Answer: Restaurant B
Step-by-step explanation:
First, Divide 14.52 by 11 as shown below to get the cost per burger for Restaurant A:
14.52/11 = 1.32
Next, divide 2.58 by 2 for the cost of the burger at Restaurant B:
2.58/2 = 1.28
Now we can see that Restaurant B's burgers are 4 cents cheaper than Restaurant A.
Good Luck!
Ricardo is half as likely to spin a 2 or 4 than an odd number
Based on the information provided, the statement "Ricardo is half as likely to spin a 2 or 4 than an odd number" is false.
Ricardo has a 2/27 chance of spinning either a 2 or a 4, and a 2/9 chance of spinning an odd number.
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes, total number of outcomes
Let's start by assigning some variables to the probabilities of spinning each type of number. Let's say:
P(odd) is the probability of spinning an odd number
P(2 or 4) is the probability of spinning a 2 or a 4
According to the problem, we know that:
P(2 or 4) = 1/2 * P(odd)
We also know that the sum of the probabilities of spinning all possible numbers must equal 1. Since there are 5 odd numbers and 2 even numbers (2 and 4) on a standard six-sided die, we can write:
P(odd) + P(2 or 4) = 5/6 + 1/3 = 7/6
However, this equation doesn't make sense because the sum of probabilities should never exceed 1. This means that our assumption about P(2 or 4) being half as likely as P(odd) is incorrect.
To correct this, we can use the fact that P(odd) + P(even) = 1, where P(even) is the probability of spinning an even number (either 2 or 4). Since Ricardo is half as likely to spin a 2 or 4 than an odd number, we can write:
P(even) = 1/3 * P(odd)
Substituting this into the equation P(odd) + P(2 or 4) = 1, we get:
P(odd) + 1/2 * P(odd) = 1 - 1/3 * P(odd)
Simplifying this equation, we get:
3/2 * P(odd) = 1 - 1/3 * P(odd)
Multiplying both sides by 2/3, we get:
P(odd) = 2/9
Substituting this back into our equation for P(even), we get:
P(even) = 1/3 * P(odd) = 2/27
Therefore, Ricardo has a 2/27 chance of spinning either a 2 or a 4, and a 2/9 chance of spinning an odd number.
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Complete Question:
Use the information from the spinner to determine if the statement is True or False.
Ricardo is half as likely to spin a 2 or 4 than an odd number.
You spin the spinner once. 9 7 Submit 8 What is P(9)? ◄)) Write your answer as a fraction or whole number. Work it out help
The probability of obtaining the value P(9) is fraction 1/4.
What is equally likely outcomes in probability?Equally probable occurrences are those that have the same theoretical probability (or likelihood) of taking place. For instance, after a very high number of flips, the relative frequency of Head and Tail is equal. In light of the fact that Head and Tail are both equally likely possibilities, flipping a coin is a fair and impartial way to choose between two choices.
Given that, the spinner spins the dial.
The probability of obtaining the value P(9) is:
P (9) = 1 / 4
Hence, the probability of obtaining the value P(9) is fraction 1/4.
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The complete question is:
please help show all steps too please
the trigonometric identity is proven below
cos(3x/2 - α) = cos(3x/2)cos(α) + sin(3x/2)sin(α)
tan(α) = sin(α) / cos(α)
sec(α) = 1 / cos(α)
therefore:
cos(3x/2 - α) = cos(3x/2)cos(α) + sin(3x/2)sin(α)
What is trigonometry?The study of the correlation between a right-angled triangle's sides and angles is the focus of one of the most significant branches of mathematics in history: trigonometry. Hipparchus, a Greek mathematician, introduced this idea.
