The equation of the plane tangent to the surface z = x²y + xy² + ln x + R at (1, 0, R) is z = x + y + (R - 1).
To find the equation of the plane tangent to the surface z = x²y + xy^2 + ln x + R at the point (1, 0, R), we'll need to find the partial derivatives with respect to x and y, and then use the point-slope form of the tangent plane equation. Here are the steps:
1. Find the partial derivatives of the surface function with respect to x and y:
∂z/∂x = 2xy + y² + (1/x)
∂z/∂y = x² + 2xy
2. Evaluate the partial derivatives at the given point (1, 0, R):
∂z/∂x(1, 0) = 2(1)(0) + (0)² + (1/1) = 1
∂z/∂y(1, 0) = (1)² + 2(1)(0) = 1
3. Use the point-slope form of the tangent plane equation:
z - z₀ = a(x - x₀) + b(y - y₀)
4. Substitute the point (x₀, y₀, z₀) = (1, 0, R) and the partial derivative values a = ∂z/∂x = 1, b = ∂z/∂y = 1:
z - R = 1(x - 1) + 1(y - 0)
5. Simplify the equation:
z - R = x - 1 + y
6. Rearrange the equation to the standard form:
z = x + y + (R - 1)
The equation of the plane tangent to the surface z = x²y + xy² + ln x + R at (1, 0, R) is z = x + y + (R - 1).
Learn more about Tangent: https://brainly.com/question/19064965
#SPJ11
A die has six sides, with the numbers 1, 2, 3, 4, 5, and 6.
What is the probability of rolling an integer? (An integer is a whole number.)
Fraction:
Percent:
Likelihood:
The probability of rolling an integer is
Fraction: 6/6Percent: 100%Likelihood: LikelyWhat is the probability of rolling an integer?From the question, we have the following parameters that can be used in our computation:
Sides = 6
Integer sides = 6
using the above as a guide, we have the following:
P(Integer) = Integer sides/Total sides
So, we have
P(Integer) = 6/6
Evaluate
P(Integer) = 1
Hence, the probability is 1
Read more about probability at
https://brainly.com/question/24756209
#SPJ1
Let f be defined as f(x)= (x-2)(x+3)
1- Expand the expression to make sure that it is a function of the second degree.
2- Complete the table of values with the calculator:
x -4 -3 -2 -1 0 1 2 3
y=x² + x -6
3- At what points does the representative curve of f intersect the axes of the reference frame?
4- Does f have a minimum or a maximum? Give its value using a graphing calculator.
graphing calculator.
5- Draw the parabola on [-4 ;3 ]
The expression to make sure that it is a function of the second degree is x² + x - 6
What is the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator
When the expression is expanded, it can be represented by f(x) = (x-2)(x+3), which further simplifies to x^2 + x(-2+3) - 2(3) and ultimately results in x^2 + x - 6. Evidently, the highest power of x within the expression is 2, indicating that it's a second-degree function.
Learn more about expressions on
https://brainly.com/question/723406
#SPJ1
The balance on a credit card, that charges a 10.5%
APR interest rate, over a 1 month period is given in
the following table:
Days 1-3: $200 (initial balance)
Days 4-20: $300 ($100 purchase)
Days 21-30: $150 ($150 payment)
What is the finance charge, on the average daily
balance, for this card over this 1 month period?
finance charge = $ [?]
Round to the nearest hundredth.
Based on the average daily balance, the finance charge for this credit card that charges 10.5% APR is $2.10.
What is the finance charge?The finance charge consists of the interest and other fees that lenders charge borrowers.
One of the methods for computing the finance charge is the average daily balance, which takes the sum of the daily balances and divides by the number of days in the billing cycle.
APR interest rate = 10.5%
Monthly period days = 30
Days 1-3: $200 (initial balance) 3 days $600 ($200 x 3)
Days 4-20: $300 ($100 purchase) 17 days $5,100 ($300 x 17)
Days 21-30: $150 ($150 payment) 10 days $1,500 ($150 x 10)
Total balances = $7,200
Average daily balance = $240 ($7,200 ÷ 30)
Finance charge = $2.10 ($240 x 10.5% x 30/360)
Learn more about the finance charge under the average daily balance method at https://brainly.com/question/21285117.
