Answer: 1. 286 different combinations of players are possible.
2. The probability of selecting a team of 5 girls and 5 boys is [tex]\frac{63}{143}[/tex] and the decimal is 0.4405...
Step-by-step explanation:
1. Number of girls is 6 and number of boys is 7.
So, the total number of players = 6+7 = 13
A team of 10 players is to be selected from the class.
So, the total possible number of different combinations of players will be: [tex]^1^3C_{10} = \frac{13!}{10! (13-10)!}=\frac{13*12*11*10!}{10!*3!}= \frac{13*12*11}{6}=286[/tex]
2. Number of girls is 6 and number of boys is 7.
The possible number of teams by selecting 5 girls and 5 boys will be: [tex]^6C_{5}\times ^7C_{5} =6\times 21= 126[/tex]
and the number of total possible teams of 10 players [tex]= ^1^3C_{10} =286[/tex]
Thus, the probability of selecting a team of 5 girls and 5 boys [tex]=\frac{126}{286}= \frac{63}{143}[/tex] or [tex]0.4405...[/tex]
You invest $2000 in an account at 4.5% per year simple interest. How much will you have in the account at the beginning of the 8th year? Round your answer to the nearest whole dollar.
A. $2560
B. $2640
C. $2720
D. $2630
answer is 2720
solution below
First, converting R percent to r a decimal
r = R/100 = 4.5%/100 = 0.045 per year.
solving our equation:
A = 2000(1 + (0.045 × 8)) = 2720
A = $2,720.00
the total amount accrued, principal plus interest, from simple interest on a principal of $2,000.00 at a rate of 4.5% per year for 8 years is $2,720.00
a small of pretzels costs $0.99 and contains 4 ounces. A large bag of pretzels costs $2.99 and contains 15 ounces. Which is the better buy
The large bag of pretzels is the better buy as it has a lower cost per ounce at $0.1993 compared to $0.2475 per ounce for the small bag.
To determine which bag of pretzels is the better buy, we need to calculate the cost per ounce for each bag. For the small bag, we divide $0.99 by 4 ounces to get the cost per ounce. For the large bag, we divide $2.99 by 15 ounces to find its cost per ounce. Once we have both costs per ounce, we can compare them to see which bag offers the lower cost per ounce and hence the better value.
For the small bag:
$0.99 / 4 ounces = $0.2475 per ounce
For the large bag:
$2.99 / 15 ounces = $0.1993 per ounce
Comparing the two, we can see that the large bag of pretzels offers a lower cost per ounce and is therefore the better buy.
Help!
"Stacy is planting a vegetable garden. She has 27 tomato plants, 45 bean plants, and 54 carrot plants. Stacy wants each row of her garden to have the same number of each type of plant. What is the greatest number of rows that Stacy can have if she wants to use all of her plants? How many of each type of plant will she have in each row?"
To determine the number of rows and the number of each type of plant Stacy can have, we need to find the greatest common factor (GCF) of the plant counts. The GCF represents the number of plants in each row. The GCF of 27, 45, and 54 is 9, so Stacy can have 9 rows with 3 tomato plants, 5 bean plants, and 6 carrot plants in each row.
Explanation:To determine the greatest number of rows that Stacy can have in her vegetable garden while still using all of her plants, we need to find the greatest common factor (GCF) of the numbers 27, 45, and 54. The GCF will represent the number of plants Stacy can have in each row.
First, we can find the GCF of 27 and 45 by listing their factors:
27: 1, 3, 9, 27
45: 1, 3, 5, 9, 15, 45
The greatest common factor of 27 and 45 is 9.
Next, we find the GCF of 9 and 54:
9: 1, 3, 9
54: 1, 2, 3, 6, 9, 18, 27, 54
The greatest common factor of 9 and 54 is 9.
Therefore, Stacy can have 9 rows in her garden, and each row will have 3 tomato plants, 5 bean plants, and 6 carrot plants.
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solve the proportion t+4 / t-2 = 1/4
t+4 / t-2 = 1/4
t=-6 for your answer!