From the question:
The following trigonometric identities can be used to demonstrate the trigonometric identity cos(α) - tan(α) - cos(3x/2 - α) = sec(α)
cos(3x/2 - α) = cos(3x/2)cos(α) + sin(3x/2)sin(α)
tan(α) = sin(α) / cos(α)
sec(α) = 1 / cos(α)
When we enter these identities into the equation's left-hand side (LHS), the following results:
cos(α) - tan(α) - cos(3x/2 - α)
= cos(α) - sin(α)/cos(α) - cos(3x/2)cos(α) - sin(3x/2)sin(α)
By locating a common denominator for the first two terms, we can reduce the expression:
[tex]cos(\alpha ) - sin(\alpha )/cos(\alpha )[/tex]
= [tex](cos^2(\alpha ) - sin^2(\alpha )) / cos(\alpha )[/tex]
= [tex]cos(2\alpha ) / cos(\alpha )[/tex]
Reintroducing this into the LHS results in:
[tex]cos(\alpha ) - tan(\alpha ) - cos(3x/2 - \alpha )= cos(2) / cos(\alpha ) - cos(3x/2)cos(\alpha ) - sin(3x/2)sin(\alpha )[/tex]
Using the identity [tex]cos(2\alpha ) = 1 - 2sin^2(\alpha ),[/tex] we can simplify the expression further:
cos(α) - tan(α) - cos(3x/2 - α)
= [tex](1 - 2sin^2(\alpha )) / cos(\alpha ) - cos(3x/2)cos(\alpha ) - sin(3x/2)sin(\alpha[/tex])
= [tex](1 - 2sin^2(\alpha ) - cos^2(3x/2 - \alpha ))[/tex] / cos(α) (using the identity[tex]sin^2(x) + cos^2(x) = 1)[/tex]
Using the identity, we can now reduce the complexity of the equation in the numerator:
cos(3x/2 - α) = cos(3x/2)cos(α) + sin(3x/2)sin(α)
Substituting this identity into the numerator, we get:
[tex]1 - 2sin^2(\alpha ) - cos^2(3x/2)cos^2(\alpha ) - 2sin(3x/2)cos(3x/2)sin(\alpha )cos(\alpha )[/tex]
In order to further simplify the expression, we can use the identity
sin(2x) = 2sin(x)cos(x):
[tex]1 - 2sin^2(\alpha ) - cos^2(3x/2)cos^2(\alpha ) - sin(3x)sin(\alpha )[/tex]
Now, using the identity[tex]cos^2(x) + sin^2(x) = 1,[/tex] we can simplify the expression to:
[tex]cos^2(\alpha ) - sin^2(\alpha ) - cos^2(3x/2) + cos^2(3x/2)sin^2(\alpha )[/tex]
Using the identity[tex]cos(2x) = 1 - 2sin^2(x)[/tex], we can further simplify the expression to:
[tex]cos(\alpha )cos(2\alpha ) - cos^2(3x/2)(1 - sin^2(\alpha ))[/tex]
[tex]= cos(\alpha )(1 - 2sin^2(\alpha )) - cos^2(3x/2)cos^2(\alpha )sin^2[/tex]
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A roll has 12 yardsof ribbon. Haley uses 6 feet of the ribbon for a swing project. How many feet of ribbon are left on the roll? Show your work?
Answer:
30 feet
First, we have to make sure that the numbers have the same units of measurementWe can see that the roll had 12 yards, and Haley used 6 feetThere are 3 feet in a yard6 feet would be equal to 2 yards because 6 is double the amount of 3 feet; and 2 is double the amount of 1Now, we have to subtract 2 from 12 12-2= 10Remember: The question is asking for feet, so we can multiply 10 by 3 to get the number of feet left10 x 3 = 30,
So, 30 feet of ribbon is left on the roll
Describe an activity for Grade R to teach Subtraction that will accommodate each type of learning modality
Grade R learners can be best taught using hands-on experience, thus use physical beads or objects to practically teach subtraction.
How should learners in grade R be taught?A manipulatives-based project can be a fantastic method to teach subtraction to grade R students, who frequently learn best via hands-on experiences. This activity can be modified to accommodate students who learn better visually, aurally, or kinesthetically.