#SPJ1
the normal force is equal to the perpendicular component of object's weight, which decreases as the angle of inclination increases.
true or false
The statement "The normal force is equal to the perpendicular component of the object's weight, which decreases as the angle of inclination increases" is true.
As the angle of inclination increases, the object's weight can be divided into two components: one perpendicular to the inclined surface (the normal force) and one parallel to it. As the angle increases, the perpendicular component (normal force) decreases, while the parallel component increases.
So to directly answer your question, the normal force is never equal to the weight of the object on an inclined plane (unless you count the limiting case of level ground). It is equal to the weight of the object times the cosine of the angle the inclined plane makes with the horizontal.
Learn more about the inclination: https://brainly.com/question/4598225
#SPJ11
the national center for health statistics (nchs) report published in 2005 entitled health, united states indicated that in 2002 americans paid an average of $3,302 per year on health care and prescription drugs. researchers hypothesized that in 2005 average expenditures decreased primarily due to the availability of generic drugs. 100 americans were sampled and their expenditures on health care and prescription drugs in 2005 recorded. the sample data are: n
The analysis of the sample data (n=100) would help understand the impact of generic drugs on healthcare and prescription drug costs in the United States.
To understand how the availability of generic drugs may have affected the average expenditures on healthcare and prescription drugs in 2005, according to the National Center for Health Statistics (NCHS) report.
In 2002, Americans paid an average of $3,302 per year on healthcare and prescription drugs, as stated in the NCHS report titled "Health, United States." Researchers hypothesized that by 2005, the average expenditures would decrease primarily due to the increased availability of generic drugs. To test this hypothesis, a sample of 100 Americans was taken, and their expenditures on healthcare and prescription drugs in 2005 were recorded.
The sample data (n=100) would then be analyzed to determine if there was a significant decrease in average expenditures compared to the 2002 average of $3,302. This analysis would help understand the impact of generic drugs on healthcare and prescription drug costs in the United States.
More on sample data: https://brainly.com/question/13236722
#SPJ11
If X is an exponential random variable with parameter λ, and c>0, show that cX is exponential with parameter λ/c.CDF Method:Let X be a continuous random variable and let Y=g(X)be a function of that random variable, where g(X) is some function of X. Let fX(x) be the probability density function (PDF) of X and fY(y) be the PDF of Y. Recall that the cumulative distribution function (CDF) of X is defined as the probability that X is less than or equal to some value x, for any real value of x. Mathematically,FX(x)=P(X≤x)Similarly, FY(y)=P(Y≤y).To find the distribution of Y, we can use the CDF method. We start by expressing the CDF of Y (FY(y)) in terms of X. We do this by using the fact that Y=g(X)and then solving the resulting inequality for X. Mathematically,FY(y)=P(Y≤y)=P(g(X)≤y)=⋯=P(X ???⋯)We isolate X in the inequality and we get an inequality which can be changed into CDF terms (the CDF of X).After we find the CDF of Y, we can differentiate it to get the PDF of Y. Recall that for any random variable, the first derivative of its CDF is equal to its PDF. In mathematical terms,fY(y)=ddyFY(y)We do this using the CDF of Y we obtained earlier. After completing this step, you will have the PDF of Y.
We have shown that cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ and c > 0.
