The ratio of chocolate bars More Preferred: (9 chocolate bars, 3 glasses of milk); Equally Preferred: (6 chocolate bars, 3 glasses of milk); Less Preferred: (3 chocolate bars, 2 glasses of milk) and (9 chocolate bars, 2 glasses of milk).
The ratio of chocolate bars to glasses of milk that Isabel consumes is 3-to-1. This means that whenever she has 3 chocolate bars, she also has 1 glass of milk. Currently, Isabel has 6 chocolate bars and 2 glasses of milk. The bundles listed above are compared to Isabel's current consumption. Out of the five bundles, the one with 9 chocolate bars and 3 glasses of milk is more preferred than what Isabel currently has because it has more of the ratio than Isabel's current consumption. The bundle with 6 chocolate bars and 3 glasses of milk is equally preferred because it holds the same ratio as Isabel's current consumption. The bundles with 3 chocolate bars and 2 glasses of milk and 9 chocolate bars and 2 glasses of milk are less preferred because they both have less of the ratio than Isabel's current consumption.
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Find the values of a and b that make the following piecewise defined function both continuous and differentiable everywhere. - 6 x <5 f(x) = { -27 *"ax + b, 125
The values of a = 17 and b = - 56
that make the following piece wise defined function both continuous and differentiable everywhere.
What is continuous function?A continuous function in mathematics is one that doesn't change value unexpectedly due to discontinuities, or breaks in the function's continuity. A continuous function in mathematics is a function that causes the value of the function to continuously vary as a result of a continuous variation of the argument, or a change without a leap. Thus, there aren't any discontinuities—rapid changes in value.
conditions are:
1.
f(x) is continuous if,
[tex]\lim_{x \to \ 5^{-}}f(x)[/tex] = [tex]\lim_{x \to \ 5^{+}}f(x)[/tex] = f(5)
2.
differentiable if,
[tex]\lim_{x \to \ 5^{-}}f^'(x)[/tex] = [tex]\lim_{x \to \ 5^{+}}f^'(x)[/tex]
for 1st condition:
⇒ [tex]\lim_{x \to \ 5^{-}}f(x) = \lim_{x \to \ 5^{+}}f(x)[/tex]
⇒ [tex]\lim_{x \to \ 5^{-}}(-3x -6) = \lim_{x \to \ 5^{+}}(-2x^2+ax+b)[/tex]
⇒ (-3 × (-5) - 6) = - 2(5)² + a(5) + b
⇒ - 21 = - 50 + 5a + b
⇒ 5a + b = 29 ................... (1)
For 2nd condition:
⇒ [tex]\lim_{x \to \ 5^{-}}f^'(x) = \lim_{x \to \ 5^{+}}f^'(x)[/tex]
⇒ [tex]\lim_{x \to \ 5^{-}} \frac{d}{dx} (-3x - 6) = \lim_{x \to \ 5^{+}} \frac{d}{dx}(-2x^2 + ax + b)[/tex]
⇒ - 3 = - 4x + a
⇒ - 3 = - 4 (5) + a
⇒ a = 17
Substitute a = 17 in equation (1) we get:
5(17) + b = 29
or, b = - 56
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The complete question is as follows:
Donna, Alonzo, and Kevin served a total of 85 orders Monday at the school cafeteria. Donna served 10 fewer orders than Alonzo. Kevin served 3 times as
many orders as Alonzo. How many orders did they each serve?
Answer:
So, Donna served 9, Alonzo served 19 and kevin served 57 orders.
Step-by-step explanation:
Let orders be :
Donna - x, Alonzo - y, Kevin - z
x = y - 10 - eqn i
z = 3y - eqn ii
Now, By the question,
x + y + z = 85
we know from eqn i and eqn ii,
y - 10 + y + 3y = 85
or, 5y = 95
so, y = 19
Now,
z = 3(19) = 57
x = 19 - 10 = 9
23. Nurse Nancy says that dilations will result in the congruence of corresponding angles.
Do you agree?
Answer:
Yes, dilation does not change the angle measurements.
Step-by-step explanation:
there are 41 students in group 2. Twice has many students playing the Trump elect as playing the trombone but eight students play the saxophone how many students in group to play each instrument use reasoning to write an expression then solve
The following numbers are the result:
22 play trumpet, 11 play trombone, and 8 play saxophone.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Given:
There are 41 students in group 2.