The activity that can be used to teach grade R learners to subtract is by using physical objects, and asking them to count the initial number.
Remove some items and recount them.
The objects removed will denote the subtraction.
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What is the solution to the system of equations: 2x + 2y = 14 and 4x – 2y = 10?
On solving the given system of equations, we found the values of the variables x and y as 4 and 3 respectively.
What is meant by the system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system. A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations. A group of equations that are all satisfied by the same set of variables are referred to as a system of linear equations.
The given system of equations is:
2x + 2y = 14
4x - 2y = 10
To solve this, we have to first get rid of one variable.
Here the coefficient of variable y is the same.
So adding the equations, we get
6x = 24
x = 4
Now substituting this value of x in any one of the equations we get y.
2*4 + 2y = 14
8 + 2y = 14
2y= 6
y = 3
Therefore on solving the given system of equations, we found the values of the variables x and y as 4 and 3 respectively.
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Five years have passed and Jamie Lee, 34, is considering taking the plunge--not only is she engaged to be married, but she is also deciding on whether to purchase a new home. Jamie Lee’s cupcake café is a success! It has been open for over a year now and has earned itself rave reviews in the local press and from its regular customers who just cannot get enough of her delicious varieties of cupcakes. One such customer, who stopped by on a whim in the café’s first week of business, is Ross. After a whirlwind courtship, Ross, a self-employed web designer, proposed, and Jamie Lee agreed to be his wife. The bungalow that Jamie Lee has been renting for the past five years is too small for the soon-to-be newlyweds, so Jamie Lee and Ross have purchased a brand new three-bedroom, 2 ½ bath home in a quiet neighborhood for $276,000. Use the provided information and the table below to calculate the affordable mortgage amount that would be suggested by a lending institution based on Jamie Lee and Ross’s income. You will need to make note of the purchase price (above) of their home for future questions. Use the following for Jamie Lee and Ross's calculations: 10% down payment $650 per month for estimated combined property taxes and insurance 5% interest rate for 30 years Refer to Exhibit 7-7 for current mortgage rates
Therefore , the solution of the given problem of interest comes out to be $882.75 monthly affordable mortgage amount recommended by a lending organisation .
What does interest actually mean?To determine simple interest, divide the sum by the cost of borrowing, the amount of time left, and other factors. Principal plus interest plus hours is the straightforward return strategy in marketing. The simplest approach to calculate interest is to use this method. The most popular method of calculating revenue is as a fraction of the principal amount.
Here,
We can use an internet mortgage calculator to determine the affordable monthly mortgage payment. With the provided data, we can determine the monthly mortgage payment to be $1,187.25 using a mortgage calculator.
Assume that Jamie Lee and Ross earn $8,000 per month in gross revenue.
Affordable debt amount
=> $1,837.25 ($8,000 x 0.43)
=> $2,720 - $1,837.25
is an affordable mortgage sum.
=> $882.75 is an affordable mortgage sum.
This indicates that the $882.75 monthly affordable mortgage amount recommended by a lending organisation based on Jamie Lee and Ross's income.
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Which of these cannot be an r2-value?
The value given that cannot be an r ² value is A. - 0.75.
What is the r ² value ?The r² value, also known as the coefficient of determination, is a statistical measure that represents the proportion of variance in the dependent variable that can be explained by the independent variable(s). It is a value between 0 and 1, with higher values indicating a better fit of the regression model to the data.
It is not possible for the r² value to be negative because it is the square of the correlation coefficient. - 0.75 cannot possibly be a value of r ² as a result.
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What is the like term for 4x?
Answer:
The answer could be any number, with the variable x (not x^2, x^3, x^#). So it can be, for example, 6x, 8x, 109x, etc., as long as the variable is the same in each number.
determine whether each pair of expressions is equivalent 4(x + y) and 4y + 4x
Therefore , the solution of the given problem of expression comes out to be 4(x + y) and 4y + 4x are identical expressions.