What is 41/6 simplified into 12
41/6 = - 41/6 = - 6 5/6 = - 6.833333333333; Result written as a negative improper fraction, a mixed number (also called a mixed fraction) and a decimal number. Ordinary (simple, common) math fraction reducing to lowest terms (simplifying), answer with explanations below.
I believe it is 5/6 but I am not sure
what is 936,292 rounded to the nearest hundred thousand
To round 936,292 to the nearest hundred thousand, you look at the ten thousand place. Since it's 3, which is less than 5, 936,292 rounds down to 900,000.
To round 936,292 to the nearest hundred thousand, we need to look at the ten thousand digit, which is 3. Since this number is less than 5, we do not round up the hundred thousand digit. Therefore, 936,292 rounded to the nearest hundred thousand is 900,000.
Rounding to the nearest hundred thousand means replacing all the digits to the right of the hundred thousand place with zeros. If the digit in the ten thousand place is five or higher, we add one to the hundred thousand digit. If it's lower than five, we keep the hundred thousand digit the same.
Tawny is grocery shopping and needs broccoli and cauliflower for a recipe she is making for dinner. Broccoli is $1.05 per pound and cauliflower is $0.76 per pound. She knows she wants to spend exactly $10 on veggies. If b represents pounds of broccoli and c represents pounds of cauliflower, which equation represents this situation?
A) 1.05c + 0.76b = 10
B) 1.05b + 0.76c = 10
C) 1.81v = 10
D) b + c = 10
Well I think that the answer is B because if you add all those up you'll get ten.
The equation that represents this situation is 1.05c + 0.76b = 10.
Explanation:The equation that represents this situation is option A, which is 1.05c + 0.76b = 10.
To understand why this is the correct equation, let's break it down. The equation represents the total cost of the broccoli and cauliflower Tawny needs to buy. The cost of broccoli is given as $1.05 per pound, so we multiply this cost by the number of pounds of broccoli (b) Tawny wants to buy. Similarly, the cost of cauliflower is given as $0.76 per pound, so we multiply this cost by the number of pounds of cauliflower (c) Tawny wants to buy. The sum of these two costs should be equal to $10, which is Tawny's desired spending amount.
32,111÷181=
whats is the remainder
The answer would be 177.4
The division of 32,111 by 181 gives a quotient of 177 and a remainder 104. In essence, when 32,111 is divided by 181 completely, there is left an undivided 104.
Explanation:In Mathematics, to determine the remainder of a division problem, you perform the division operation as usual and then observe the residual value. That residual value is the remainder. In your case, when 32,111 is divided by 181, the result is 177 with a remainder of 104. Therefore, the answer to your question '32,111 ÷ 181, what is the remainder?' is 104, this is the amount that can't be evenly divided over 181. It is known as the remainder of the division operation.
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How do you write 0.326 in expanded form
[tex]0.000+0.300+0.020+0.006[/tex] is the expanded form of 0.326
(2 x 10000000) + (0 x 1000000) + (7 x 100000) + (6 x 10000) + (9 x 1000) + (0 x 100) + (3 x 10) + (3 x 1)
Determine if the pair of ratios or rates are equivalent.
$18 for 3 bracelets ; $30 for 5 bracelets
Are these equivalent yes or no
Answer:
yes they are equivalent
May I get some help please?
See the attached picture:
Shane deposited $200 into an account and earned $36 in interest after 3 years. Use the formula I = prt, where I represents simple interest, p represents principal, r represents interest rate, and t represents time in years. What is the interest rate?
Answer:
The interest rate = 6 %
Explanation:
We have I = prt, where I represents simple interest, p represents principal, r represents interest rate, and t represents time in years.
Here principal, p = 200 $
Number of years , t = 3
Interest received, I = 36$
We need to find rate of interest.
Substituting
36 = 200 x r x 3
r = [tex]\frac{36}{200*3}[/tex]= 0.06 = 6%
The interest rate = 6 %
Answer:20%
Step-by-step explanation:
Let r represent rate of interest.
We have been given that Mika invested $200 into a certificate of deposit. After 6 months, the balance was $220.