To show that cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ, and c>0, we will use the CDF method:
1. Define the transformation: Let Y = cX be a function of the random variable X, where c > 0.
2. Find the CDF of Y: We want to find P(Y ≤ y), which is equal to P(cX ≤ y) or P(X ≤ y/c).
3. Express CDF of Y in terms of X: Since P(X ≤ y/c) is the CDF of X at y/c, we have FY(y) = FX(y/c).
4. Find the PDF of X: The exponential distribution has the PDF fX(x) = λ * exp(-λx) for x ≥ 0.
5. Differentiate the CDF of Y to find its PDF: To find fY(y), we differentiate FY(y) with respect to y. Using the chain rule, we have:
fY(y) = d(FX(y/c))/dy = fX(y/c) * (1/c)
6. Substitute the PDF of X: Now, we replace fX(y/c) with its exponential form λ * exp(-λ(y/c)):
fY(y) = (λ * exp(-λ(y/c))) * (1/c)
7. Simplify the expression: fY(y) = (λ/c) * exp(-λ(y/c))
This is the PDF of an exponential distribution with parameter λ/c. Therefore, cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ and c > 0.
Learn more about "variable": https://brainly.com/question/82796
#SPJ11
there are 26 members of a basketball team. (3) from the 14 players who will travel, the coach must select her starting line-up. she will select a player for each of the five positions: center, right forward, left forward, right guard, left guard. however, there are only 4 of the 14 players who can play center. otherwise, there are no restrictions. how many ways are there for her to select the starting line-up?
The number of ways there are for her to select the starting line-up is 68,640 ways.
To determine the number of ways for the coach to select the starting line-up, we need to consider the choices for each position:1. Center: There are 4 players who can play this position, so there are 4 choices.
2. Right Forward: Since one player has been selected as Center, there are now 13 players remaining. So, there are 13 choices for this position.
3. Left Forward: After selecting the Center and Right Forward, 12 players remain, resulting in 12 choices for this position.
4. Right Guard: With three players already chosen, there are 11 players left to choose from, giving us 11 choices.
5. Left Guard: Finally, after selecting players for the other four positions, 10 players remain, providing 10 choices for this position.
Now, we can calculate the total number of ways to select the starting line-up using the counting principle by multiplying the number of choices for each position:
4 (Center) × 13 (Right Forward) × 12 (Left Forward) × 11 (Right Guard) × 10 (Left Guard) = 68,640 ways
So, there are 68,640 ways for the coach to select the starting line-up.
Learn more about counting principle here: https://brainly.com/question/29774420
#SPJ11
The histogram displays the ages of 50 randomly selected users of an online music service. Based on the data, is advertising on the service more likely to reach people who are younger than 30 or people who are 30 and older?
Answer:
Based on the histogram displaying the ages of 50 randomly selected users of an online music service, it is more likely that advertising on the service will reach people who are younger than 30, as the frequency (or height) of the bars appears to be higher in the younger age group compared to the 30 and older age group.
Step-by-step explanation:
(5) Let р and q be two distinct primes. Show that p9-1+qp-1 is congruent to 1 (mod pq).
By using the Chinese Remainder Theorem separate the statement into two congruences we have x(p-1)(q−1)+1 (mod pq) for all x € Z.
Under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1), the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can uniquely determine the remainder of the division of n by the product of these integers.
It suffices to show pq divides x(x(p-1)(q-1) - 1) for all x e Z. We consider three cases. Consider gcd (x, pq). It has 3 possibilities.
Case 1: If gcd(x, pq) 1. Then applying using Euler's Theorem we have
= x(pq) = 1 (mod pq)
= x(p-1)(−1) = 1 (mod pq)
= x(p-1)(q-1)+1 (mod pq)
and so the result holds if gcd(x, pq) = 1. EX
Case 2: If gcd(x, pq) p. This means x = 0 (mod p). In this case we have
= 0 = x (mod p).
Since gcd(x, pq) = p therefore qx and = 1 (mod q) by Fermat's Little Theorem. This gives us that x(p-1)(q-1)+1 so we have x9-1 x(p−1)(q−1) = 1 (mod q) = x(p-1)(q-1)+1 = x (mod q).
We have shown that x(p-1)(q-1)+1 = x (mod p) and x(p-1)(q-1)+1 = x (mod q). Using the Chinese Remainder Theorem we get x(p-1)(q−1)+1 = x (mod pq).
Case 3: If gcd(x, pq) = q. This case is same as Case 2, with p being replaced by q.
