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The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. The equation 9 x 5 = 45 consists of the two equations are separated by the 'equal' sign.
Detailed explanation:Assume that a team has N players.
Each squad may have anywhere from 3 to 5 players, so
3 ≤ 5 ...(i)
Let P represent a player's total points in a single game round.
Each round of the game allows for a maximum of 10 points for each player, so
0 ≤ p ≤ 10 ....( i)
(1) Elena assembled a team of five people.
As a result, 5 players' points in 1 round equal 5P.
Equation (ii) yields the range of
0 ≤ 5p ≤ 50.
As a result, Elena's team's points total ranges from 0 to 50.
(2) If each shot is off by one point, then
One player's points in one round are equal to 10-1=9.
So, 9 x 5 = 45 points were collected by 5 players in 1 round.
(3) Assume that R represents the number of teams as an integer.
the game involves at least three teams, therefore
R ≥ 3 ...( iii)
Given that N players make up one team,
R team has NR players, where R is 3, 4, or more.
Next, using equation (i)
3R ≤ 5R
Therefore, the number of players ranges from 3R to 5R if there are at least 3 teams.
The game can have anywhere from 3x3=9 to 5x3=15 players when R=3.
Answer:
(I) Between 0 and 50.
(ii) Between 3 and 5.
(iii) Between 3R and 5R, where R = 3,4,5,...
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Related Questions
Easy math, 50 points.
Answers
Answer:
2 1/2 (D)
Step-by-step explanation:
1 8/12 + 5/6
you have to make the denominator on the right equal to the denominator on the left. in order to do that, multiple the numerator and denominator on the left my two.
5/6 become 10/12.
1 8/12 + 10/12
1 18/12
Simplify,
2 6/12 (1/2)
Answer:
[tex]1\frac{8}{12}+\frac{5}{6}=2\frac{1}{2}[/tex]
Solve −5d +2≥7 or 2d −2>8
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Answer:
for the first one: d ≥ 1
for the second one: d > 5
I want to know how I can solve this question.
Answers
For the right triangle shown in the picture, recall the trigonometric identity of the cosine function:
[tex]\cos (B)=\frac{a}{c}[/tex]Isolate a from the equation:
[tex]a=c\cdot\cos (B)[/tex]Substitute for c=6.3 and B=43.8°:
[tex]a=6.3\cos (43.8)[/tex]Use a calculator to evaluate the expression:
[tex]\begin{gathered} a=4.547089437\ldots \\ \approx4.6 \end{gathered}[/tex]Find the distance between the two points rounding to the nearest tenth (if necessary).
(6,-8) and (1,4)
Answers
Answer: (8,
-4) and (3,8)
Step-by-step explanation:
(01.06 MC)
Ray IL bisects angle HIJ. If mzHIL = (6x - 7)° and mzJIL = (5x + 4)°, what is mzJIL?
118°
59°
44°
11°
Answers
Option C, 59° is correct answer, The angle JIL is equal to 59 degree.
What is angle?
Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned. Angles are also produced when two planes intersect. These are what are known as dihedral angles. Another characteristic of intersecting curves is the angle generated by the rays that are perpendicular to the two crossing curves at the point of junction.
Given information in the question,
∠HIL = (6x-7)°
∠JIL = (5x+4)°
The ray IL bisects the ∠HIJ
Since, IL bisects angle HIJ then, angle HIL = angle JIL
So,
6x - 7 = 5x + 4
x = 11
Putting the value of x in given value of JIL to get the angle JIL
∠JIL = (6x-7)°
∠JIL = (6(11)-7)°
∠JIL = 59°
Therefore angle JIL is equal to 59 degrees.
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Mrs. Frank asks four of her students to measure four different objects. Here are the results.
Which student had the greatest percent error?
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The student that has the greatest percent error is Ebony.
How to calculate the percentage error?The percentage error will be calculated as:
= Change in value / Initial values × 100
From the table, we can see that Ebony had the greater difference in values. This will be illustrated as:
= (Measured length - Actual length) / Actual length × 100
= (2.1 - 1.6)/1.6 × 100
= 0.5 / 1.6 × 100
= 31.25%
Ebony had the higher percentage error.
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What are the vertex and range of y = |x + 3| + 2?
a (−3, 2); 2 ≤ y < ∞
b (−3, 2); −∞ < y < ∞
c (0, 5); 2 ≤ y < ∞
d (0, 5); −∞ < y < ∞
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The vertex of the equation is (-3, 2). And the range will be the set of all real numbers equal to or larger than 2, written as:
y ≥ 2.
