The minimum number of students required in a school are 102 , it can be calculated by multiplying the 2 quantities.
What is arithmetic?
Arithmetic is an elementary a part of mathematics that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.
Main body:
Total grades = 1 to 6 = 6
minimum students in each grade required = 17
total students required = 6*17
= 102
hence total minimum number of students required in a school are 102.
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(x+2)(x+1) expand and simplify
Hello!
To expand:
==> we must multiply each variable with each other
[tex](x+2)(x+1)=x*x+x*1+2*x+2*1=x^2+x+2x+2=x^2+3x+2[/tex]
Thus: when (x+2)(x+1) is expanded and simplified
==> [tex]x^2+3x+2[/tex]
Answer:
Step-by-step explanation: First we will expand so
x times x = x^2
x times 1 = x ( don’t need to put 1 in front)
2 times x is = 2x
2 times 1 = 2
Now we line them all up and look out if there are any like terms.
x^2 + x + 2x + 2 = x^2 +3x + 2
The graph of y=√x is translated 4 units left and 1 unit up to create the function h(x). The graph of h(x) is shown on the coordinate grid.What is the range of h(x)?
{y|y ≥-4}
{y|y ≥ -1}
{y|y ≥ 1}
{y|y ≥ 4}
Answer:
(c) {y|y ≥ 1}
Step-by-step explanation:
You want the range of the square root function after it has been translated left 4 units and up 1 unit.
RangeThe range of the function is the vertical extent of its graph. The original square root function has a range of y ≥ 0. Translating it up 1 unit gives it a range of ...
y ≥ 1
the height of a cylinder is increasing at a constant rate of 2 centimeters per second, and the volume is increasing at a rate of 1152 cubic centimeters per second. at the instant when the height of the cylinder is 33 centimeters and the volume is 403 cubic centimeters, what is the rate of change of the radius? the volume of a cylinder can be found with the equation v
Answer:
about 2.758 cm/s
Step-by-step explanation:
You want the rate of change of a cylinder's radius, when its height is 33 cm increasing at 2 cm/s, and its volume is 403 cm³ increasing at 1152 cm³/s.
Rate of changeThe volume of a cylinder is given by the equation ...
V = πr²h
Solving for the radius gives ...
r = √(V/(πh))
Differentiating, we have ...
[tex]r'=\dfrac{1}{\sqrt{\pi}}\left(\dfrac{1}{2}V^{-\frac{1}{2}}h^{-\frac{1}{2}}V'-\dfrac{1}{2}V^{\frac{1}{2}}h^{-\frac{3}{2}}h'\right)=\dfrac{hV'-Vh'}{2h\sqrt{\pi Vh}}[/tex]
Filling in the values V = 403, V' = 1152, h = 33, h' = 2, we have ...
r' = (33·1152 -403·2)/(2·33·√(π·403·33)) = 37210/(66√(13299π))
r' ≈ 2.758 . . . . . cm/s
The rate of change of the radius is about 2.758 cm/s.
If company JCN made a $1196.7 million profit last year, with $798.9 million of that profit brought in by the sales department, then approximately what percent of the total profit was not brought in by the sales department?
3.3%
6.6%
20%
33%
67%
The required percent of the total profit was not brought in by the sales department is 33%.
Explain simple interest.Simple Interest (S.I.) is the strategy for working out the premium sum for a specific chief measure of cash at some pace of revenue. For instance, when an individual takes a credit of Rs. 5000, at a pace of 10 p.a. for a considerable length of time, the individual's advantage for quite some time will be S.I. on the acquired cash.
According to question:profit amount = $1196.7
Amount used in sales = $798.9
Amount was not used in sales = $1196.7 - $798.9 = $397.8
Now, then approximately percent of the total profit was not brought in by the sales department.
($397.8/$1196.7) × 100 = 33%
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Harper runs 2200 meters in 10 minutes. How many meters can Harper run in one minute?
Answer: 220 meters in 1 minute
Step-by-step explanation:
if harper can run 2200 meters in 10 min then that means you can run 220 in 1 min
2200/10 = 220
Answer:
220
Step-by-step explanation:
2200/10 is 220
Find equations of the tangents to the curve x = 9t2 + 3, y = 6t3 + 3 that pass through the point (12, 9). (enter your answers as a comma-separated list. ).
y - 9 = 1(x - 15) is the required equation for the tangent.
What are equations?Equations come in two varieties: identities and conditional equations.
All possible values of the variables result in an identity.
Only certain combinations of the variables' values make a conditional equation true.