Thus we have extinguished all cases and we have shown x(p-1)(q−1)+1 (mod pq) for all x € Z.
Learn more about Chinese Remainder Theorem:
https://brainly.com/question/30811240
#SPJ4
Complete question:
Let р and q be distinct primes. Show that for all x € Z, we have the congruence x(p-1)(9–1)+1 x (mod pq). (Hint: Use the Chinese Remainder Theorem/Sun Ze's Theorem to separate the statement into two congruences.)
Draw a right triangle with a tangent ratio of 3/2 for one of the acute angles.
Then find the measure of the other acute angle to the nearest tenth of a degree.
cosine
The measure of the other acute angle to the nearest degree is 34°, since the trigonometric tangent ratio of one acute angle is 3/2.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
we shall call the acute angles X and Y such that;
tan X = 3/2 {opposite/adjacent}
X = tan⁻¹(3/2) {cross multiplication}
X = 56° approximately to the nearest degree
Y = 180° - (56 + 90)° {sum of interior angles of a triangle}
Y = 180° - 146°
Y = 34°
Therefore, the measure of the other acute angle to the nearest degree is 34°, since the trigonometric tangent ratio of one acute angle is 3/2.
Read more about trigonometric ratios here: https://brainly.com/question/11967894
#SPJ1
The question and answer are in the picture
Answer:
15.8
Step-by-step explanation:
mean is the average in math so 9 + 14 + 11 + 31 + 14 =79 then you have to count how many numbers there is and minus it from the total which there is 5 numbers so 79 divided by 5 = 15.8
How do you solve this problem step by step please hurry I will get anxious if someone don’t answer quickly.
The equation is in the photo I took off of my phone that I do for fun I really love math so this is what I do for fun so please help me solve this problem please and thank you.
The value of the expression is 5.
We have,
(|-52 + 1| (-1) + 4²) / (-84 ÷ 7 + 5)
Now,
PEMDAS is an acronym used to remember the order of operations in arithmetic and algebraic expressions. It stands for:
Parentheses: Simplify expressions inside parentheses first.
Exponents: Simplify any expressions involving exponents or powers.
Multiplication and Division: Perform multiplication and division in order from left to right.
Addition and Subtraction: Perform addition and subtraction in order from left to right.
Now,
(|-52 + 1| (-1) + 4²) / (-84 ÷ 7 + 5)
We solve | | first and exponents second.
|-52 + 1| = |-51| = 51
4² = 16
And,
-84 ÷ 7 = -84/7 = -12
So,
(|-52 + 1| (-1) + 4²) / (-84 ÷ 7 + 5)
= 51 x -1 + 16 / -12 + 5
= -51 + 16 / -12 + 5
= -35/-7
= 5
Thus,
The value of the expression is 5.
Learn more about PEMDAS here:
https://brainly.com/question/36185
#SPJ1
Una caja de 25 kg se encuentra en reposo sobre un plano inclinado de 30 grados. Si la fuerza de rozamiento es de 50 N, ¿cuál es la magnitud de la fuerza que se debe aplicar paralela al plano para que la caja suba el plano con una aceleración de 2 m/s²?
The magnitude of the force that must be applied parallel to the plane is 92 N, under the condition that the box moves up the plane with an acceleration of 2 m/ s².
The force needed to move a box up an inclined plane can be evaluated as
Fp = W sin α = m ag sin α
Here
Fp = pulling force (N),
W = weight of the box (N),
α = angle of incline (degrees),
m = mass of the box (kg),
a = acceleration of the box (m/s²), and
g = acceleration due to gravity (9.8 m/s²).
For the given case, we possess a 25 kg box at rest on a 30 degree incline with a friction force of 50 N acting on it.
Now
We have to evaluate the weight of the box using
W = mg
= 25 kg x 9.8 m/s²
= 245 N.
Then, we have to calculate the force required to overcome friction using Ff = μFn where μ is the coefficient of friction and Fn is the normal force acting on the box. Since the box is at rest on an incline, Fn can be calculated as Fn = W cos α = 245 N cos(30°) ≈ 212 N. Therefore, Ff = μFn = 0.2 x 212 N ≈ 42 N.