Twice as many students play the trumpet as play the trombone,
but 8 students play the saxophone.
Let x be the number of students playing the trombone.
So, according to the question,
x + 2x + 8 = 41
3x = 33
x = 11
Hence, 22 play trumpet, 11 play trombone, and 8 play saxophone.
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hey thank for helping me
Answer: -1
Step-by-step explanation:
When the graph g hits g=2, the y is -1
In a group of 21 students, 8 students take Art courses, 7 students take Music courses. Two students take both courses. A student is chosen randomly from this group.
What is the probability that the student takes either Art or Music courses?
please help with finsing the lemgth of x
Answer:
x = 5
Step-by-step explanation:
You want the length of x in the figure showing similar triangles.
ProportionThe bottom edge of the triangle is 2/3 of the left edge.
The similar triangles have the same ratio of side lengths. That means x is 2/3 of (3+4.5):
(2/3)(7.5) = 5
The length x is 5 units.
rewrite the expression $6j^2 - 4j 12$ in the form $c(j p)^2 q$, where $c$, $p$, and $q$ are constants. what is $\frac{q}{p}$?
The expression 6j^2 - 4j 12 can be rewritten as [tex]$-24(j\frac{1}{2})^2 -12$[/tex]where , and [tex]$q=-12$[/tex]. Thus,[tex]$\frac{q}{p}=-24$[/tex].
The expression[tex]$6j^2 - 4j 12$[/tex] can be rewritten in the form [tex]$c(j p)^2 q$[/tex], where c, p, and q are constants. To do this, we can factor out a common factor from the expression. In this case, the common factor is j. Then, we can rewrite the expression as [tex]$j(6j - 12)$[/tex] which simplifies to [tex]$-24j^2 -12$[/tex]. Dividing both sides by j, we can rewrite the expression as [tex]$-24(j\frac{1}{2})^2 -12$[/tex] where [tex]$c=-24$[/tex], [tex]$p=\frac{1}{2}$[/tex] and [tex]$q=-12$[/tex]. Thus, [tex]$\frac{q}{p}=-24$[/tex]. To summarize, the expression [tex]$6j^2 - 4j 12$[/tex] can be rewritten in the form [tex]$c(j p)^2 q$[/tex] where c, p, and q are constants, and [tex]$\frac{q}{p}=-24$[/tex].
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Gage drove 96 miles on country roads before driving 66 miles on mountain roads. Gage’s rate of travel on the country roads was 2.4 times the rate of the travel on the mountain roads. His whole travel time was 5.3 hours. What is the equation that can be used to solve the problem? What was gage rate of travel on the punta in roads? What was gage’s rate of travel on country roads ?
The equation that can be used to solve the problem is 66/x + 40/x = 5.3
gage rate of travel on the mountain roads is 20 mph and on the country roads is 48 mph.
What is an equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Finding the values of the variables that result in the equality is the first step in solving an equation with variables.
Given that:
In mountain Road
distance = 66 miles ; rate = x mph
⇒ time = d/r = 66/x hrs
In country Road
distance = 96 miles ; rate = 2.4x mph
⇒ time = d/r = 96/(2.4x)
⇒ time = d/r = 40/x hrs.
Equation:
time + time = 5.3 hrs
⇒ 66/x + 40/x = 5.3
⇒ 106/x = 5.3
⇒ 5.3x = 106
⇒ x = 20 mph on mountain Roads
⇒ 2.4x = 2.4*20 mph on country Roads
⇒ 48 mph on country Roads
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An emergency plumber charges $65 as a call out few plus an additional $75 per hour. He arrives at the house at 9:30 and works to repair a water tank. The total repair bill is $196.25. Use the variable t for the number of hours.
Answer:
Step-by-step explanation:
Answer:
Around 11:15 am
Step-by-step explanation:
Let h represents the number of hours the plumber works
Since the plumber charges $65 fee plus $75 per hour, the bill can be calculated by:
→ bill = 65 + 75h
Since the bill is $195.25
→ 195.25 = 65 + 75h
→ 75h = 130.25
→ h = 1.74
1.74 implies that the plumber worked almost 1 hour and 45 minutes. Since the plumber started at 9:30, the repair was completed around 11:15 am.
I really need help with these questions pls?
