 - 16 = 72 - 16
2s + 2s = 56
combine s terms:
4s = 56
divide both sides by 4:
4s/4 = 56/4
s = $14
pls i will give top rating
Answers
A summation, also known as a sum, is the result of arithmetic addition of numbers or quantities.
The value of x = 6 and y = 6 then the number exists 6 and the sum of the digits is 9.
How to find the value of x?Any of the following algebraic expressions should be used: addition, subtraction, multiplication, and division. Bring the variable to the left and all the remaining values to the right to find the value of x.
From the given information, we get
x - y = 6 ...............(1)
"if five times the smaller number is two times the larger number"
from the above information, we get
5y = 4x + 2
5) To simplify the value of y:
y = (4x +2) / 5 ...............(2)
Substitute y = (4x +2) / 5 in (1), then we get
x - (4x + 2) / 5 = 6
5x / 5 - (4x + 2) / 5 = 6
simplifying the above equation, we get
(5x - 4x - 2) / 5 = 6
x - 2 = 5 x 6
x -2 = 30
x = 32
Substitute the value of x in (2)
y = 4(32) + 2 / 5
simplifying the above equation, we get
y = 130 / 5
y = 26
From (1), we get
x - y = 6
substitute the value of x and y in the above equation,
32 - 26 = 6
6 = 6
6) T is the 10s digit
X is the one's digit
The two digit number is 10T + X
It is 7 times the sum of the digits, so the 2 digit number is 7 times as large as the sum of the digits
10T + X = 7(T+X)
By using distributive law
10T + X = 7T + 7X
10T + X - 7T - 7X = 0
simplifying the above equation, we get
3T - 6X = 0
3(T - 2X) = 0
T - 2X = 0
T = 2X
The tens digit is 3 more than the one's digits, so
T = X + 3
Then we have
T = 2X = X + 3
Subtracting X from both sides,
T - 3 = X + 3 - 3
X = 3
The Tens digit is 6.
The number is 63.
The sum of the digits is 9.
9 × 7 = 63.
Therefore, the value of x = 6 and y = 6 then the number exists 6 and the sum of the digits is 9.
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HELPPP FOR BRAINLEST????
Answers
Answer:
[tex]2,8,14,20[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]2[/tex] and the common difference is [tex]6[/tex], then each successive term in the sequence is [tex]6[/tex] more than the previous term:
[tex]a_n=6n-4[/tex]
Therefore, the first term is [tex]2[/tex], followed by [tex]8[/tex], [tex]14[/tex], and [tex]20[/tex].
What are two other names for AB?
Will give Brainliest, answer quick please.
Answers
The other names of AB in the given figure are
collinear pointsline segmentWhat are collinear points?Collinear points refers to points that lies on the same plane and on the same straight line.
The figure shows two planes and point A, B and C are collinear points, while points Q and R are collinear
Points A, B and C are non colinear to points Q and R
Points AB are still part of line AC hence can be noted as part of line segment BC.
The line has arrow head and may also be called rays. In this case the are part of an arrow
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Nolan went shopping for a new pair of sneakers because of a sale. The store was offering a 25% discount. What number should he multiply the prices on the tags by to find the price he would have to pay, before tax, in one step?
Answers
The number is 0.75.
From the question, we have
The store was offering a 25% discount.
number = 1-0.25
=0.75
Subtraction:
Subtraction serves as a representation for the act of removing items from a collection. The minus sign stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above figure) are then moved to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, or equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.
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The length of a rectangle is 6 m longer than its width. If the perimeter of the rectangle is 64 m find its length and width in meters
Answers
The length and width of the rectangle with a perimeter of 64m are 19m and 13m respectively.
What is the length and width of the rectangle?The perimeter of a rectangle is expressed as;
P = 2( l + w )
Where l is length and w is width.
Given the data in the question;
Let x represent the width be represented by variable x.
Width w = xLength l = x + 6Perimeter = 64Plug the values into the equation above above.
P = 2( l + w )
64 = 2( (x + 6 ) + x )
64 = 2( 2x + 6 )
64 = 4x + 12
64 - 12 = 4x
52 = 4x
x = 52/4
x = 13
Hence, the dimensions of the rectangle are;
Width = x = 13m
Length = x + 6 = 13 + 6 = 19m
Therefore, the dimension of the rectangle are 13m by 19m.
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write 10 forms for 1 over 8 as you can think of, be creative and use positive and negative powers or other forms of number.
Answers
The 10 forms 1/8 can be written is as follows;
1/81 ÷ 81/2³1/√64[tex]{8}^{ - 1} [/tex][tex]{√64}^{ - 1} [/tex]1 : 8[tex]{2}^{ - 3} [/tex]2/164 : 32How to write 1/8 in different forms?A fraction refers to a number which consists of a numerator and a denominator.
A numerator is the upper value of a fraction.
A denominator is the lower value of a fraction.
1 over 8 can be written in the following ways;
1/8
1 ÷ 8
1/2³
= 1 / 2×2×2
= 1/8
1/√64
= 1/8
[tex]{8}^{ - 1} [/tex]
= 1/8
1 : 8
= 1/8
[tex]{√64}^{ - 1} [/tex]
= 1/√64
= 1/8
[tex]{2}^{ - 3} [/tex]
= 1/2³
= 1/8
2/16
= 1/8
4 : 32
= 4/32
= 1/8
In conclusion, 1/8 can be written in different forms including using square root and ratios.