Now we can evaluate the force applied to move the box up the incline utilizing
Fp = ma + Ff
Here,
a = desired acceleration
Ff = frictional force acting on the box.
Staging the values
Fp = ma + Ff
Fp = (25 kg)(2 m/s²) + 42 N
Fp ≈ 92 N
Hence, a force of approximately 92 N must be applied parallel to the plane so that the box moves up the plane with an acceleration of 2 m/s².
To learn more about acceleration
https://brainly.com/question/30595126
#SPJ4
The complete question is
A 25 kg box is at rest on a 30 degree incline. If the friction force is 50 N, what is the magnitude of the force that must be applied parallel to the plane so that the box moves up the plane with an acceleration of 2 m/ s²?
If each interior angle of a regular polygon measures 150°, how many sides does the polygon have?
Formula for the interior angle of a regular polygon = [ (n - 2) x 180 ] / n
---n is the number of sides of the polygon
[ (n - 2) x 180 ] / n = 150
(n - 2) x 180 = 150n
180n - 360 = 150n
-360 = -30n
n = 12
Answer: 12 sides
Hope this helps!
HEY GUYS NEED SOME HELP!
When would the vertex of an angle have the same coordinates after a rotation?
The vertex of an angle would have the same coordinates after a rotation if it is rotated at angle of 360 degrees.
What is a rotation?In Mathematics and Geometry, a rotation refers to a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
Generally speaking, when a point (x, y) is rotated about the center or origin (0, 0) in a counterclockwise (anticlockwise) direction by an angle θ, the coordinates of the new point (x′, y′) formed include the following:
x′ = xcos(θ) − ysin(θ)
y’ = xsin(θ) + ycos(θ).
(x′, y′) → (x, y) ⇒ (360 degrees rotation).
Read more on angle of rotation here: brainly.com/question/12428507
#SPJ1
- n kids randomly line up for recess. two kids are named paula and quentin. (a) what is the probability that either paula or quentin is last in line?
The probability that either Paula or Quentin is last in line when n kids randomly line up for recess can be calculated using the concept of permutations and combinations.
To calculate the probability, we can consider two cases: (1) Paula is last in line, and (2) Quentin is last in line.
Case 1: Paula is last in line
In this case, the probability that Paula is last in line is 1/n, since there is only one way for her to be at the end of the line. The other (n-1) kids can be arranged in any order, so there are (n-1)! possible arrangements. Therefore, the probability that Paula is last in line is:
P(Paula is last) = 1/n * (n-1)! = (n-1)! / n!
Case 2: Quentin is last in line
Similarly, the probability that Quentin is last in line is also 1/n. The other (n-1) kids can be arranged in any order, so there are (n-1)! possible arrangements. Therefore, the probability that Quentin is last in line is:
P(Quentin is last) = 1/n * (n-1)! = (n-1)! / n!
To calculate the probability that either Paula or Quentin is last in line, we can add the probabilities of the two cases:
P(Paula or Quentin is last) = P(Paula is last) + P(Quentin is last)
= (n-1)! / n! + (n-1)! / n!
= 2(n-1)! / n!
Therefore, the probability that either Paula or Quentin is last in line when n kids randomly line up for recess is 2(n-1)! / n!.
To learn more about Permutations, visit:
https://brainly.com/question/1216161
#SPJ11
use the upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). (round your answers to three decimal places.) y
To use the upper and lower sums to approximate the area of a region, we need to first divide the region into subintervals of equal width. Let's say we have n subintervals.
The lower sum is the sum of the areas of rectangles whose heights are the minimum value of y in each subinterval. The upper sum is the sum of the areas of rectangles whose heights are the maximum value of y in each subinterval.