Two expressions joined by the equals symbol ("=") form an equation.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
A formula would be 3x - 5 = 16, for instance.
When this equation is solved, we discover that the value of the variable x is 7.
So, the equation of the tangent is:
First, with respect to t, differentiate the function as follows:
dx/dt = d(9t² + 6)/dt
dx/dt = 18t
Like this, we have:
dy/dt = d(6t³ + 3)/dt
dy/dt = 18t²
Now, we will obtain:
dy/dx = 18t²/18t
dy/dx = t
We know that (15, 9) occurs on the curve, so we got:
d(9t² + 6)/dt and d(6t³ + 3)/dt ⇒ t = ±1 and t = 1 ⇒ t = 1
So, (15, 9) is the slope.
y - 9 = 1(x - 15) is the equation of the tangent.
Therefore, y - 9 = 1(x - 15) is the required equation for the tangent.
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Correct question:
Find the equations of the tangents to the curve x = 9t2 + 6, y = 6t3 + 3 that passes through the point (15, 9).
a biologist collected 326 fern and moss samples. there were 66 fewer ferns than moss samples. how many fern samples did the biologist collect?
There are 130 fern samples did the biologist collect.
What is fern and moss samples?
In contrast to ferns, which are vascular plants, mosses are nonvascular primitive plants that produce spores. Furthermore, unlike ferns, which have a plant body that is divided into real stems, leaves, and roots, mosses have none of these features. Ferns also have circinate vernation, which is not true of mosses.
Given:
A biologist collected 326 fern and moss samples. there were 66 fewer ferns than moss samples.
Let, f denotes the number of ferns collected and
m denotes the number of mosses collected
From the given information,
m + f = 326 ..(1)
m - 66 = f ..(2)
Plug equation (2) in equation (1),
m + m - 66 = 326
2m = 326 + 66
2m = 392
m = 196
Plug m = 196 in equation (2),
f = 196 - 66
f = 130
Hence, there are 130 fern samples did the biologist collect.
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5.) A store pays $43 for a DVD player. The store marks up the price by 30%. What is the new price?
Answer25
Week good :
Step-by-step explanation:
the hypotenuse of a right triangle is 6 inches and one of the legs is 6 inches, the exact value of the other leg is
Answer:
h
Step-by-step explanation:
the volume of a sample of nitrogen is 6.00 liters at 35oc and 0.974 atm. what volume will it occupy at stp?
5.152 L volume will it occupy at STP.
What is ideal gas law?
The equation of state for an ideal gas, in theory, is known as the ideal gas law. Even though it has a number of shortcomings, it provides a good approximation of the behavior of several gases under various circumstances. Theoretical point particles that move randomly and only collide in elastic ways make up an ideal gas.
Using the ideal gas equation PV=nRT, where n is the number of moles, it is possible to determine the volume that will be present at STP as follows.
n= PV/RT
p=0.974 atm
V=6.0 L
R = 0.0821 L.atm/k.mol
T= 35 +273= 308k
n= (0.974 atm x 6.0 L)/( 0.0821 L.atm/k.mol x 308 k)= 0.178 moles
STP 1 mole= 22.4 L what obout 0.23 moles
=22.4 x0.178moles/ 1moles =5.152 L
Hence, 5.152 L volume will it occupy at STP
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When two pipes fill a pool together, they can finish in 4 hours. If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours. How long will it take each pipe to fill the pool if it were working alone?
How many hours for one pipe to fill the pool? How many hours for the other pipe to fill the pool?
One pipe takes 6 hours to fill the pool and the other takes 12 hours.
Pipe A fills 1/x of the pool per hour, and Pipe B fills 1/y of the pool per hour. In other words, A takes x hours to fill the pool and B takes y hours to fill the pool.
Together, they fill 1/x + 1/y of the pool per hour. So, 4 hours times that rate should equal 1 full pool, since together they take 4 hours to fill the pool. That gives you your first equation:
4(1/x + 1/y) = 1
You're also told that if one pipe fills half the pool and the other takes over to fill the rest, it will take 9 hours. We don't know how long Pipe A works, so call that number of hours t. Pipe B must work for 9 - t hours.