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5. Point A is 3 units directly below (2, 2). What are the coordinates of point A? Answer: Point A (___)
Answers
The X axis will not change since A is not going left or right of (2,2). You would count down 3 spaces for the y-axis and that would land you at -1 or you could solve by subtraction.
2-3= -1
Write as a single fraction in its lowest terms: 3(2x-1)/5 -2 (4x -2)/2
Answers
The single fraction in its lowest terms will be;
⇒ - 7(2x - 1)/2
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Or, A number which is expressed as a quotient is called fraction.
It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The fraction is,
⇒ 3 (2x - 1)/5 - 2 (4x - 2)/2
Now,
Solve the fraction as;
The fraction is,
⇒ 3 (2x - 1)/5 - 2 (4x - 2)/2
⇒ 3 (2x - 1)/5 - (4x - 2)
⇒ 3 (2x - 1)/5 - 2 (2x - 1)
⇒ (2x - 1) (3/5 - 2)
⇒ (2x - 1) (3 - 10)/2
⇒ (2x - 1) (- 7/2)
⇒ - 7(2x - 1)/2
Thus, The single fraction in its lowest terms will be;
⇒ - 7(2x - 1)/2
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The table shows the fraction of the world's surface land area taken up by each continent. In other words, the continent of Africa makes up StartFraction 20 Over 100 EndFraction of the land in the world. How much greater is the fractional part of the continent of North America than the fractional part of the continent of Europe ?
Answers
Answer:
[tex]\frac{9}{100}[/tex]
Step-by-step explanation:
According to the map, North America makes up [tex]\frac{16}{100}[/tex] of the world's land surface area, while Europe makes up [tex]\frac{7}{100}[/tex]. Since both fractions already have a common denominator ( [tex]\frac{n}{100}[/tex] ), we can simply subtract the two to find how much greater the fractional part of North America is than the fractional part of Europe:
[tex]\frac{16}{100}-\frac{7}{100}=\frac{9}{100}[/tex]
Directions - Write an equation in slope-intercept (y = mx + b) form for each line.
Answers
The equation in slope intercept form of the line that passes through the graph is y = 2/3x + 2
How to determine the equation of the line?From the graph, we have the points to be given as
(-3,0) and (0,2)
Start by calculating the slope of the points using the following slope equation
m = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (-3,0) and (0,2)
So, we have
m = (2 - 0)/(0 + 3)
Evaluate
m = 2/3
The equation is then calculated as
y = m(x - x₁) + y₁
Where
(x, y) = (0, 2) and m = 2/3
So, we have
y = 2/3(x - 0) + 2
Expand
y = 2/3x + 2
Hence, the equation in slope intercept form of the line is y = 2/3x + 2
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A frozen yogurt stand charges per ounce of frozen yogurt purchased. There is an extra charge for a waffle bowl. The total cost (c), in dollars, for f ounces of frozen yogurt in a waffle bowl, is described by the function c = 0.45f + 1.
Which statement is true?
A. The cost of 0.45 ounce of frozen yogurt in a waffle bowl is $1.
B. Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.
C. Each ounce of frozen yogurt costs $0.45 and a waffle bowl is $1 extra.
D. The cost of 0.45 ounce of frozen yogurt in a waffle bowl is $1.45.
Answers
The true statement when the frozen yogurt stand charges per ounce of frozen yogurt purchased is B. Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.
How to explain the function?In the scenario, the total cost (c), in dollars, for f ounces of frozen yogurt in a waffle bowl, is described by the function c = 0.45f + 1.
In this case, it is important to note that Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.
For example, for 2 ounces, this will be:
= 0.45f + 1
= 0.45(2) + 1
= 0.9 + 1
= $1.9
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{ ( - 4, 2 ), ( - 1, 0 ), ( - 3, 1 ), ( 2, - 3 ) } Write the set using set notation and in ascending order.
Answers
By using set notation, the elements of the given data set in ascending order include {-4, -3, -3, -1, 0, 1, 2, 2}.
What is a listing method?In Mathematics, a listing method can be defined as a technique which is used to list all the elements or members of a data set, while separating each of them with a comma and enclosing the data set within curly braces.
Generally speaking, set notation is typically used in mathematics for listing the elements of a set such as objects, numbers, or outcomes, especially by making use of curly brackets.
For this exercise, the elements of the given data set would be listed in ascending order as follows:
Set = {-4, -3, -3, -1, 0, 1, 2, 2}
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Please refer to picture
Answers
Using the corresponding angle theorem, the value of x is 15 and y is 12.
In the given question we have to find the value of x and y.
From the graph we can see that
From the corresponding angle theorem
4x+2=62
Subtract 2 on both side, we get
4x=60
Divide by 4 on both side, we get
x=15
So the value of x is 15.
Similarly from the corresponding angle theorem
12y=144
Divide by 12 on both side, we get
y=12
So the value of y is 12.
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The monthly cost of operation at a company, C, given in dollars as a function of the number of units produced per month, u, is given below.
C = $3,173 + $31u
If the company wants to keep the cost of operation under $14,000 per month, what is the maximum number of units they can produce?
A. 3,490
B. 350
C. 3,491
D. 349
Answers
If the company wants to keep the cost of operation under $14,000 per month, The maximum number of units they can produce is: D. 349.
How to find the number of units?Given function:
C = $3,173 + $31u
Hence,
Let u represent number of units
Let c represent the operation cost
Where c = $14,000 per month
$14,000 = $3,173 + $31u
Combine like terms
$14,000 - $3,173 = $31u
$10,827 = $31u
Divide both side by $31u
u = $10,827 / 31
u = 349 units
Therefore the correct option is D.
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