To approximate the area using the lower sum, we would calculate:
lower sum = (width of subinterval) x (minimum y value in subinterval) for each subinterval
area = sum of lower sums for all subintervals
To approximate the area using the upper sum, we would calculate:
upper sum = (width of subinterval) x (maximum y value in subinterval) for each subinterval
area = sum of upper sums for all subintervals
It's important to note that as the number of subintervals increases, the accuracy of our approximation improves. However, it also increases the amount of calculation needed. Therefore, we must find a balance between accuracy and efficiency in our calculations.
To learn more about Intervals, visit:
https://brainly.com/question/17034620
#SPJ11
The following table shows the number of lemons that grew on Mary’s lemon tree each season last year. Number of lemons. Winter 3. Spring 15 summer 21 fall 13 find the mean number of lemons
Therefore, the mean number of lemons that grew on Mary's lemon tree is 13.
The sum of the data divided by the total amount of data determines the mean of a set of numbers, also known as the average. Only numerical variables—regardless of whether they are discrete or continuous—can be used to determine the mean. Simply dividing the total number of values in a data collection by the sum of all of the values yields it.
Mean number of lemons that grew on Mary's lemon tree, we need to sum up the number of lemons from all four seasons and then divide by the total number of seasons. So, the sum of the number of lemons from all four seasons is:
3 + 15 + 21 + 13 = 52
Since there are four seasons, the mean number of lemons is:
=52/4
= 13
Learn more about mean visit: brainly.com/question/1136789
#SPJ4
add the author's third and final claim to complete the chart. HELP ASAPPP!!!!
Claim: ___________-
Evidence- Only 6 percent of countries allow 16 year olds to vote.
questions:
1:Youth voting should be banned around the world.
2:Countries allowing youths to vote a irresponsible.
3:Youth's voting are required in a few countries.
4:The world isn't ready for young teens to vote.
Claim: Youth voting can be beneficial for democracy and civic engagement.
Evidence: Only 6 percent of countries allow 16 year olds to vote which indicates is potential for more countries to explore this option.
What is the author's third claim regarding youth voting?Based on evidence, the author's third and final claim is that youth voting can be beneficial for democracy and civic engagement as its shows that allowing 16 and 17 year old to vote has been associated with higher voter turnout and increased civic engagement among young people.
The fact that only 6 percent of countries currently allow 16 year olds to vote suggests that there is potential for more countries to explore this option.
Read more about voting practice
brainly.com/question/30598697
#SPJ1
The sample space refers to
a. both any particular experimental outcome and the set of all possible experimental outcomes are correct
b. any particular experimental outcome
c. the set of all possible experimental outcomes
d. the sample size minus one
The sample space refers to option (c) the set of all possible experimental outcomes. In probability theory and statistics, a sample space represents all possible outcomes of an experiment or a random event.
The correct answer is c. The sample space refers to the set of all possible experimental outcomes. This includes every possible outcome that could occur in an experiment, whether or not it actually occurs. For example, if you flip a coin, the sample space would be {heads, tails}. This encompasses every possible outcome of the experiment. It provides a foundation for calculating probabilities and understanding the range of results that may occur in a given situation. Sample spaces can vary in size and complexity, depending on the nature of the experiment or event being studied. Understanding the sample space is crucial for making accurate predictions and informed decisions based on data.
Option a is also correct to some extent, as any particular experimental outcome can be considered a part of the sample space. However, it is not a complete definition of the sample space as it only focuses on one outcome and not all possible outcomes.
Option b is incorrect, as the sample space is not limited to just one particular experimental outcome. It is the set of all possible outcomes.
Option d is also incorrect as the sample space has nothing to do with the sample size or the number of participants in the experiment. It is solely based on the set of all possible outcomes of the experiment.
In conclusion, the sample space is the set of all possible experimental outcomes, including both successful and unsuccessful outcomes. It is an important concept in probability theory and is used to calculate the probability of specific events occurring in an experiment.
To learn more about probability, click here:
brainly.com/question/30034780
#SPJ11
rewrite 6 2/7 as an improper fraction
The improper fraction can be written as:
44/7
How to rewrite this as an improper fraction?An improper fraction is a fraction where the numerator is larger than the denominator.