So, Pipe A, working for t hours, fills half the pool:
t(1/x) = 1/2
And Pipe B, working for 9 - t hours, fills half the pool:
(9-t)(1/y) = 1/2
You now have a system of three equations (because this is an exceptionally complicated pipe-filling-pool problem):
4(1/x + 1/y) = 1
t(1/x) = 1/2
(9-t)(1/y) = 1/2
Solve for t in that second equation, then plug it into the third equation:
t(1/x) = 1/2
t = x(1/2)
t = x/2
(9 - x/2)(1/y) = 1/2
Now you've got a system of two equations:
4(1/x + 1/y) = 1
(9 - x/2)(1/y) = 1/2
Solve for y in the second equation, then plug that into the first equation:
(9 - x/2)(1/y) = 1/2
(9 - x/2) = y(1/2)
2(9 - x/2) = y
18 - x = y (this is a really nice-looking form of that equation; we'll use it again later)
4(1/x + 1/y) = 1
4(1/x + 1/(18-x)) = 1
4/x + 4/(18-x) = 1
(4(18-x))/(x(18-x)) + (4x)/(x(18-x)) = 1
(4(18-x) + 4x)/(x(18-x)) = 1
4(18-x) + 4x = x(18-x)
72 - 4x + 4x = 18x - x2
72 = 18x - x2
x2 - 18x + 72 = 0
(x - 6)(x - 12) = 0
x - 6 = 0 OR x - 12 = 0
x = 6 OR x = 12
So, Pipe A takes either x = 6 or x = 12 hours to fill the pool alone.
When Pipe A takes 6 hours to fill the pool, Pipe B takes 12. When Pipe A takes 12 hours to fill the pool, Pipe B takes 6.
These cases are equivalent, since the original problem makes no distinction between the pipes.
Hence, one pipe takes 6 hours to fill the pool and the other takes 12 hours.
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the top 5% of applicants on a test will receive a scholarship. if the test scores are normally distributed with a mean of 76 and a standard distribution of 12, what is the lowest test score that still qualifies for a scholarship?
As per the standard distribution, the lowest test score is 27.76%
Standard distribution:
In statistics, standard distribution means a normal distribution with a mean of zero and standard deviation of 1.
Given,
The top 5% of applicants on a test will receive a scholarship. if the test scores are normally distributed with a mean of 76 and a standard distribution of 12.
Here we need to find the lowest test score that still qualifies for a scholarship.
As per the given question, we have identified the value of
=> μ = 76 (mean)
=> σ = 12 (standard deviation)
Then we need to take the value of x as,
x < 5% (find the probability)
Now, converting the problem in standard form
=> Z = (5 − 76) / 12
=> Z = -5.91
Then as per the z table the value is 0.2786
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Your college costs $8,792 for the first year but is expected to rise at a rate of 5% per
year. You really work hard to graduate in 4 years, what would the total cost be for all 4
years? Round to 2 decimal places.
Answer:when you're working hard for 4 year graduation and will cost you, 10177.84 for whole 4 year
the times to complete an obstacle course is normally distributed with mean (μ) 73 seconds and standard deviation (σ) 9 seconds. what is the probability using the empirical rule that a randomly selected finishing time is less than 100 seconds? provide the final answer as a percent rounded to two decimal places.
68.18% is the right answer
you are instructed to subtract four points from each score, square the resulting value, and find the sum of the squared numbers. how would this set of instructions be expressed in summation notation?
The summation is Σ(xᵢ-4)², i=1,2,3...
What is summation ?
When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total. Functions, vectors, matrices, polynomials, and, generally, any sort of mathematical object on which an operation labelled "+" is defined can all be added together, in addition to numbers.
Series are summations of infinite sequences. They are related to the idea of limit but are not covered in this article.
Let x serve as the definition of a score.
Each score will be xi, i.e. x1, x2, x3, x4... for the first four consecutive scores, and so on.
By deducting 4 from each score, you get xi-4.
Squaring the Resulting Value = (xi-4)²
The sum of the squared numbers is equal to (xi-4)²
where i=1, 2, 3.
Σ(xᵢ-4), The set of instructions written in summation notation is 2.
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Σ(xᵢ-4)² is the set of instruction expressed in summation notation.
What is Summation Notation?
The summation symbol, S, tells us to add up the sequence's components. To the right of the summation sign is a typical component of the sequence that is being summed. An index that appears below the summation sign designates the variable of summation.
Let a score be defined by x,
Each score will be xᵢ i.e. x₁, x₂, x₃, x₄... for the first four consecutive scores and so on.
Subtracting 4 from each score = xᵢ-4
Squaring the Resulting Value = (xᵢ-4)²
The sum of the squared numbers = Σ(xᵢ-4)², i=1,2,3...
Σ(xᵢ-4)² is the set of instruction expressed in summation notation.
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Select all the equations that are equivalent to
8k = 20.
Answer: The first and the last answer choice
Step-by-step explanation:
They are equal to 8k=20 because they are the same equation but reduced or increased by the same multiple.