What is the vertex and range of the absolute value function?
For an absolute value function of the form:
y = |x - a| + b
The vertex is a the point (a, b).
And the range (the set of the possible values of y that we can get with the function) will be the set of all real values equal or larger than b.
In this case, the absolute value function is:
y = |x + 3| + 2
Comparing it with the general one, we can see that the vertex is (-3, 2)
And then the range is y ≥ 2.
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45 POINTS PLEASE HELP!!!
Decide whether inductive or deductive reasoning is used to reach the conclusion
the wolf population in a park has increased each year for the last 10 years. So, the wolf population will increase again next year
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in how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may not sit next to each other in the same row, and no child may sit directly in front of their sibling?
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Three pairs of siblings from different families can be seated in two rows of three chairs so that siblings may not sit next to each other in the same row, and no child may sit directly in front of their sibling in 96 ways.
There are 3 pairs of siblings. We can name them as a₁, a₂, b₁, b₂, c₁ and c₂, a total of 6 children.
There are 2 rows of 3 seats each.
We will try to find the number of ways each seat can be filled.
So considering the first seat in first row, it can be filled in 6 different ways. Because any one from 6 children, say a₁, can be seated.
Now for the second seat in first row can only be filled by one of b₁, b₂, c₁ or c₂ because the first seated child a₁ along with the sibling a₂ of the same cannot be seated in the second seat. So in 4 different ways.
For the third seat remaining in the first row, one out of the remaining pair of siblings c₁ or c₂ can be seated. This can be done in 2 ways.
Now after filling the first row in this manner, the second row can be filled in only 2 ways.
So total number of ways the children can be seated = 6 x 4 x 2 x 2 = 96 ways
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graph the line that passes through the point (0,3) and is parallel to another line whose slope is 1.2.
please do it quick i need it asap
Answers
Hello,
Two parallel lines have the same slope, which means that our line's slope, will also be 1.2.
So now we have a point and a slope, so we can use the following formula to find the equation of the line:
y-y1 = m (x-x1)
Where:
y1 - y coordinate of a point on the line
x1 - x coordinate of the same point on the line
m - slope
Plugging in we get:
y+3 = 1.2 (x-0)
y = 1.2x - 3 (slope intercept form)
or
5y-6x = -15 (standard form)
Cheers
The sides of an equilibrium triangle are 9.4cm,correct to the nearest milimetre. Work out the upper bound of the perimeter of this triangle.
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The perimeter of the given equilateral triangle would be 28.2 cm if the sides of the triangle are 9.4 cm.
What are the upper and lower bounds of an approximation?The numerical value that is rounded up to represent the supplied value's next value serves as its upper bound.
The numerical number that is rounded off for the previous value or the predicted value of the provided value is the lower bound for the supplied value.
The sides of an equilateral triangle are 9.4 cm
The perimeter of an equilateral triangle = 3 × length of the side
The perimeter of an equilateral triangle = 3 × 9.4
The perimeter of an equilateral triangle = 28.2 cm
Hence, the perimeter of the given equilateral triangle would be 28.2 cm if the sides of the triangle are 9.4 cm.
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) assembly comprises 769 team members. given that tmm operates two shifts a day, and assembly has 353 stations, what is the proportion of team members not assigned to one of the stations?
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Among the 769 team members, 706 of them are assigned to operates in 2 shifts schedule. The proportion of team members not assigned to one of the stations is 63 / 769
Proportion means a share from total set being discussed.
Data from the given case:
- The assembly has 769 team members.
- The assembly has 353 stations
- At each station, there are 2 shifts operations.
Assuming that 1 person is assigned to 1 shift operation, then there will:
353 x 2 = 706 person assigned.
The remaining team members that not assigned is:
769 - 706 = 63 person.