Here we want to write.
6 + 2/7 as an improper fraction, to do so, we just need to write 6 as a fraction with a denominator of 7 and then add them.
We know that:
6 = 6*(7/7) = 42/7
Then we can write:
6 + 2/7 = 42/7 + 2/7 = 44/7
That is the improper fraction.
Learn more about improper fractions at:
https://brainly.com/question/387381
#SPJ1
Jan went grocery shopping and only bought items which had been marked down. The items she bought, along with their prices, can be seen below.
Item
Final Price
Markdown
Chicken
$8.47
15%
Milk
$2.16
20%
Onions
$0.89
10%
Potato chips
$1.45
12%
Oranges
$1.36
25%
Flour
$4.39
18%
What would be the total of Jan's grocery bill if she purchased all of the items before they were marked down?
a.
$15.85
b.
$16.50
c.
$22.46
d.
$24.66
Jan's total grocery bill, if she only bought things that were marked down, would be c. $22.46
How to find the total grocery bill ?First, find the marked down price of all the items on discount ;
Chicken :
= 8. 47 / 0.85
= $ 9. 96
Milk :
= 2. 16 / 0. 80
= $ 2.70
Onions :
= 0. 89 / 0. 90
= $ 0.99
Potato chips = $ 1. 65
Oranges = $ 1. 81
Flour = $ 5. 35
The total grocery bill of the things Jan bought is:
= 9. 96 + 2. 70 + 0. 99 + 1. 65 + 1. 81 + 5. 35
= $ 22. 46
Find out more on total bill at https://brainly.com/question/28533281
#SPJ1
Consider the differential equation
x' = sin(2x), x € [0, 3π/2] (a) Find all equilibria of the differential equation. (Enter your answers in ascending order. ) (b) Find the stability of the equilibria
(a) To discover the differential equation of x' = sin(2x), we set x' to zero and fathom for x:
sin(2x) =
This condition is fulfilled at whatever point 2x is a number different from π, i.e.,
x = nπ/2, where n is a number.
Be that as it may, we got to limit the arrangements to the interim [0, 3π/2], so the equilibria are:
x = 0, π/2, π, 3π/2
(b) To decide the soundness of each equilibrium point, we assess the sign of x' within the region of the balance point. In the event that x' is positive (resp. negative) on one side of the harmony and negative (resp. positive) on the other side, at that point the balance is unsteady. In the event that x' has the same sign on both sides, at that point the harmony is steady.
Close x = 0, we have sin(2x) ≈ 2x, so x' ≈ 2x. Since x is a little close to 0, x' is positive for x > and negative for x < xss=removed xss=removed> π/2, so x = π/2 could be a steady harmony.
Close x = π, we have sin(2x) ≈ -1, so x' ≈ -1. Hence, x' is negative for x < π and positive for x > π, so x = π is an unsteady harmony.
Close x = 3π/2, we have sin(2x) ≈ -2x+3π, so x' ≈ -2x+3π. Since x is near to 3π/2, 2x is near to 3π and 2x-3π is negative, so x' is negative for x < 3> 3π/2. Subsequently, x = 3π/2 could be a steady harmony.
In outline, the solidness of the equilibria is:
x = is unsteady
x = π/2 is steady
x = π is unsteady
x = 3π/2 is steady.
To learn about differential equations visit:
https://brainly.com/question/31583235
#SPJ4
Which equation represents the relationship between the x value and y values in the table
x | y
0. 4
2. 16
4. 28
6. 40
10 64
The equation of the linear relationship that represents the table given is: y = 6x + 4.
How to Find the Equation that Represents a Linear Relationship?The linear relationship between x and y can be represented as an equation which can be expressed in slope-intercept form as:
y = mx + b [m is the slope and b is the y-intercept]
The y-intercept of the equation is the value of y, when x = 0, which is b = 4.
Using any two points, (0, 4) and (2, 16), we have:
Slope (m) = change in y / change in x = 16 - 4 / 2 - 0
Slope (m) = 12/2 = 6
Substitute m = 6 and b = 4 into y = mx + b:
y = 6x + 4.