We will use simple interest formula to solve our given problem.
I = Amount of interest,
P = Principal amount,
r = Rate of interest in decimal form,
t = Time in years.
First of all, we will find amount of interest by subtracting $200 from $220 as:
6 month = 1/2 year = 0.5 year
Upon substituting our given values in simple interest formula, we will get:
Upon dividing both sides by $100, we will get:
Since interest rate is given in decimal, so we will multiply 0.2 by 100 to convert our answer in percentage.
Therefore, the interest rate on the deposit was 20% and option B is the correct choice.
Which expression is the completely factored form of x6−64y3 ?
Answer:
(x^2 - 4y)( x^4 + 4x^2y + 16y^2)
Step-by-step explanation:
x^6−64y^3
- using the identity a^3 - b^3 = (a - b)(a^2 + ab + b^2) with a = x^2 and b = 4y we have:-
(x^2 - 4y)( x^4 + 4x^2y + 16y^2)
Factored form of x6−64y3 is (x^2-4y)(x^2+2xsqrt(y)+4y)(x^2-2xsqrt(y)+4y)
What is factorisation?
The process of factorisation involves dividing mathematical algebraic formulas into the sum of their factors. When the factors are multiplied once more, the original phrase is obtained.#x^6-64y^3#
#=(x^2)^3-(4y)^3#
#=(x^2-4y))(x^4+4x^2y+16y^2)#
#=(x^2-4y)[(x^2)^2+(4y)^2+4x^2y)]#
#=(x^2-4y)[(x^2+4y)^2-2*x^2*4y+4x^2y)]#
#=(x^2-4y)[(x^2+4y)^2-8x^2y+4x^2y)]#
#=(x^2-4y)[(x^2+4y)^2-(2xsqrt(y))^2]#
#=(x^2-4y)(x^2+2xsqrt(y)+4y)(x^2-2xsqrt(y)+4y)#
The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.Finding the roots of a quadratic equation includes factorization of quadratic equations. In order to factor a quadratic equation, the given quadratic expression must be transformed into the product of two linear factors.To learn more about factorisation refer to:
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Which is a definition of a ray
A point extending forever in one direction
A ray is a portion of a line which starts at a point and goes off in a particular direction to infinity.
In which quadrant does the point (-4,15) lie
The point (-4,15) is found in the second quadrant, where x-values are negative (here, -4) and y-values are positive (here, 15) in the Cartesian coordinate system.
The point (-4,15) lies in the second quadrant of the Cartesian coordinate system. In the second quadrant, the x-coordinate is negative and the y-coordinate is positive. This is because the Cartesian coordinate system is divided into four quadrants based on the signs of the x (horizontal) and y (vertical) values: Quadrant I (positive x, positive y), Quadrant II (negative x, positive y), Quadrant III (negative x, negative y), and Quadrant IV (positive x, negative y).
what Is the square root of 9
the square root of 9 would be 3. as 3 x 3 =9
the square root of any number is asking what number times itself will give you the given number you are trying to square root. for example, the square root of 36 would be 6, as 6 x 6 = 36. I hope this helped
Doing a square root of one digit numbers is just multiplying by 2 so 18 is your answer.
A rectangle has an area of 364.5cm^2 if it’s length is 27 cm find its perimeter
When, a rectangle has an area of 364.5cm² if it’s length is 27 cm. Then, the perimeter of the rectangle is 81 cm.
To find the perimeter of a rectangle when the area and the length are known, first calculate the width using the area formula. The area of a rectangle is given by the formula Area = length x width. Given that the area is 364.5 cm² and the length is 27 cm, the width can be found as follows:
Width = Area / Length = 364.5 cm² / 27 cm = 13.5 cm
Once you have both the length and width, the perimeter can be calculated using the formula Perimeter = 2 x (length + width). So, the perimeter would be:
Perimeter = 2 x (27 cm + 13.5 cm) = 2 x 40.5 cm = 81 cm
Hence, the perimeter of the rectangle is 81 cm.