Therefore, the share or the proportion of unassigned team members is:
63/769
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7+[-8-5^2]/(1-4)^3+17
Answers
2.6
Explanations:Given the expression;
[tex]\frac{7+\lbrack-8-5^2\rbrack}{(1-4)^3+17}[/tex]Simplify the expression in the bracket to have:
[tex]\begin{gathered} =\frac{7+\lbrack-8-25\rbrack}{(-3)^3+17} \\ =\frac{7+(-33)}{(-3\times-3\times-3)+17} \\ =\frac{7+(-33)}{-27+17} \end{gathered}[/tex]Simplify the result to have;
[tex]\begin{gathered} =\frac{7-33}{-10} \\ =\frac{-26}{-10} \\ =2.6 \end{gathered}[/tex]Hence the result of the given function on simplification is 2.6
Hey , I have a quick question about a Homework in math I got confused on how to solve the listed to formula [tex] \frac{x - 3}{2} - 4 \ \textless \ \frac{x}{3} [/tex]
Answers
Solution
- The question would like us to solve the following
[tex]\frac{x-3}{2}-4<\frac{x}{3}[/tex]- The solution is outlined below:
[tex]\begin{gathered} \frac{x-3}{2}-4<\frac{x}{3} \\ \\ Collect\text{ like terms:} \\ Add\text{ 4 to both sides and Subtract }\frac{x}{3}\text{ from both sides} \\ \\ \frac{x-3}{2}-\frac{x}{3}<4 \\ \\ We\text{ need the LCM of 2 and 3. } \\ The\text{ LCM is }2\times3=6 \\ \\ Thus,\text{ multiply both sides by 6 in order to remove the denominator} \\ 2\frac{}{} \end{gathered}[/tex][tex]\begin{gathered} 6\left(\frac{x-3}{2}\right?-6\left(\frac{x}{3}\right?<4\times6 \\ \\ 3\left(x-3\right)-2x<24 \\ Expand\text{ the bracket} \\ 3x-9-2x<24 \\ x-9<24 \\ Add\text{ 9 to both sides} \\ x<33 \end{gathered}[/tex]Final Answer
The answer is x < 33
a bike that goes from 6m/s to 16m/s in 20 seconds.
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The initial velocity = vi = 6m/s
The final velocity = vf = 16 m/s
The total time = t = 20 seconds
The rate of change in velocity is called acceleration (a) that can be written as:
[tex]a\text{ = }\frac{Change\text{ in velocity}}{time}[/tex]
or
[tex]a\text{ = }\frac{vf-vi}{t}[/tex]Put the values in the equation to get the value of 'a'.
[tex]a\text{ = }\frac{16\text{ - 6}}{20}[/tex][tex]a\text{ = }\frac{10}{20}[/tex]or
[tex]a\text{ = }\frac{1}{2}[/tex]hence, the value of a is 1/2.
Which number is greatest?
-1
-4
-6
Answers
Answer:
Step-by-step explanation:
-1>-4>-6
-1 is the greatest number.
You’re talking about negatives therefore the bigger your negative number is the less it’s going to be, the smaller your negative number is the bigger it’s going to be.
Kinda confusing but just don’t overthink it
The following are daily customer numbers at an outerwear store. You've calculated themedian number of customers for the first six days of the week:Monday Tuesday Wednesday Thursday Friday Saturday Sunday175132A. IncreaseB. DecreaseC. Stay the same121129145160Q. If the store has 173 visitors on Sunday, will the median increase, decrease, or stay thesame?
Answers
Answer:
[tex]A\text{ : Increase}[/tex]Explanation:
Here, we want to deduce the median change
The median is a measure of central tendency that represents the middle number is a set of numerical observations
Firstly, let us get the previous median
We start by sorting the numbers from bottom to top
We have that as:
121,129,132,145,160,175
Since the count of observations is even, we have the median as the average of the two mid-values
We have that as:
[tex]\frac{132+145}{2}\text{ = 138.5}[/tex]Adding the last value, the set becomes
121,129,132,145,160,173,175
In this case, the median value would be 145 which shows an increase in the value of the median
Answer:
A. Increase
Step-by-step explanation:
I took the
What is the slope of the line? No need to answer the one above because I already know it. All I want to know is the slope. Thanks
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What is the area, in square centimeters, of the shaded part of the rectangle shown below
Answers
Answer:100 cm
Step-by-step explanation: first, you would find the area of the whole rectangle.
L x W = A
10x14=140
Next, find the area of the unshaded part. To do this, you would subtract 6 from 14
14-6=8
After that, times 8 by 10, then divide by 2
10x8=80
80÷2=40
Take 40 and subtract it from the area of the whole rectangle
140-40=100
simplify 4√(384.5)³ using logarithm
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After simplification of 4√(384.5)³ using logarithm, the resulting answer is 30158.13684.