Expression : What is it ?Mathematical processes like multiplying, dividing, joining, and now even removing are required. If they were merged, the following would be stated: An equation, some statistics, and a mathematical formula A statement of truth is made up of values, components, and mathematical processes like additions, subtractions, errors, divisions, and algebraic formulas. Words and sentences can be analysed and evaluated.
Here,
Yes, 4(x + y) and 4y + 4x are identical expressions.
We can use the distributive principle of multiplication over addition to understand why.
=> 4(x + y) = 4x + 4y
This is so that we can see what happens when we assign the 4 to both the x and y values enclosed in parentheses:
=> 4(x + y) = 4x + 4y
In fact, this is identical to the expression 4y + 4x, which is nothing more than the same words in a different order:
=> 4y + 4x = 4x + 4y
As a result, 4(x + y) and 4y + 4x are identical expressions.
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The area of each figure can be calculated using the given dimensions. Which of the
figures has an area formula that is a linear function?
The figure that has an area formula that is a linear function is the rectangle.
What is area?Area is the size or measurement of a two-dimensional space. It is usually expressed in square units such as feet, meters, or kilometers. Area is a fundamental concept in mathematics, and is used to measure the size of shapes and surfaces. Area is also used to calculate the amount of material or resources needed to cover a given space. In addition, it can be used to measure the cost or value of a piece of land.
The formula for the area of a rectangle is A=lw, where l is the length and w is the width. This formula is a linear equation because it is a product of two variables, where the relationship between the two variables is a constant. Thus, the area of a rectangle is a linear function of its dimensions.
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Algebra l
Find an exponential model for the data.
ANSWER THIS: The exponential model for the data is y=___
The exponential model for the data is y=0.646(1.087)ˣ.
What is the exponential function?Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
From the table we have, (8, 1.26), (10, 1.49)
We know that, the general form of exponential model is y=abˣ.
Here, substitute (8, 1.26) in y=abˣ, we get
1.26=ab⁸ -------(i)
a=1.26/b⁸
Here, substitute (10, 1.49) in y=abˣ, we get
1.49=ab¹⁰ -------(ii)
a=1.49/b¹⁰
1.26/b⁸ = 1.49/b¹⁰
1.26=1.49/b²
b²=1.49/1.26
b=1.087
Substitute b=1.087 in equation (i), we get
1.26=a(1.087)⁸
1.26=a(1.95)
a=1.26/1.95
a=0.646
So, the equation is y=0.646(1.087)ˣ
Therefore, the exponential model for the data is y=0.646(1.087)ˣ.
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When 16 is subtracted from the square of a number, the result is 6 times the number. Find the positive solution.
The positive solution is t = 8.
What are quadratic equations?A quadratic equation is a polynomial which has variables in which one has the highest power of 2.
Considering the question, let the unknown number be represented by t. So that;
16 is subtracted from the square of a number = t^2 - 16;
the result is 6 times the number = 6t
So that;
t^2 - 16 = 6t
t^2 - 6t - 16 = 0
t^2 + 2t - 8t - 16 = 0
(t^2 + 2t)(-8t - 16) = 0
t(t + 2)-8(t + 2)
So that
(t + 2)(t - 8) =0
t + 2 = 0 or t - 8 = 0
t = -2 or t = 8
Thus the positive solution is t = 8.
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The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rate
T.
P = $2300, A = $2762, t = 6 months
The loan's simple interest is %.
***
Based on the information provided, it can be concluded the loan's simple interest is 4.01%.
What is the loan's simple interest?The simple interest is the difference between the future value of the loan and the loan amount.
Simple interest = future value - loan amount $2762 - $2300 = $462
The simple interest rate is a linear function of the loan amount, the interest rate, and the duration of the loan. The simple interest that is paid is the same each year for each period of the duration of the loan.