Answer:
it's the first option, 3rd option, and fifth option because the rest of the equation cancels out on them (ex. for the first option, divide each side by 3 that would remove the •3 from each side and leave you with 8k=20)
Which statements are true about the ordered pair (−1, 5) and the system of equations? {x+y=4x−y=−6 Select each correct answer. Responses The ordered pair (−1, 5) is a solution to the first equation because it makes the first equation true. The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is a solution to the first equation because it makes the first equation true. The ordered pair (−1, 5) is a solution to the second equation because it makes the second equation true. The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is a solution to the second equation because it makes the second equation true. The ordered pair (−1, 5) is not a solution to the system because it makes at least one of the equations false. The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is not a solution to the system because it makes at least one of the equations false. The ordered pair (−1, 5) is a solution to the system because it makes both equations true. The ordered pair , begin ordered pair negative 1 comma 5 end ordered pair, is a solution to the system because it makes both equations true.
The statements that are true about the ordered pair (−1, 5) and the system of equations include the following;
A. The ordered pair (−1, 5) is a solution to the first equation because it makes the first equation true.
B. The ordered pair (−1, 5) is a solution to the second equation because it makes the second equation true.
D. The ordered pair (−1, 5) is a solution to the system because it makes both equations true.
How to determine the true statement?In order to determine if this ordered pair is a true solution based on the given system of linear equations, we would have to test the ordered pair (-1, 5) by substituting it into each of the linear equation as follows;
For the first linear equation, we have the following:
x + y = 4
-1 + 5 = 4
4 = 4 (True).
For the first linear equation, we have the following:
x - y = -6
-1 - 5 = -6
-6 = -6 (True).
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what is the answer to the picture the two answers on there
In the expression given as -5 - (-7) = -5 + x, the value of x is 7.
What is the value of the expression?In Mathematics, expression simply means the mathematical statements which have at least two terms which are then related by an operator. It should be noted that they illustrate the relationship between the data given.
In this situation, it should be noted that the expression is given as:
-5 - (-7) = -5 + x
Collect like terms
-5 + 7 = -5 + x
x = -5 + 5 + 7
x = 7
The value of x is 7.
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after so-called play-in games, the ncaa men’s basketball tournament is a 64-team single-elimination tournament. after the teams are assigned, in how many ways can the tournament unfold? how many (base-10) digits does this number have?
This is a total of 2^32×2^16×2^8×2^4×2^2×2^1 possible outcomes that is 2^63 outcomes.
What is counting principle?The basic counting concept is a method for keeping track of all the potential outcomes in a scenario. It indicates that there are nm methods to carry out both of these activities if there are n ways to carry out one action and m ways to carry out another action after that. How selection is made based on options is determined by the Fundamental Principle of Counting. The approach of selection, taking into account all of the potential options and their combinations for calculating the probability, is made simpler by the Fundamental Principle of Counting.
Here,
Since I don't know anything about NCAA's March Madness, I'll assume that you're talking about a 64-team single-elimination tournament.
In the first round, there are 32 games, each with 2 possible outcomes. This provides for a total of 2^32 possibilities.
In the next round, there are only 16 games, again each with 2 possible outcomes, for a total of 2^16 possibilities.
You keep going, eliminating half of the players each round and taking half as long as the previous round to play the games out, until the finals, at which point there is 1 game with 2 possible outcomes.
This is a total of 2^32×2^16×2^8×2^4×2^2×2^1 possible outcomes that is 2^63 outcomes.
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I spent $2000 to get
Brownie Town up and running. We make all sorts of brownies. Some have peanuts, some have chocolate chips, and others have icing.
Every month I earn $200
from Brownie Town sales.
The equation form as per the statement in the question will be y = -200x - 2000.
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
As per the given information in the question,
They spent $2,000 therefore that would be -2,000, and they make $200 per month selling brownies.
So simply add -2,000 each time on the chart under "Income made," and the final amount should be 600.
So, the equation will be,
y = -200x - 2000.
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Drag statements and reasons to each row to show why the slope of the line between D D and E E is the same as the slope between E E and F F , given that triangles A A and B B are similar.
By definition of slope , we have seen that Slope = 4/3 and 4/3 = 16/12
How to find the slope of a Line?The slope of a line is basically a measure of its steepness. Mathematically, the slope is calculated as rise over run.
To find the slope, we divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points. This is change in y divided by change in x.
