A soccer team has won 1/2 of the games they played. they won 12 games. how many games did they play? Show your working/calculations
they won 1/2 of their games and won 12 games
1/2 = 50% , multiply by 2 to make 100%
so 12 x 2 = 24 games were played
To calculate the number of games played by the soccer team, multiply the number of games they won (12) by 2, because winning 12 games represents winning [tex]\frac{1}{2}[/tex] of all games played. The soccer team thus played a total of 24 games.
To find how many games the soccer team played in total, we can set up a proportion using the information that they won [tex]\frac{1}{2}[/tex] of their games. This means for every game they won, they played two (since [tex]\frac{1}{2}[/tex] represents one out of two games). If the team won 12 games, and that represents [tex]\frac{1}{2}[/tex] of the total games, we can use a simple equation to solve for the total number of games (T).
The proportion is as follows: [tex]\frac{1}{2}[/tex] = [tex]\frac{12}{T}[/tex], where 12 is the number of games won, and T is the total number of games played.
To solve for T, we multiply both sides of the equation by T to get rid of the fraction: [tex]\frac{T}{2}[/tex] = 12. To find T, we then multiply both sides of the equation by 2 to isolate T on one side of the equation: T = 12 * 2.
Therefore, the team played a total of T = 24 games.
What is a quartic function with only the two real zeros given?
x = -4 and x = -1
A.
y = x4 + 5x3 + 5x2 + 5x + 4
B.
y = x4 - 5x3 - 5x2 - 5x - 4
C.
y = -x4 + 5x3 + 5x2 + 5x + 4
D.
y = x4 + 5x3 + 5x2 + 5x - 5
A rectangular vegetable garden will have a width that is 3 feet less than the length, and an area of 54 square feet. if x represents the length, then the length can be found by solving the equation: x(x−3)=54x(x-3)=54 what is the length, x, of the garden? the length is _____ feet.
Answer
Length of rectangular garden = x feet
As, Width is 3 feet less than Length.
Width = (x-3 ) feet
Area of Rectangle = Length × Breadth
Area = 54 square feet
→54 = x × (x-3)
→ x²-3 x-54=0
Splitting the Middle term
→x² - 9 x + 6 x- 54=0
→x × (x-9)+6 × (x-9)=0
→ (x+6)(x-9)=0
→x+6=0 ∧ x-9=0
x≠-6, as length can't be negative.
So, x=9
Length of Rectangular garden = 9 feet
what is the algebraic expression for the product of 9 and a number t
Question text
Which volume formula or formulas show(s) a joint variation?
I V=8^3
II V=πr^2h
III V=Bh
Select one:
a. III only
b. I only
c. II and III only
d. I, II, and III
The correct answer is: c. II and III only
To determine which volume formula(s) exhibit joint variation, we need to consider if the volume (V) varies directly with two or more variables. In joint variation, V is directly proportional to the product of two or more variables.
Let's analyze each formula:
I. V = 8^3 → This is not a joint variation as V is solely dependent on the constant 8.
II. V = πr^2h → This shows joint variation as V varies directly with both r and h.
III. V = Bh → This also exhibits joint variation since V varies directly with both B (base area) and h (height).
Evaluate the function rule for the given value. Y=6*4^x for x=-3
Answer:
[tex]y = \frac{3}{32}[/tex]
Step-by-step explanation:
Using the exponent rule:
[tex]a^{-n} = \frac{1}{a^n}[/tex]
Given the function:
[tex]y = 6 \cdot (4)^x[/tex] ......[1]
To evaluate the function rule for x = -3.
Substitute x = -3 in [1] we have;
[tex]y = 6 \cdot (4)^{-3}[/tex]
⇒[tex]y = 6 \cdot \frac{1}{4^3} = 6 \cdot \frac{1}{64}=\frac{3}{32}[/tex]
Therefore, the function rule for the given value when x = -3 is:
[tex]y = \frac{3}{32}[/tex]
A certain bag of potting soil is 1/4 peat moss,and the rest is dirt. What part is dirt?
The part of the bag that consist of dirt is:
3/4
Step-by-step explanation:It is given that the amount of peat moss that is present in a bag of potting soil is:
1/4
Hence, the remaining space that is left in the bag consist of dirt.
Remaining space is calculated as :
[tex]1-\dfrac{1}{4}\\\\\\=\dfrac{3}{4}[/tex]
( Since we subtract 1/4 from a whole of a bag)
Hence, the part that is dirt in the bag of potting soil is:
3/4
Diana can earn money for the tickets she sells. Which of the following statements describes the variables in this situation correctly?