Simple interest = loan amount x time x interest rate
Interest rate = simple interest / (loan amount x time) = 462 ÷ (6/12 x 2300) = 0.401= 4.01%
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reduce 42/84 what is the answer
Answer:
1/2
Step-by-step explanation:
42/84=1/2
Write in index form using negative powers 7/2 x × 2 x
Answer:
7withax2
Step-by-step explanation:
Write the recursive formula for the sequence 4,2,1, 1/2,…
The recursive formula for an, the nth term of the sequence 4,2,1,1/2... is a(n) = a(n-1) / 2 where a(1) = 4.
What is the recursive formula of the sequence?A recursive formula is simply a way to define a sequence by explicitly defining one or more initial terms, and then providing a formula that allows us to calculate any term in the sequence using one or more previous terms.
In other words, to find the nth term of a sequence defined recursively, we need to know the (n-1)th term or the (n-2)th term, and so on.
Given the sequence in the questionis 4,2,1, 1/2,…
In the sequence 4, 2, 1, 1/2, we can observe that each term is half of the previous term.
So, to write a recursive formula for this sequence, we can say:
a(1) = 4 (the first term is 4)
a(n) = a(n-1) / 2
(each subsequent term is half of the previous term)
Therefore, the sequence is a(n) = a(n-1) / 2 where a(1) = 4
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In ΔABC, c = 720 inches, m∠A=74° and m∠B=75°. Find the length of a, to the nearest 10th of an inch.
As a result, length of a side is around 1347.1 inches to the nearest 10th of an inch.
How is length of a side determined?The Law of Sines, which states that the ratio of the length of a side to the sine of the angle opposite that side is equal for all sides and angles in a triangle, can be used to determine the length of side an in ABC.
The following equation can be created by applying the Law of Sines:
C/sin(31°) = a/sin(74°)
If we are aware that c = 720 inches, we can use a calculator to determine sin(31°):
sin(31°) ≈ 0.51504
As a result, we can find a:
A is equal to sin(74°)*c/sin(31°)
a ≈ 0.96231 * 720 / 0.51504 \sa ≈ 1347.11
With a 10th-inch precision, we obtain:
1354.7 inches
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Answer:
its actually 1343.8
Step-by-step explanation:
Write your own question that involves time conversion and ask someone to solve it.
Make sure you solve it too so you know if they get the correct answer!
Answer: If a movie starts at 2:45 PM and has a duration of 2 hours and 10 minutes, what time does it end?
To solve this, we need to add the duration of the movie to the start time and convert it back to the 12-hour clock format.
Adding 2 hours and 10 minutes to 2:45 PM, we get:
2:45 PM + 2 hours + 10 minutes = 4:55 PM
So, the movie ends at 4:55 PM.
Step-by-step explanation:
Evaluate and match each expression on the left to it's value on the right, when x=6 and y=5?
12+x
[tex]12 + x = 12 + 6[/tex]
[tex]\implies 12 + x = 18[/tex]
Consider the following figure.
(Note that the figure is not drawn to scale.)
74°
55°
63°
59°
Order the side lengths HI, IK, HJ, IJ, and KJ from least to greatest.
O
X
5
The side lengths from least to greatest are HJ, HI, IJ, JK and IK
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Angle H is 67 degrees
∠HIJ is 51 degrees
∠HJI is 61 degrees
Angle K is 63 degrees
∠KJI is 70 degrees
∠KIJ is 57 degrees
From least to greatest
HJ<HI<IJ<JK<IK
Hence, the side lengths from least to greatest is HJ, HI, IJ, JK and IK
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a candidate is contesting for both national and provincial seats.
(A)what is the probability that he'll win both seats.
(B)what is the probability he'll loose both seats.
(C)what is the probability he'll win one seat.
A. The probability that he'll win both seats is 0.48.
B. The probability he'll loose both seats is 0.52.
C. The probability he'll win one seat is 0.92.
What is probability?The probability of an event is calculated using the mathematical notion of probability. We can only use it to determine the likelihood that an event will occur. On a scale from 0 to 1, where 0 denotes impossibility and 1 denotes a specific occurrence.