From definition of slope, we know that;
Slope between line D and E is; Slope = 4/3
Similarly, by definition of slope, we know that;
Slope between line D and E is; Slope = 16/12
Now, 16/12 can be reduced to 4/3 and as such;
4/3 = 16/12
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52=2(x+19)
Please help me
what is the quotient of 7.81\times 10^67.81×10 6 and 7.1 \times 10^37.1×10 3 expressed in scientific notation?
The quotient of 7.81 × 10⁶ and 7.1 × 10³ expressed in scientific notation is approximately 1.10 × 10³.
To find the quotient of 7.81 × 10⁶ and 7.1 × 10³ expressed in scientific notation, we can perform the division first and then convert the result into scientific notation.
Step 1: Perform the division: (7.81 × 10⁶) ÷ (7.1 × 10³)
Step 2: Divide the numerical values: 7.81 ÷ 7.1 = 1.09859155 (approximately)
Step 3: Divide the exponents of the powers of 10: 10⁶ ÷ 10³ = 10³ (since 6 - 3 = 3)
Step 4: 1.09859155 × 10³
Step 5: Adjust the result to be in scientific notation format: 1.09859155 × 10³ ≈ 1.10 × 10³
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The complete question:
What is the quotient of 7.81 × 10⁶ and 7.1 × 10³ expressed in scientific notation?
A soap maker wants to ship as many bars of soap as she can to a store. Each bar of soap weighs 1/5 pound. The box that she will use to ship the soap can hold a maximum of 18 pounds of soap.
How many bars of soap can the soap maker ship to the store?
The number of bars of soap that the soap maker ship to the store is 90.
How to calculate the number of bars?From the information, the soap maker wants to ship as many bars of soap as she can to a store. Each bar of soap weighs 1/5 pound.
Since the box that she will use to ship the soap can hold a maximum of 18 pounds of soap. The number of soaps will be:
= 18 ÷ 1/5
= 18 × 5
= 90
The number of soaps is 90.
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pls help mary christmas!!
Answer:
1. 918
2. 2880
3. 2678
4. 22554
5. 66014
6. 44208
what is the sampling process used on dollar street? in other words, the sample of families on the dollar street page were collected using a sample that is .
The sampling process used on dollar street is stratified sampling.
Given,
Use of dollar street;
Dollar street offers a fresh perspective on families all throughout the world. Every family is arranged down a street, with the wealthiest household on the right and the lowest on the left. Each family's earnings are expressed in US dollars.
Here,
Stratified sampling;
To complete the sampling process, stratified sampling is a form of sampling technique in which the entire population is divided into smaller groups or strata.
Therefore,
Stratified sampling is used in dollar street for sampling process.
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Graph:
3/4 times 2^x
Answer:
According to graph calculators online, there is no solution to this equation.
Step-by-step explanation:
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 2 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
x + 4y = 10
2x + 8y = 20
Answer:
x = 2, y = 2
Step-by-step explanation:
Looking at the equations,
x + 4y = 10
2x + 8y = 20
If x = 2, and y = 0 then it would look something like this:
2 + (4×2) = 10
Let's apply that to the next equation:
(2×2) + (8×2) = 20
In conclusion, x = 2, y = 2
Number of Text Messages
Amara Sent
0, 2, 5, 6, 9, 10, 15
Number of Text Messages
Marquis Sent
0, 9, 10, 10, 10, 11, 16
1.1 Whose data has a smaller mean? (Circle one.)
Marquis
They're the same
Amara
ale one.)
Answer:
Amara
Step-by-step explanation:
You can find mean by adding the total number of texts sent by each person and dividing it by the number of days.
In this case, the mean of Amara's texts sent is 6.714...
The mean of Marquis' texts sent is 9.428...
Therefore, Amara has the smaller mean.
In Exercise 5.18, Y1 and Y2 denoted the lengths of life, in hundreds of hours, for components of types I and II, respectively, in an electronic system. The joint density of Y1 and Y2 isReferenceAn electronic system has one each of two different types of components in joint operation. Let Y1 and Y2 denote the random lengths of life of the components of type I and type II, respectively. The joint density function is given by(Measurements are in hundreds of hours.) Find P(Y1 > 1, Y2 > 1).
In an electrical system, components of categories I and II have a life expectancy measured in hundreds of hours, respectively. The probability of finding the combined density of Y1 and Y2 is equal to e^(−2).
The components of type I and type II, respectively, have random life spans denoted by the letters Y1 and Y2, respectively. Given by is the joint density function (Measurements are in hundreds of hours.)
Probability P(Y1 > 1, Y2 > 1) = ∫2¹∫1¹ (1/2)e^(−x−y) dx dy = e^(−2).
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