Which graph represents the equation y = 3/4x - 3
In the equation y = 3/4x -3, 3/4 is the slope and -3 is the y-intercept. To graph this, start at -3 on the y-axis, then for each increase of 1 in the x direction, go up by 3/4 in the y direction, drawing a line through these points.
Explanation:The equation y = 3/4x - 3 represents a straight line in mathematics. The first step to getting your graph is to understand the equation structure: y = mx + b, in which 'm' is the slope and 'b' is the y-intercept. Hence, in your equation the slope is 3/4 and the y-intercept is -3. When x = 0, y will be -3. This is your starting point on the graph.
To construct the graph of this equation, you'd use the slope (3/4), which means to every 1 unit increase in 'x', 'y' will increase by 3/4 units. Start at your y-intercept (-3), then rise 3 units and run 4 units to the right to plot your next point. Continue this until you have a several points. Once you have enough points, you can draw a line through them to represent the equation y = 3/4x - 3.
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choose the letter corresponding to the best answer which is a true statment
-10 > -2
Hope this helped hun
- Laura <3
i have a math question it is... what is g - 3/7 = 2/7 ?
g - 3/7 = 2/7 is an equation.
[tex]\displaystyle\bf\\g-\frac{3}{7}=\frac{2}{7}\\ \\g=\frac{2}{7}+\frac{3}{7}=\frac{2+3}{7}=\frac{5}{7}\\\\\boxed{\bf g=\frac{5}{7}}[/tex]
What type of number is 52i+7.5?
Real
Pure imaginary
Complex
Answer:
Complex looking (not mathematical term)... I think it's real?
52i + 7.5 = 59.5i
(I'm probably wrong)
Step-by-step explanation:
Answer:
complex
Step-by-step explanation:
solve 4x+x+4=8x-3x+4. Does this equation have one solution, no solution or infinitely many solutions?
One Solution: Simplify to get 5x+4=5x+4
The equation 4x + x + 4 = 8x - 3x + 4 has infinitely many solutions.
How to determine the solution to the equationTo solve the equation 4x + x + 4 = 8x - 3x + 4, we first simplify both sides
5x + 4 = 5x + 4
Next, we subtract 5x from both sides:
4 = 4
Since the equation simplifies to a true statement (4 = 4), this means that the equation is true for any value of x.
Hence, the equation has infinitely many solutions.
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Choose the correct equation in point-slope form for the line that passes through the point with the given slope.
(2, -1), m = -3
A) y + 1 = 3x - 6
B) y - 1 = -3x + 2
C) y - 2 = -1 [ x - (-3)]
D) y - 1 = -3 (x + 2)
E) y + 1 = -3 (x - 2)
Answer:
E) y + 1 = -3 (x - 2)
Step-by-step explanation:
y-y1=m(x-x1)
Use this equation to solve a question like this. Just plug in the numbers you have to get the equation.
Bob is driving along a straight and level road toward a mountain. At some point on his trip, he measures the angle of elevation to the top of the mountain and finds it to be 23°29'. Find the height of the mountain to the nearest foot if Bob is 16,194.6 feet from the center of the mountain at the base.
Final answer:
To find the height of the mountain, the tangent of the angle of elevation is multiplied by the distance to the base of the mountain. With an angle of 23°29' and a distance of 16,194.6 feet, the height of the mountain is approximately 7,026 feet.
Explanation:
To find the height of the mountain when Bob is 16,194.6 feet from the mountain's base and the angle of elevation is 23°29', we can use trigonometry, specifically the tangent function which is the ratio of the opposite side to the adjacent side in a right triangle.
Steps to Solve:
Convert the angle 23°29' to decimal degrees: 23° + 29'/60 = 23.483°.
Use the tangent function: tan(angle) = opposite side/adjacent side, where the adjacent side is the distance from Bob to the base of the mountain and the opposite side is the height of the mountain.
Calculate the height: height = tan(angle) * distance to the base.
Substitute the known values and solve: height = tan(23.483°) * 16,194.6 feet.
Using a calculator, tan(23.483°) ≈ 0.4338. Multiplying this by 16,194.6 gives us approximately 7026.03668 feet.