We are given that a candidate is contesting for both national and provincial seats.
Event A = Winning national seat
Event B = Winning provincial seat
A. The probability that he'll win both seats is
P(A) × P(B) = 0.8 × 0.6 = 0.48
B. The probability he'll loose both seats is
1 - 0.48 = 0.52
C. The probability he'll win one seat is
Probability = 0.8 + 0.6 - 0.48
Probability = 0.92
Hence, the required probabilities have been obtained.
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Question: a candidate is consisting for both national and provincial assembly seats. the probability that he will win the national seat is 0.8 and will win the provincial seat is 0.6. what is the probability that
a) he will win both seats
b) he will lose both the seats
c) he will win at least one seat
Which of the following is equal to 4/7 x 11/15
A. 4 x 7/11 x 15
B. 4 x 15/ 7 x 11
C. 4 x 11/ 7 x 15\
D. 7 x 15/4 x 11
The correct answer is option C: 4 x 11/ 7 x 15.
What is the fractions?
A fraction is a numerical quantity that represents a part of a whole. It is expressed as one number, called the numerator, written above a line, and a second number, called the denominator, written below the same line.
The product of 4/7 and 11/15 is:
(4/7) x (11/15)
= (4 x 11)/(7 x 15) (Multiplying the numerators and denominators separately)
Hence, the correct answer is option C: 4 x 11/ 7 x 15.
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Assuming and y are both positive, write the following expression in simplest
radical form.
4xy³√ 27x^2y^5
Answer:
We can simplify the given expression using the rules of exponents and radicals:
4xy³√ 27x^2y^5
= 4xy * ³√(27x^2y^5) (since y and ³√(27) cannot be simplified further)
= 4xy * ³√(3^3 * x^2 * y^3 * y^2)
= 4xy * 3xy * ³√y^2
= 12x^2y^2 * ³√y^2
Therefore, the expression 4xy³√ 27x^2y^5 simplifies to 12x^2y^2 * ³√y^2.
Step-by-step explanation:
Find the measure of the three missing angles in the parallelogram below.
Answer:
[tex]x[/tex] = 67 , [tex]y[/tex] = 113 , [tex]z[/tex] = 67
Step-by-step explanation:
What we need to know:
A parallelogram has two pairs of equal angles
Opposite angles are equal
Angles in a quadrilateral add up to 360
1) Find out as many angles we can
We know that the opposite angles are equal, this means that y would be equal to 113
y = 1132) Find the remaining angles
We already know that two of our angles are 113, this means that our total is 226 for now. We have two angles left which are equal so to find them we have to subtract 226 by 360 then divide by 2
360 - 226 = 134134 ÷ 2 = 67[tex]x[/tex] = 67[tex]z[/tex] = 67Hope this helps, have a lovely day! :)
Answer:
x = 67
y = 113
z = 67
Step-by-step explanation:
The properties of a parallelogram are:
The opposite sides are equal and parallel.Opposite angles are congruent.Adjacent angles are supplementary (sum to 180°).Two angles are said to be adjacent when they share a common vertex.
Therefore, both angle x and angle z are adjacent to the angle that measures 113°.
Since adjacent angles in a parallelogram are supplementary:
⇒ x° + 113° = 180°
⇒ x° = 67°
⇒ x = 67
Similarly:
⇒ z° + 113° = 180°
⇒ z° = 67°
⇒ z = 67
As opposite angles in a parallelogram are equal:
⇒ y° = 113°
⇒ y = 113
The probability of a student taking a statistics class is 0.83, and the probability of a student taking a calculus class and a
statistics class is 0.66. What is the probability of a student taking a calculus class given that the student takes a statistics
class?
Round your answer to three decimal places.
Answer:
Step-by-step explanation:
We can use the conditional probability formula to find the probability of a student taking a calculus class given that the student takes a statistics class:
P(calculus | statistics) = P(calculus and statistics) / P(statistics)
We are given that P(statistics) = 0.83 and P(calculus and statistics) = 0.66.