What is a logarithm?The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number. When measuring the relative change of a value rather than its absolute difference, logarithmic scales are helpful. Moreover, logarithmic scales are used to compress large-scale scientific data because the logarithmic function log(x) grows very slowly for large x. Common logarithms, with a base of 10, binary logarithms, with a base of 2, and natural logarithms, with a base of e 2.71828, are the four most popular types of logarithms.So, 4√(384.5)³ using logarithm:
(Refer to the image attached below for calculations.)= 30158.13684Therefore, after simplification of 4√(384.5)³ using logarithm, the resulting answer is 30158.13684.
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How do I know when to subtract or add or divide when it comes to the end of the solution?
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Given a rectangular peice of paper
Length = 34 cm
Width = 16 cm
So, the area of the rectangle = 34 x 16 = 544 cm²
Two semicircles cut out of it
The diameter of the circle = d = 16 cm
So, the radius of the circle = r = d/2 = 8 cm
The area of the two semicircles = area of the complete circle
so, the area of the circle = πr² = 3.14 x 8² = 200.96 cm²
So, the area of the remaining paper = area of the rectangle - area of the circle
= 544 - 200.96 = 343.04 cm²
So, the answer will be Area = 343.04 cm²
2x + y = 2
Step 2 of 2: Determine the missing coordinate in the ordered pair (?, -3) so that it will satisfy the given equation.
Answers
Answer:
2.5
Step-by-step explanation:
Plug is -3 for y and solve for x
2x -3 = 2 Add 3 to both sides
2x = 5 Divide both sides by 2
x = [tex]\frac{5}{2}[/tex] o r 2[tex]\frac{1}2}[/tex] or 2.5
Factor the monomial 16x²y
Answers
The factors of the given monomial are given below
What is a monomial?
A monomial is, broadly speaking, a polynomial with just one term in mathematics. There are two definitions of a monomial: A monomial, often known as a power product, is a product of powers of variables with nonnegative integer exponents, or a product of variables with repeats. The constant 1 is a monomial, which means that it is equivalent to the empty product and to for any variable x. If just one variable, x, is examined, a monomial is either 1 or a power xn of x, where n is a positive integer. If many variables, say x,y,z, are examined, each can be assigned an exponent, such that each monomial has the form xaybzc with a,b,c non-negative integers.
The factors of the monomial 16x²y are 2.2.2.2.x.x.y
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The factors of the monomial are given below
What is a monomial?
A monomial is, broadly speaking, a polynomial with just one term in mathematics. there are two definitions of a monomial: A monomial, often known as a power product, is a product of powers of variables with nonnegative integer exponents, or a product of variables with repeats. The constant 1 is a monomial, which means that it is equivalent to the empty product and to for any variables x. If just one variable, x, is examined, a monomial is either 1 or a power xn of x, where n is a positive integer, if many variables, say x, y, z, are examined, each can be assigned an exponent, such that each monomial has the form xaybzc with a, b, c non-negative integers.
The factors of the monomial 16x²y are 2.2.2.2.x.x.y
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Which polynomial represents the difference below?2x^2 + 7x+6(3x^2 - x)O A. 2x^2 + 5x + 6B. 2x^2 + 4x + 6c. - x^2 + 6x + 6D. - x^2 + 8x+ 6
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The given polynomials are as ,
[tex]\begin{gathered} 2x^2+7x+6\text{ and} \\ 3x^2-x \end{gathered}[/tex]We have to subtracrt these given polynomials,
[tex]\begin{gathered} =2x^2+7x+6-3x^2-(-x) \\ =2x^2+7x+6-3x^2+x \\ =-3x^2+2x^2+7x+x+6 \\ =-x^2+8x+6 \end{gathered}[/tex]Option D is correct.
A blueprint for a rectangular warehouse has a length of 18 inches and a width of 10 inches. It uses a scale of 1 inch for every 20 feet. 1. What is the actual area of the warehouse in square feet? 2. How do you know?
Answers
Answer:
The actual area of the warehouse would be:
[tex]72000~\text{feet}^{2}[/tex]
Step-by-step explanation:
Step 1: Convert all the blueprint lengths into real lengths:
Each inch in the blueprint represents 20 feet in the real world.