Therefore, the height of the mountain to the nearest foot is 7,026 feet.
A laboratory technician needs to make a 117-liter batch of a 20% acid solution. How can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 10% to get the desired concentration?
Given
A laboratory technician needs to make a 117-liter batch of a 20% acid solution.
How much the technician combine an acid solution that is pure acid with another that is 10% to get the desired concentration.
To proof
let us assume that the solution that is pure acid = x liters
let us assume that the anthor solution that is 10% = y liters
Than
the equation becomes
x + y = 117
As given in the question
technician needs to make a 117-liter batch of a 20% acid solution
laboratory technician combine an acid solution that is pure acid with another that is 10% to get the desired concentration
Convert 20% in the simpler form
[tex]=\frac{20}{100}[/tex]
= 0.2
Convert 10% in the simpler form
[tex]=\frac{10}{100}[/tex]
= 0.1
Than the equation becomes
0.2 × 117 = x + 0.1y
234 = 10x + y
Than the two equation are
x + y = 117
234 = 10x + y
subtracted x + y = 117 from 234 = 10x + y
10x+y -x -y = 234 -117
9x = 117
x= 13
put this in the equation x + y = 117
13 + y =117
y = 117 - 13
y = 104
Therefore
The solution that is pure acid be 13 liters.
than the other solution that is 10% is 104 liters.
Hence proved
Please Help <3 Please Help <3
evaluate (1/4) to the power-2 -(5 to the power of 0 .2).1 to the power -2
Solution
[tex](\frac{1}{4} )^{-2} - 5^{0.2} .1^{-1}[/tex]
Using the exponents rule, we get
[tex]4^{2} - 1.38 . 1[/tex]
= 16 - 1.38
= 14.62
The answer is 14.62
Thank you.
Answer: It is just 14 !!!
Step-by-step explanation: when taking a test you just right it as 14.
Write an expression that shows how you can multiply 9x475 using expanded form and Distributive property
To write an expression that shows 9 * 475 multiply using expanded form an distributive property we break 475 into three numbers
475 can be break into 400 + 70 + 5
Now we multiply by 9
9 x 475
9 x (400 + 70 + 5) (expanded form of 475)
We use distributive property here.
We distribute 9 inside the parenthesis
9 x 400 + 9 x 70 + 9 x 5
3600 + 630 + 45
4,275
a jet airplanes hose about 65,000 gallons of gas he uses about 7460 gallons when flying between New York City and Los Angeles. Round each number to the largest place value then find about how many trips the plane can take between cities before running out of fuel
8 trips the plane can take between cities before running out of fuel.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Given that,
Total gas available 65000 gallons round down as 60000
Gas is consumed between New York and Los Angeles = 7460 round-up as 7000
The number of trips from New York and Los Angeles = 60000/7000 = 8.57.
Since the number of trips should be a whole number so 8 will be the correct answer.
Hence "8 trips the plane can take between cities before running out of fuel".
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0.001 rewritten as a square or a cube
0.001 = 1 thousandth = 1/1000
We can write 1000 as 10^3. Note how 1000 has 3 zeros and the exponent for 10^3 is 3
So, 1/1000 = 1/(10^3) = (1/10)^3 = (0.1)^3
Therefore, 0.001 = (0.1)^3
0.001 rewritten as a cube = (0.1)³.
What is meant by Cube?Cube values are the results of multiplying a number by itself three times. Cubes can be found for any number, whether an integer or a fraction. A whole number's cube (x) yields a perfect cube ( x³), and the cube root of x³ yields x once more.A cube number is essentially a number formed by multiplying three identical numbers together. The volume of a cube is the best example of a cube number in geometry.A cube's volume is equitable to a³, where a = length + height + width. This means that the volume of a cube is a cube number.To cube a number, simply multiply it by itself twice. This applies to all numbers.Given,
0.001 can written as
0.001 = 1/1000
We can write 1000 as 10³.
Note how 1000 has 3 zeros and the exponent for 10³ is 3
So,
1/1000 = 1/(10³) = (1/10)³ = (0.1)³
Therefore, 0.001 = (0.1)³
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