Substituting the values we have:
P(calculus | statistics) = 0.66 / 0.83
Simplifying the fraction:
P(calculus | statistics) = 0.795
Therefore, the probability of a student taking a calculus class given that the student takes a statistics class is 0.795. Rounded to three decimal places, the answer is 0.795.
Q.3. Dennis charges $1.75 for gasoline plus $7.50 per hour for mowing lawns. Which inequality
represents x, the number of hours Dennis must work to earn at least $100?
A. 1.75x+7.50 ≥ 100
B. 7.50x+1.75 ≥ 100
C. 1.75x+7.50 ≤ 100
D. 7.50x +1.75 ≤ 100
Answer:
. 1.75x+7.50 ≥ 100
Step-by-step explanation:
Use synthetic division to evaluate for the indicated x value.
x³ + x²-3x +9; ƒ (-4)
f(-4)=
The first step to calculate the indicated x value using synthetic division is to assemble the synthetic division table, which will be:
Column 1 | Column 2-4 | 11 -3 91 -3 9 -63 |The first number on the top line, 1, is the coefficient of the highest degree term in the polynomial. The remaining coefficients are written in order, with 0 placeholders for any missing terms. The divisor, -4, is written to the left of the table.
How to calculate synthetic division?We must reduce the first coefficient, which is 1. Then we multiply -4 by 1 to get -4 and write that in the next coefficient, which is 1. We add the two numbers to get -3 , which we write under the next coefficient , which is -3. We multiply -4 by -3 to get 12 and write that under the last coefficient, which is 9. We add the two numbers together to get -51, which is the remainder.Therefore, we find ƒ(-4) = -51.
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The demand equation for a certain product is given by p = 128 − 0.04 x , where p is the unit price (in dollars) of the product and x is the number of units produced. The total revenue obtained by producing and selling x units is given by R = x p . Determine prices p that would yield a revenue of 7840 dollars. Lowest such price = dollars Highest such price = dollars
So the lowest price that yields a revenue of $7840 is $32 and the highest price is $64.
What constitutes the basic unit of a number?The first ten integers are the basic numbers in mathematics. The range of these vital values is 0 to 9. Basic integers in the 0 to 9 range include 0 through 1, 2, 3, 4, 5, 6, 7 and 8.
The total revenue from selling x units is given by:
R = xp
Substituting the demand equation p = 128 - 0.04x, we get:
R = x(128 - 0.04x)
R = 128x - 0.04x²
To find the prices that yield a revenue of $7840, we can set R equal to 7840 and solve for x:
7840 = 128x - 0.04x²
0.04x² - 128x + 7840 = 0
Dividing both sides by 0.04, we get:
x² - 3200x + 196000 = 0
Using the quadratic formula, we can solve for x:
x = [3200 ± √(3200² - 4(1)(196000))] / 2
x = [3200 ± √(10240000)] / 2
x = [3200 ± 3200] / 2
x = 1600 or x = 2400
Therefore, the corresponding prices that yield a revenue of $7840 are:
p = 128 - 0.04x
p = 128 - 0.04(1600) = 64 dollars
p = 128 - 0.04(2400) = 32 dollars
So the lowest price that yields a revenue of $7840 is $32 and the highest price is $64.
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So NL + y = 5. What would NL be?
NL would be 3.1 cm
What are similar triangles?
These are set of triangles which have some common relations on comparing their corresponding properties. But similarity of the triangles does not imply that they are congruent.
From triangle PQN, applying the trigonometric function. We have;
Tan θ = opposite/ adjacent
Tan 60 = 3.2/ y
1.7321 = 3.2/ y
y = 3.2/ 1.7321
= 1.8475
y = 1.9 cm
To determine the value of NL,
NL + y = 5
NL = 5 - y
= 5 - 1.9
= 3.1
NL = 3.1 cm
The value of NL would be 3.1 cm.
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