Learn more about the equation of a linear relationship on:
https://brainly.com/question/28847058
#SPJ1
What’s the answer ? I need help pls answer
The distance between (2 + i) and (4 +3i) would be,
⇒ d = 2√2
We have to given that;
To find distance between (2 + i) and (4 +3i).
Now, We can formulate;
Two points are (2, 1) and (4, 3).
We know that;
The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Hence, The distance between (2 + i) and (4 +3i) would be,
⇒ d = √(4 - 2)² + (3 - 1)²
⇒ d = √4 + 4
⇒ d = √8
⇒ d = 2√2
Thus, The distance between (2 + i) and (4 +3i) would be,
⇒ d = 2√2
Learn more about the coordinate visit:
https://brainly.com/question/24394007
#SPJ1
‼️WILL MARK BRAINLIEST‼️
The probabilities are given as follows:
a. P(number greater than 10) = 1/6.
b. P(number less than 5) = 1/3.
c. The solid is fair, as each side of the dice has the same probability of coming up.
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 total number of outcomes for this problem is given as follows:
12.
2 of the numbers are greater than 10, which are 11 and 12, hence the probability is given as follows:
p = 2/12
p = 1/6.
4 of the numbers, which are 1, 2, 3 and 4, are less than 5, hence the probability is given as follows:
p = 4/12
p = 1/3.
More can be learned about probability at https://brainly.com/question/24756209
#SPJ1
PLEASE HELP I HAVe TO SUBMIT THIS NOW!! my current grade in math is a 28 :( and if I do this assignment my grade will go 40% percent up :)
i need help with this slide...
The calculated slopes of the relations are -5, 9, -1/3 and 3
Finding the slopes of the relationsThe table 1
The slope is calculated as
Slope = change in y/x
So, we have
Slope = (13 - 18)/(-2 + 3)
Evaluate
Slope = -5
Ordered pair 2
The slope is calculated as
Slope = change in y/x
So, we have
Slope = (9 + 27)/(1 + 3)
Evaluate
Slope = 9
Graph 3
The slope is calculated as
Slope = change in y/x
So, we have
Slope = (0 - 1)/(3 - 0)
Evaluate
Slope = -1/3
The table 4
The slope is calculated as
Slope = change in y/x
So, we have
Slope = (2 + 1)/(-2 + 3)
Evaluate
Slope = 3
Hence, the values of the slopes are -5, 9, -1/3 and 3
Read more about linear relations at
https://brainly.com/question/30318449
#SPJ1
From the attachment, what is the missing side
From the attachment, the missing side is B. 21.0.
Trigonometric functions.Trigonometric functions are basic functions which can be used to determine the missing value of a right angled triangle when given the value of one of its internal angles. Some of these functions are; sine, cosine, tangent etc.
To determine the value of the missing side x, we have to apply the appropriate trigonometric function. Thus we have;
Sin θ = opposite/ hypotenuse
Sin 65 = 19/ x
So that;
x = 19/ 0.9631
= 20.964
x = 21
From the attachment, the missing side is 21.0. Thus option B.
Learn more about trigonometric function at https://brainly.com/question/15068258
#SPJ1
Find the surface area
The surface area of the pyramid is 179 sq. m.
What is surface area of a shape?The surface area of a given shape is the summation of all the area of each figure that forms its sides called surfaces.
The given pyramid has triangular shaped surfaces, so that;
area of a triangle = 1/2 *base*height
To determine the area of one of the surfaces, we have;
area of the triangular surface = 1/2x base x height
base = 8 m, and slant height of the surface = 11.2 m
So that;
the area of one triangular surface = 1/2*8*11.2
= 44.8 sq. m.
Thus since the pyramid has 4 equal triangular surfaces, then;
the surface area of the pyramid = 4 x 44.8
= 179.2
The surface area of the pyramid is 179 sq. m.
Learn more about surface area at https://brainly.com/question/31507420
#SPJ1