The variables in this situation are the price of the tickets and the quantity of tickets sold. The relationship between price, quantity, and revenue can be analyzed using the concept of price elasticity of demand. Diana should lower the price if demand is elastic, raise the price if demand is inelastic, and can maintain the same revenue if demand has unitary elasticity.
Explanation:The variables in this situation are the price of the tickets and the quantity of tickets sold. These two variables directly affect the total revenue generated by Diana from ticket sales. The relationship between price, quantity, and revenue can be analyzed using the concept of price elasticity of demand.
If demand for tickets is elastic, Diana should lower the price to increase total revenue. A decrease in price will result in a larger percentage increase in the quantity sold, leading to a higher total revenue. On the other hand, if demand is inelastic, Diana should raise the price to increase revenue. A certain percentage increase in price will result in a smaller percentage decrease in quantity sold, ultimately raising total revenue.
If demand has unitary elasticity, an equal percentage change in quantity will offset a moderate percentage change in price. In this case, Diana can earn the same revenue regardless of a moderate increase or decrease in ticket price.
a game spinner has regions that are numbered 1 through 8. if the spinner is used twice, what is the probability that the first number is a 3 and the second is a 7?
The probability that the first number is a 3 and the second is a 7 is 1/64
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given:
spinner had region numbered from 1 to 8
So, the probability on the spinner has an equally likely chance of being selected= 1/8.
P(3) = 1/8
P(7) = 1/8
Thus, probability that the first number is a 3 and the second is a 7
=(1/8) * (1/8)
= 1/64
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Solve for x.
The length of a rectangle is equal to 2 times the width plus 3 feet. If the area of the rectangle is 20 square feet, what are the dimension of the rectangle?
How to determine if a series has a sum?
which rectangular equation is equivalent to the polar equation r sin theta=-2
Answer:
The rectangular equation that is equivalent to the given polar equation is:
y= -2
Step-by-step explanation:
We know that the polar coordinate of a equation are related to the rectangular coordinates of the equation as:
[tex]x=r\sin \theta\\\\y=r\cos \theta[/tex]
where,
[tex]r=\sqrt{x^2+y^2}[/tex]
Now we are given that:
[tex]r\sin \theta=-2[/tex]
Also,
[tex]\theta=\arctan \dfrac{y}{x}[/tex]
Hence, on converting the given polar equation to the rectangular equation we get:
[tex]y=-2[/tex]
Which expression is equivalent to (5^-2) (5^-1)
-1/125
-1/5
1/125
1/5
Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6). Match each set of vertices of quadrilateral EFGH with the transformation that shows it is congruent to ABCD.
Answer:
Answers a little bit more simplified, all credit to the expert :)
E(4, 4), F(8, 3), G(10, 6) and H(8, 6) <-----> a translation 7 units right
E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6) <-----> a reflection across the y-axis
E(-3, -1), F(1, -2), G(3, 1), and H(1, 1) <-----> a reflection across the x-axis
E(-3, -1), F(1, -2), G(3, 1) and H(1, 1) <-----> a translation 5 units down
Step-by-step explanation:
A Sporting good store charges $30 for 12 cans of tennis balls. The tennis coach orders 100 cans of tennis balls for the tennis team. How much were the coach pay for the tennis balls?
How can ΔABC be mapped to ΔXYZ?
First, translate .
Next, rotate ΔABC about B to align the sides and angles.
To map ΔABC to ΔXYZ, you need to translate the triangle and then rotate it about a point.
Explanation:In order to map ΔABC to ΔXYZ, you can follow these steps:
First, translate ΔABC by moving it horizontally and vertically to a new position.Next, rotate ΔABC about point B to align the sides and angles with ΔXYZ.By performing these steps, you can map one triangle to another.
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Rewrite the rational exponent as a radical by extending the properties of integer exponents.
A round-robin tournament has 66 pairings. How many teams are in the tournament?
Kris wanted to understand whether studentstudents at her school were in favor of an extended school day. She surveyed some students and displayed the results in the table below:
In favor
Opposed
Undecided
Grade 9
6
4
8
Grade 10
10
11
9
Grade 11
12
15
11
Grade 12
15
6
14
If the principal randomly selects a student in grade 10 from this survey, what is the probability that the student is opposed to extending the school day?
Answer:
The probability that the student is opposed to extending the school day is 0.3666 or 36.67% approx.
Step-by-step explanation:
Arranging the table properly and adding a column of total students.