Answer:
Top one is 3/8
Middle is 4/7
Bottom is 1/3
Step-by-step explanation:
An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modelled by the function p(x) = -x²+ 350x-6600 where p(x) is the profit in thousand Rupees and x is the number of automobiles made and sold. Answer the following questions based on this
model:
(i) When no cars are produce what is a profit/loss?
(ii) What is the break even point? (Zero profit point is called break even)?
(iii) What is the profit/loss if 400 cars are produced?
i) The profit/loss when no cars are produced is a loss of 6600 Rupees.
II) The break even point is at 20 cars
III) The profit/loss if 400 cars are produced is; a loss of 13400Rupees.
How to solve Profit functions?(i) When no cars are produced, x = 0.
Thus, plugging this value into the function p(x) = -x² + 350x - 6600, we have;
p(0) = -0² + 350(0) - 6600 = -6600.
Therefore, the profit/loss when no cars are produced is a loss of 6600 thousand Rupees.
(ii) The break-even point is the point at which the profit is zero, i.e., p(x) = 0. Setting p(x) = 0 and solving for x, we find that;
-x² + 350x - 6600 = 0
x = 20
Therefore, the break-even point is x = 20 cars. T
(iii) If 400 cars are produced, the profit can be found by plugging this value into the function p(x) = -x² + 350x - 6600.
We find that p(400) = -400² + 350(400) - 6600
= -160000 + 140000 + 6600 = -13400. Therefore, the profit/loss if 400 cars are produced is a loss of 13400 Rupees.
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Given a simplified rate of (2), determine the percent change.
The percent change of an object is the ratio of its final value to its initial value.
What is meant by percent change?The percentage of an item's final value versus its starting value is its percent change. By dividing the difference in data by the starting value, you can get the percent change.
"Rate" simply refers to the quantity divided by another number, typically 100, 1,000, or another multiple of 10. A rate per 100 is known as a percentage.
Percentage Change is the difference that results from deducting the old value from the new value, dividing by the old value, and multiplying the result by 100 to represent it as a percentage. In most cases, multiplying a fraction by 100 results in a percent conversion.
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There are 80 people at the movie theater today 2/5 of the people are eating popcorn one for eating chocolate candy and the rest are eating record twist how many people are eating record toys
The people that are eating record toys are 48
How many people are eating record toysFrom the question, we have the following parameters that can be used in our computation:
People at the movies = 80
People are eating popcorn = 2/5
Using the above as a guide, we have the following:
Record toys = (1 - People are eating popcorn) * People at the movies
Substitute the known values in the above equation, so, we have the following representation
Record toys = (1 - 2/5) * 80
Evaluate
Record toys = 48
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A parking lot is arranged with 9 parking spots in the first row, 15 parking spots in the second row, and 21 parking spots in the third row. If a person is aiming to park in first row, what is his probability in decimal form of getting a parking spot?
Answer:
21+15+9=45/4=that the answer
Math 5th grade
Roshaun walks around the city park. The square park measures 61 1/4 yards on each side. How far does Roshaun walk?
Answer: 245 yds
Step-by-step explanation:
61 1/4 times 4 = 245
what is the smallest number that you can add to 17,438 that will make the sum divisible by 25?
Check the picture below.
Imagine that your instructor chose to use the Keep the Highest scoring method in Grade it Now mode. Here are your scores:First attempt: 2/10Second attempt: 10/10Third attempt: 3/10What would be your final score?
The instructor chose to use the highest score now mode, hence the score of the second attempt would be used that is 10/10.
What is mode?In statistics, the value that consistently appears in a particular set is referred to as the mode. The mode or modal value in a data set is sometimes referred to as the value or number that occurs most frequently in the data set. In addition to mean and median, it is one of the three measures of central tendency.
The scores at different attempts are:
First attempt: 2/10 = 0.2
Second attempt: 10/10 = 1
Third attempt: 3/10 = 0.3
The instructor chose to use the highest score now mode, hence the score of the second attempt would be used that is 10/10.
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Angel read for 1/2 hour. Margo read 1/6 hour. Who read for the greater amount of time.
