A box contains 42 red counters, 90 yellow counters and no other counters.
A group of students share these counters between them so that they each receive the
same number of red counters and the same number of yellow counters.
There are no counters left over,
How many students could be in the group?
Give all possible answers and show your reasoning.

Please help

Answer:

36

Step-by-step explanation:

Answer:

(6)⁷/(6)⁵ = 6²

Step-by-step explanation:

Given problem,

→ (6)⁷/(6)⁵

Let's solve the problem,

→ (6)⁷/(6)⁵

→ 279936/7776

→ 36 = 6²

Thus, the answer is 6².

Answer:

the answer is D

Step-by-step explanation:

Answer: Yes

Step-by-step explanation:

x = 3

y = -7

10x + 20y ≥ -3

10 (3) + 20 (-7) ≥ -3

30 + (-140) ≥ -3

30 - 140 ≥ -3

-110 ≥ -3

(3, 7) is a solution

To produce 200 watts of power, the speed of wind must be about 11 miles per hour for the windmill.

The relationship between power generated by a windmill and wind speed can be expressed as:

P = k * V^3

where P is the power generated in watts, V is the wind speed in miles per hour, and k is the variation constant.

We are given that k = 0.15, and we need to find the wind speed V that produces 200 watts of power. We can solve for V as follows:

200 = 0.15 * V^3

V^3 = 200 / 0.15

V^3 = 1333.33

V = (1333.33)^(1/3)

V ≈ 10.68

Rounding to the nearest mile per hour gives a wind speed of 11 miles per hour. Therefore, the wind needs to be blowing at about 11 miles per hour for the windmill to produce 200 watts of power.

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Answer:

me either

Step-by-step explanation:

Answer:

will your self

Step-by-step explanation:

................................

Answer:

answers rounded to the nearest tens: 1730, 480, 4832720, and 130.

The solution of inequality 3x + 12 – 6x ≤ –9 will be greater than or equal to 7.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

3x + 12 – 6x ≤ –9

Simplify the equation, then the value of 'x' is calculated as,

3x + 12 – 6x ≤ –9

6x – 3x ≥ 12 + 9

3x ≥ 21

x ≥ 21 / 3

x ≥ 7

The solution of inequality 3x + 12 – 6x ≤ –9 will be greater than or equal to 7.

The solution is shown on the number line.

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Answer:

6

Step-by-step explanation:

2+5=7

21/7=3

2 x 3=6

The ratio is 6:15

The number of chefs is 6

Answer:

D, X^2 -18 + 81 = -45 + 81

Step-by-step explanation:

it is complating squer method that used for solving x in a quadratic equetion . in this step you will add

(y/2)^2 if y is the cofitient of x .

In both cases, the given sets of values represent a function, and the domain is all real numbers. The range consists of the distinct output values in each set

Let's analyze each of the given sets of values to determine if they represent a function or not, and if so, state their domain and range.

6, 4, 2, -6-

Function: Yes

Domain: There are no restrictions on the input values, so the domain is all real numbers.

Range: The range consists of the distinct output values, which in this case are 6, 4, 2, and -6. Therefore, the range is {6, 4, 2, -6}.

Function? Yes

Domain: There are no restrictions on the input values, so the domain is all real numbers.

Range: The range consists of the distinct output values, which are 2, 4, and 6. Therefore, the range is {2, 4, 6}.

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Using the given value numbers, we can represent the number as 203,167.

To represent the given number using the value numbers 3, 80, 7, 30, 200,000, 3,000, and 50, we need to understand the place value system. In this system, each digit's position determines its value relative to the other digits in the number.

Let's break down the given value numbers:

3 represents the digit 3.

80 represents the digit 8 in the tens place and 0 in the ones place.

7 represents the digit 7.

30 represents the digit 3 in the tens place and 0 in the ones place.

200,000 represents the digit 2 in the hundred thousands place and all other digits as zeros.

3,000 represents the digit 3 in the thousands place and all other digits as zeros.

50 represents the digit 5 in the tens place and 0 in the ones place.

Now let's combine these value numbers to form a single number:

(200,000) + (3,000) + (80) + (30) + (7) + (50)

To simplify this expression, we can add up each component:

200,000 + 3,000 + 80 + 30 + 7 + 50 = 203,167

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The vectors u1 = (1, 1/2, 0) and u2 = (0, 0, 1) span the set p. Any vector in p can be written as a linear combination of u1 and u2.

To find two vectors, u1 and u2, such that the span of {u1, u2} is equal to the set p = {(x1, x2, x3) : 2x1 − x2 + 4x3 = 0}, we can solve the equation 2x1 − x2 + 4x3 = 0 and express the solution in terms of vectors.

First, we rewrite the equation as a linear combination:

2x1 − x2 + 4x3 = 0

x1 = (1/2)x2 - 2x3

Now we can express the solution as:

(x1, x2, x3) = (1/2)x2(1, 1/2, 0) + (-2)x3(0, 0, 1)

Therefore, the vectors u1 = (1, 1/2, 0) and u2 = (0, 0, 1) span the set p. Any vector in p can be written as a linear combination of u1 and u2.

The vector u1 = (1, 1/2, 0) represents a point in the plane where x1 and x2 are related by the equation 2x1 − x2 + 4x3 = 0. The vector u2 = (0, 0, 1) represents a point in the plane where x3 can take any value. Together, u1 and u2 span the entire plane defined by the equation. Any point (x1, x2, x3) in the plane p can be expressed as a linear combination of u1 and u2

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Answer:

domain is basically x and range is y, so -2,5    -2 is domain and 5 is range

Step-by-step explanation:

Answer:

the answer is 0.1km

Step-by-step explanation:

Answer:

The amount Dan will recieve after 5 years is:

1200*(1+5%)^5

=1532,correct to nearest penny

Yes, you can use the statement as a question to the knowledge base to inquire about the color of apples in the base.