In favor Opposed Undecided Total students
Grade 9 6 4 8 18
Grade 10 10 11 9 30
Grade 11 12 15 11 38
Grade 12 15 6 14 35
If the principal randomly selects a student in grade 10 from this survey, this means we will only consider grade 10 students.
The probability that the student is opposed to extending the school day is = [tex]\frac{number of opposed students}{total number of students}[/tex]
There are 11 students who are opposed and total students in grade 10 are 30.
So, probability is : [tex]\frac{11}{30}= 0.3666[/tex] or 36.67% approx.
Factor completely 36x2 − 49.
A (3x + 7)(12x − 7) B (3x − 7)(12x + 7) C (6x − 7)(6x − 7) D (6x + 7)(6x − 7)
A B C D ?
Answer:
The correct option is D.
Step-by-step explanation:
The given expression is
[tex]36x^2-49[/tex]
It can be written as
[tex](6x)^2-(7)^2[/tex]
Using the formula
[tex]a^2-b^2=(a-b)(a+b)[/tex]
[tex](6x)^2-(7)^2=(6x+7)(6x-7)[/tex]
Therefore the complete factor form of given expression is (6x+7)(6x-7). The correct option is D.
How many cubes with 5 inches side Will completely fill a cube that is 10 inches on each side
if the lateral surface area of a square pyramid is 84ft^2 and the base edge is 6, what is the slant height?
Determine whether the cost for ordering multiple items that will be delivered is sometimes, always, or never proportional. Explain your reasoning.
HELP ROUND 604703.472883 TO THE NEAREST HUNDRED
Answer:
The required number is 604703
Step-by-step explanation:
Consider the provided number 604703.472883
The rule for rounding a number is:
If the number on the right side of rounding digit is 0, 1, 2, 3, 4 then no need to change the rounding digit and change the rest of the digit right to rounding digit with 0.
If the number on the right side of rounding digit is 5, 6, 7, 8, 9 then rounding digit rounds up by one number and change the rest of the digit right to rounding digit with 0.
The number on the hundred place is 7 and the number on right side is 0.
Thus, no need to change the rounding digit and change the rest of the digit right to rounding digit with 0.
Hence, the required number is 604703
A data set has the following characteristics: Mean: 4.9 Median: 6 Mode: 6 Variance: 4 The z-score is the number of
Answer:
Standard deviations and mean
Step-by-step explanation:
Answer:
I.
standard deviations
mean
II.
-1.95
0.05
0.8
Step-by-step explanation:
I.
The z-score is the number of standard deviations a data value is away from the mean.
II.
z1 = -1.95
z5 = 0.05
z6.5 = 0.8
Which sequence is geometric and has 1/4 as its fifth term and 1/2 as the common ratio?
Use Gauss-Jordan elimination to solve the following linear system.
x – 2z = 9
6x – 2y – 5z = 29
–5x + 5y + 3z = –14
A. (–5,–3,0)
B. (3,2,–3)
C. (5,3,–5)
D. (3,6,–4)
By using Gauss-Jordan elimination the solution to the linear equation is (3, 2, –3). The correct option is B.
What is Gauss-Jordan's elimination method?
In mathematics, the algorithm known as Gaussian elimination, commonly referred to as row reduction, is used to solve systems of linear equations. It comprises a series of operations carried out on the relevant coefficients matrix.
x – 2z = 9 so x = 2z + 9
6x – 2y – 5z = 29
–5x + 5y + 3z = –14
Substitute x = 2z + 9 into 6x – 2y – 5z = 29 and –5x + 5y + 3z = –14
6(2z + 9) – 2y – 5z = 29
12z + 54 - 2y -5z =29
-2y + 7z = - 25 (1st equation)
–5(2z + 9) + 5y + 3z = –14
-10z - 45 + 5y + 3z = -14
5y - 7z = 31 (2nd equation)
Multiply (1st) equation by 5 and (2nd) equation by 2.
-10y + 35z = - 125
10y - 14z = 62
21z = - 63
z = -3
Substitute z = - 3 into x = 2z + 9
x = 2z + 9
x = 2(-3) + 9
x = 3
Substitute x = 3 and z = 3 into 6x – 2y – 5z = 29
6x – 2y – 5z = 29
6(3) – 2y – 5(-3) = 29
18 - 2y + 15 = 29
-2y + 33 = 29
-2y = -4
y = 2
x = 3, y = 2 and z = -3
Therefore, the solution to the linear equation is (3, 2, –3). The correct option is B.
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Step by step on how to solve that equation
What is the midpoint of GH? G(7,-5) H(9,-1)
Evaluate f(x)= -x^2+1 for x=-3
A.4
B.-4
C.-8
D.-9