So, the real-life length (18 inches in blueprint) would be:
[tex]1~\text{inch}= 20~\text{feet}\\\\\text{Multiply by 18 on both sides}:\\1\times18~\text{inch}= 20\times18~\text{feet}\\18~\text{inch}= 360~\text{feet}\\[/tex]
Similarly, the real-life width would be:
[tex]1~\text{inch}= 20~\text{feet}\\\\\text{Multiply by 18 on both sides}:\\1\times10~\text{inch}= 20\times10~\text{feet}\\10~\text{inch}= 200~\text{feet}\\[/tex]
Step 2: Calculate the area
The area of the warehouse would be given by:
[tex]\text{Area}=\text{Length}\times \text{Width}[/tex]
The length is 360 feet, and the width is 200 feet, so the total area would be:
[tex]\text{Area}=\text{Length}\times \text{Width}\\\\\text{Substitute the values for the length and width}\\\text{Area}= 360\times 200\\\text{Area}=72000[/tex]
Ans
Find the Tem 90 is in the
Ap-10₁-8,-6,-4
Answers
Answer:
a₉₀ = 168
Step-by-step explanation:
there is a common difference between consecutive terms, that is
- 8 - (- 10) = - 6 - (- 8) = 4 - (- 6) = 2
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 10 and d = 2 , then
a₉₀ = - 10 + (89 × 2) = - 10 + 178 = 168
You deposit $400 in an account that earns 3. 5% interest compounded annually. What is the account balance after 2 years?
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Account balance after 2 years $441.
Based on the given condition, here the details:
P = $400
r = 5 % = 0.05
n = 1
t = 2
Formulate and substitute all above:
F = P · (1 + [tex]\frac{r}{n}[/tex][tex])^{nt}[/tex]
F = 400. 1 + [tex]\frac{0.05}{1}[/tex])²
F = $441
From this as general, account balance is:
A checkbook, a savings account, or an investment account, for example, has a balance that shows how much money is available in the account. This is also called the current account value. The current value of account balances is shown by financial institutions on both paper statements and online tools.
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a group of 90 students is to be split at random into 3 classes of equal size. all partitions are equally likely. joe and jane are members of the 90-student group. find the probability that joe and jane end up in the same class.
Answers
The probability that joe and jane end up in the same class is 0.3258 .
In the question ,
it is given that
90 students is to be split into 3 equal size classes , so ,
the three classes will have 30 students each .
let these classes be Class A , Class B and Class C .
Let Joe and Jane be in Class A .
the total number of ways of selecting 30 students for class A from 90 students is C(90,30) .
Since , we have fixed Joe and Jane in Class A , the remaining 28 spots of class A can be filled by remaining 88 students in C(88,28) ways ,
So , the probability that Joe and Jane end up in the same class is
= C(88,28)/C(90,30) .
Since there are three classes ,
the required probability is 3*C(88,28)/C(90,30) .
= 3×[tex]\frac{88!}{28!*60!}[/tex]×[tex]\frac{60!*30!}{90!}[/tex]
= 29/89
= 0.3258
Therefore , the probability that joe and jane end up in the same class is 0.3258 .
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Find the mean for n = 200 and p = 0.24 when the conditions for the binomial distribution are met.
Answers
The mean value of expected value for a binomial distribution is given by the next formula:
[tex]\mu_x=n\cdot p[/tex]Where n is the number of trials and p is the probability of success. So, using the given data:
[tex]\begin{gathered} \mu_x=200\cdot0.24 \\ \mu_x=48 \end{gathered}[/tex]So the expected value or mean is 48
When radioactive substances decay, the amount remaining will form a geometric sequence when measured over constant intervals of time. The table shows the amount of a radioactive isotope initially and after 2 hours. What are the amounts left after 1 hour, 3 hours, and 4 hours?
Answers
Answer:
Hour elapsed 0 1 2 3 4
Grams 1986 1032.7 537 279.2 145.2
Explanation:
To find the amount left after 1 hour, 3 hours, and 4 hours, we need to find the common ratio.
Since we know the initial amount and the amount left after 2 hours, the ratio of these quantities is the square of the common ratio, so
r² = 537/1986
r² = 0.2704
r = √0.2704
r = 0.52
Then, the amount left after 1 hour is the initial amount multiplied by the common ratio, so
For 1 hour
Amount left = 1986(0.52) = 1032.7 grams
In the same way, the amount left after 3 and 4 hours is
For 3 hours
Amount left = 537(0.52) = 279.2 grams
For 4 hours
Amount left = 279.2(0.52) = 145.2 grams
Therefore, the complete table is
Hour elapsed 0 1 2 3 4
Grams 1986 1032.7 537 279.2 145.2