PLS HELP me I am in need of help will mark brainiest
Answer:
Fourth option: √65/4
Step-by-step explanation:
Since the angles are similar, each of the angles of ΔEFG must be equal to each of the corresponding angles of ΔHIJ
Specifically, m ∠J in ΔHIJ = m∠G in Δ EFG
Let's first find ∠G
Since EFG is a right triangle,
tan(G) = EF/FG = √65/4
tan J must be the same as tan G = √65/4
This is the fourth option
The value of tanJ is in the right angled triangle HIJ√65 / 4
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Two triangles are similar if their corresponding angles are equal to each other.
Given that triangle EFG and triangle HIJ are similar, hence:
Angle G = Angle J
tanJ = tanG = √65 / 4
The value of tanJ is √65 / 4
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a robot building club organizes competitions by weight categories called classes each clas permit a percent error of 0.3% in the 5 kg class one robot weighs 4.925 kg
The weight of the robot is within the error limit of 0.3%.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a robot building club organizes competitions by weight categories called classes each class permit a percent error of 0.3%. In the 5 kg class one robot weighs 4.925 kg.
Let -
{x} = 0.3% of 5
{x} = 0.3/100 x 5
{x} = 3/1000 x 5
{x} = 15/1000
{x} = 3/200
{x} = 0.015 .... Eq { 1 }
Now -
For the weight of the robot to be under the weight limit -
4.925 ≤ (5 - x)
4.925 ≤ (5 - 0.015)
4.925 ≤ 4.985 ..... Eq { 2 }
which is true.
Therefore, the weight of the robot is within the error limit of 0.3%.
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a 1.20 kg block is attached to a spring with spring constant 14.0 n/m . while the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 32.0 cm/s .
The amplitude of subsequent oscillations is 0.093 m.
What is Spring constant?The spring stiffness is quantified by the spring constant, or k. For various springs and materials, it varies. The stiffer the spring is and the harder it is to stretch, the bigger the spring constant.
Given that,
Mass of a block, m = 1.2 kg
Spring constant of the spring, k = 14.0 N/m
While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 32.0 cm/s or 0.32 m/s
We need to find the amplitude of the subsequent oscillations.
We can use the conservation of energy here. Initially, the kinetic energy of the block is maximum and then it gets converted to the potential energy of the spring.
Mathematically,
[tex]\frac{1}{2} mv^2=\frac{1}{2}kv^2[/tex]
A is the amplitude of subsequent oscillations.
[tex]A=\sqrt{(\frac{mv^2}{k} )} \\\\A=\sqrt{\frac{(1.2)(0.32)^2}{14} } \\\\A=0.093m[/tex]
So, the amplitude of subsequent oscillations is 0.093 m.
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Simplify expression[5-6+1]
Answer: 0
Step-by-step explanation:
Using GEMDAS
- Grouping
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
[5-6+1]
= [-1+1] because you add/subtract from left to right
= [0] because -1+1=0.
Answer is 0
A teacher randomly chooses a two-person leadership team from a group of four qualified students. Three of the students, Sandra, Marta, and Jane, are girls. The fourth student, Franklin, is a boy.
Using the sample space of possible outcomes listed below, where each student is represented by the first letter of his or her name, answer each of the following questions.
What is P(A)P, left parenthesis, A, right parenthesis, the probability that the first student is a boy?
Answer: The sample space of possible outcomes is:
{SM, SJ, MJ, MS, JS, JM}.
There are 6 possible outcomes in the sample space, and 1 of these outcomes results in the first student being a boy (Franklin, represented by "F").
Therefore, the probability of the first student being a boy is P(A) = 1/6.
Step-by-step explanation:
Cavalleria Pizza sells only pizza. They offer five types of crust, two types of cheese, four meat toppings and
four vegetable toppings. If you must order exactly one type of cheese, one meat topping and one vegetable
topping on your pizza, how many different pizzas can you order at Cavalleria Pizza?
Answer:
3?
Step-by-step explanation:
im not sure sorry
Solve with the box method
The polynomial n² + 6n - 1 can be factored as,
(n + 3 + √10)(n - 3 + √10)(3n - 2).
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, A product of two polynomials (n² + 6n - 1)(3n - 2).
Now, The quadratic expression n² + 6n - 1 can be factored as,
n² + 6n - 1.
[- 6 ± √(36 + 4)]/2.
= [- 6 ± √40]/2.
= [- 6 ± 2√10]/2.
= - 3 ± √10.
Therefore, (n² + 6n - 1)(3n - 2)
= (n + 3 + √10)(n - 3 + √10)(3n - 2).
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What number should go in the space?