Specifically, the question seeks to confirm whether all apples in the knowledge base are either red or green.
1. Review the knowledge base to identify all statements related to apples.
2. Examine each statement to determine if it contains information about the color of the apples.
3. Check if the color mentioned in each statement is either red or green.
4. If all the relevant statements in the knowledge base confirm that apples are either red or green, then the answer to your question is "yes." Otherwise, the answer is "no."
In this process, the terms "knowledge," "statement," and "red or green" are used to analyze the information stored in the knowledge base and draw a conclusion about the colors of apples.

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Answer:

The distance between the two points is

Exact form:

√41

Decimal form:

6.40312423.......

Have a wonderful day!!!

Answer:

children = 87 ; adults = 366

Step-by-step explanation:

a + c = 453

2.25a + 1.25c = 932.25

a = 453 - c

2.25(453 - c) + 1.25c = 932.25

1019.25 - 2.25c + 1.25c = 932.25

-c = 932.25 - 1019.25

-c = -87

c = 87

a = 453 - 87

a = 366

If you invest $100 at an interest rate of 15%, you will have $264.22 at the end of eight years.

Step 1: Identify the principal, interest rate, and number of years
Principal: $100
Interest rate: 15% (0.15 in decimal form)
Number of years: 8

Step 2: Calculate the future value using the compound interest formula
The formula for compound interest is:
Future Value = Principal * (1 + Interest Rate) ^ Number of Years

Step 3: Plug the values into the formula
Future Value = $100 * (1 + 0.15) ^ 8

Step 4: Perform the calculations
Future Value = $100 * (1.15) ^ 8
Future Value = $100 * 2.64224 (rounded to 5 decimal places)
Future Value = $264.22 (rounded to 2 decimal places)

So, if you invest $100 at an interest rate of 15%, you will have $264.22 at the end of eight years.

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Answer:

0.21212121212121

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(\large\text{In order to convert a fraction to decimal, you have to DIVIDE the}\\\large\text{numerator (the TOP number) from the denominator (the BOTTOM}\\\large\text{number) \& you should be able to find the answer if you did the}\\\large\text{the equation right. }\)

\(\large\text{Converting fraction to a decimal formula is:}\)

\(\rm{\dfrac{a}{b}}\\\\\rm{= a \div b}\\\\\rm{= decimal\ form}\)

\(\large\text{Solving for the current equation:}\)

\(\large\boxed{\rm{\dfrac{21}{99}}}\\\\\\\large\boxed{\rm{= 21\div 99}}\\\\\\\large\boxed{\rm{= 0.212121}}\)

\(\huge\text{Therefore, your answer is: \boxed{\mathsf{0.212121}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

1 : 2

Step-by-step explanation:

The original ratio would be 3 : 6, so now you need to simplify it.

To simplify ratios, you divide the number on each side by their greatest common factor. The GCF(greatest common factor) for 3 and 6 would be 3, so divide 3 by 3 =1 and divide 6 by 3 =2, so then your simplified ratio of circles to triangles would be 1 : 2

Hope this helps! :)

The correct formula for the expression is,

⇒ f (x)  = - 6 cos (π/4.5x - 2π) + 2

Since, Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have a function:

f(x) = a cos(bx + c) + d

Here a is the amplitude:

Since, The value of d is the average of maximum and minimum.

Hence,  d = (9 - 5)/2 = 4/2 = 2

And, The value of 'a' is the difference between the maximum value and d.

Hence,  a = -4 -(2) = - 6

Here, the half-period is,

= π - 3π/4) = π/4

=  b = 2π/9 = π/4.5

The value of c is the value makes the cosine zero at x= 9

⇒  (π/4.5)(9) +c = 0

⇒  c = -2π

Hence, Function is,

f (x) = - 6 cos (π/4.5x - 2π) + 2

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Answer:

The correct answer would be:

f (x) = - 6 cos (π/4.5x - 2π) + 2

The minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.

In the question, we are asked to use Lagrange multipliers to find the minimum distance between the origin and the plans 3x + y + 2z = 28.

Lagrange multipliers state that if we want to minimize a function, f(x, y, z), subject to a constraint g(x, y, z) = constant, then ∇f = λ∇g.

We want to minimize the distance, and the distance formula says that the distance from the origin to a point (x, y, z), is given as:

D = √(x² + y² + z²), which can also be shown as:

D² = x² + y² + z².

The gradient of this function is: (2x + 2y + 2z), which needs to be equal to the gradient of the constraint equation multiplied by the constant, λ, that is, λ(3, 1, 2), which gives:

2x = 3λ, or, x = (3/2)λ,

2y = λ, or, y = λ/2, and,

2z = 2λ, or, z = λ.

Substituting these in the equation of the plane, 3x + y + 2z = 28, we get:

3(3/2)λ + λ/2 + λ = 28,

or, 6λ = 28,

or, λ = 28/6 = 14/3.

Thus, we get:

x = (3/2)λ = 7,

y = λ/2 = 7/3, and,

z = λ = 14/3.

Substituting these in the distance formula, we get:

D = √(7² + (7/3)² + (14/3)²) = √(49 + 49/9 + 196/9) = √(686/9) = 8.73.

Thus, the minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.

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