Multiplying by 1.15 is the same as increasing by _____%.
Answer: 115%
Step-by-step explanation:
100% = 1
10%=0.1
5%=0.05
100%+10%+5%=115%
1+0.1+0.05=1.15
Answer: 15
Step-by-step explanation:
x+x*15/100
x(1+.15)
1.15x
In a class of 27 students, 17 are dual-enrolled and 10 are not dual-enrolled. Suppose two students are randomly selected from the class (without replacement). Calculate the following probabilities. Round solutions to three decimal places, if necessary.
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases.
if 2 non-overlapping events should occur, the probability of both events happening is the product of both individual probabilities.
e.g. the probability to roll two 6 with 2 dice (or in 2 consecutive rolls with 1 die) is 1/6 × 1/6 = 1/36
if 1 of 2 possible non-overlapping events should occur, the probability of one of the events happening is the sum of the individual probabilities.
e.g. the probability to roll a 1 or a 2 with a die is
1/6 + 1/6 = 2/6 = 1/3
both students are dual-enrolled.
in our case, for the first selection we have the totally possible cases of 27.
the desired cases (dual-enrolled) are 17.
so, the probabilty to select a dual-enrolled student is
17/27
for the second selection (without replacement of the first pull) the totally possible cases are now 26 (because we pulled one student from the general pool of candidates in the first selection).
the desired cases are now 16 (because for our case we pulled a dual-enrolled student from the general pool).
the probabilty to select a dual-enrolled student in the second selection is
16/26 = 8/13
the overall probability to select two dual-enrolled students in 2 selections is
17/27 × 8/13 = 136/351 = 0.387464387... ≈ 0.387
the first student is dual-enrolled, the second is not.
for the first selection the totally possible cases are 27.
the desired cases are again 17.
the probability of the first dejection is again
17/27
for the second selection the totally possible cases are 26 (see above).
the desired cases are still 10.
the probably for this second selection is
10/26 = 5/13
the overall probability to select first a dual-enrolled student and then a not-dual-enrolled student is
17/27 × 5/13 = 85/351 = 0.242165242... ≈ 0.242
Fill in the Blank: Solve the following system of linear equations graphically. Then, fill in the blanks below with the solution.
Equation #1: y=14x−2
Equation #2: y=x+1
The solution to the system of equations is the ordered pair (
,
)
The solution to the system of equations is (13/3, 16/3).
The graph is given below.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
We have,
y = 14x - 2 _____(1)
y = x + 1 ______(2)
Now,
The graph of the equation is given below.
Now,
From (1) and (2).
14x - 2 = x + 1
14x - x = 1 + 2
13x = 3
x = 13/3
And,
y = x + 1
y = 13/3 + 1
y = 16/3
So,
The solution is (13/3, 16/3)
Thus,
The solution is (13/3, 16/3).
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Let T be the three dimensional solid bounded from above by the half cylinder described by the equation z = √(9 - y) and from below the cy plane for 0 ≤ x ≤ 2 and -3 ≤ y ≤ 3. Let S be the closed surface that completely surrounds T. Let F➜ = (x,y,y+z). Use the Divergence Theorem to calculate ∫∫S F • n dS
Using the Divergence Theorem, we get the flux of F across the closed surface S is π/2 (27√2 - 27).
To apply the Divergence Theorem, we will first compute the divergence of F as follows -
div(F) = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z
= 1 + 1 + 1
= 3
Now we will calculate the flux of F across the closed surface S that completely surrounds T. By the Divergence Theorem, this is equal to the triple integral of the divergence of F over the region T and is given by -
∫∫S F•n dS = ∭T div(F) dV
We can describe the region T using cylindrical coordinates:
0 ≤ r ≤ 2
-π/2 ≤ θ ≤ π/2
0 ≤ z ≤ √(9 - r sin θ)
The bounds on r and θ come from the fact that the half cylinder is contained within the plane x = 2, and the plane y = ±3. The bounds on z come from the equation of the half cylinder.
Now we can write the triple integral as follows -
∭T div(F) dV = ∫0^2 ∫-π/2^π/2 ∫0^√(9 - r sin θ) 3 r dz dθ dr
Evaluating this integral, we get,
∭T div(F) dV = π/2 (27√2 - 27)
Therefore, the flux of F across the closed surface S is π/2 (27√2 - 27).
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