A radioactive compound with mass 320 grams decays at a rate of 27% per hour. Which equation represents how many grams of the compound will remain after 7 hours?

Answer:

Step-by-step explanation:

1. Substitute the number for the variable in the equation.

The table with values for x or y that make this equation true : 3x + y = 15 are

x       2     4      6      0      3      5      7/3

y       9     3     -3     15      6     0       8      

What is solving an equation?

One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side.

Consider, the given equation: 3x + y = 15

We have to complete the given table for the values of x and y.

Plug x = 2 in the given equation.

⇒  3(2) + y = 15

        6 + y = 16

              y = 9

Plug y = 3  in the given equation.

3x + 3 = 15

     3x = 12

       x = 4

Plug x = 6  in the given equation.

3(6) + y = 15

 18 + y = 15

        y = -3

Plug x = 0  in the given equation.

3(0) + y = 15

         y = 15

Plug x = 3  in the given equation.

3(3) + y = 15

  9 + y = 15

        y = 6

Plug y = 0  in the given equation.

3x + 0 = 15

     3x = 15

       x = 5

Plug y = 8  in the given equation.

3x + 8 = 15

3x = 7

x = 7/3

Hence, the table with values for x or y that make this equation true : 3x+y=15 are

x       2     4      6      0      3      5      7/3

y       9     3     -3     15      6     0       8      

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Answer:

Step-by-step explanation: We will determine if ratios are proportional using cross multiplication.

first, we will check option (a)

12/15 =5/4

12*4 = 15*5

48 is not equal to 75. So, these are not proportional.

now, we will check option (b)

15/12 = 5/4

15*4 = 12*5

60 = 60.

as the left-hand side is equal to the right-hand side.

So, option (b) is correct.

Answer:

[tex]\textsf{B)} \quad \dfrac{15}{12}\; \textsf{and}\;\dfrac{5}{4}[/tex]

Step-by-step explanation:

If two fractions are equal, they form a proportion.

Therefore, to determine if two ratios form a proportion, rewrite the fractions so that their denominators are the same, then compare.

[tex]\textsf{A)}\quad \dfrac{12}{15}\; \textsf{and}\;\dfrac{5}{4} \implies \dfrac{12 \times 4}{15\times 4}\; \textsf{and}\;\dfrac{5\times 15}{4\times 15}\implies \dfrac{48}{60}\; \textsf{and}\;\dfrac{75}{60}[/tex]

As the two fractions are not equal, they do not form a proportion.

[tex]\textsf{B)} \quad \dfrac{15}{12}\; \textsf{and}\;\dfrac{5}{4}\implies \dfrac{15}{12}\; \textsf{and}\;\dfrac{5 \times 3}{4 \times 3}\implies \dfrac{15}{12}\; \textsf{and}\;\dfrac{15}{12}[/tex]

As the two fractions are equal, they form a proportion.

[tex]\textsf{C)} \quad \dfrac{6}{5}\; \textsf{and}\;\dfrac{4}{5}[/tex]

The denominators of these two fractions are already the same.

Therefore, as the two fractions are not equal, they do not form a proportion.

[tex]\textsf{D)} \quad \dfrac{5}{6} \; \textsf{and}\;\dfrac{4}{5}\implies \dfrac{5\times 5}{6\times 5} \; \textsf{and}\; \dfrac{4\times 6}{5\times 6}\implies \dfrac{25}{30}\; \textsf{and}\;\dfrac{24}{30}[/tex]

As the two fractions are not equal, they do not form a proportion.

Answer: A problem is said to be intractable if there is no efficient algorithm to solve it.

Intractable problems are common. We need to discuss how we approach it when we actually encounter it.

Step-by-step explanation:

How many colours do you need to colour a graph such that no adjacent vertices are of the same colour showed in the image below?

Conclusion : Provided the graph with a large number of vertices, we see that we are again faced with resorting to a systematic tracing of all paths, comparison of the neighbour's colours, backtracking, etc resulting in exponential time complexity once again.

Answer: 6.2

Step-by-step explanation:

The equation 2x + 3y = 5 has one real solution.

To find it, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable.

For example, you can solve for y to get y = (5 - 2x)/3, and then substitute this into the equation to get 2x + 3((5 - 2x)/3) = 5, which you can then solve for x. Doing this will give you x = 5/4, which means that the solution is (5/4, 5/3).

Linear equations are equations that involve two variables and can be expressed in the form ax + by = c, where a and b are constants and x and y are the variables. These equations have one real solution, which can be found by solving for one of the variables and then substituting the result into the equation to find the other variable. Once both variables are known, the solution to the equation is the point (x,y) that satisfies both equations.

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Answer:

I have graphed a line with a slope of 3/5 and attached a screenshot in the explanation.

Step-by-step explanation:

Based on the 2:5 quantity of concentrate and water, the amount of water required for 90 mililitres will be 225 mililitres of water.

Firstly we will be creating the ratio for the mentioned information. It will be as follows-

Amount of concentrate/Amount of water

The proportion will be -

2/5 = 90/Concentration of water

Concentration of water = 90×5/2

Now perform multiplication in numerator on Right Hand Side of the equation

Concentration of water = 450/2

Then work out the division on Right Hand Side of the equation

Concentration of water = 225 mililitres

Thus, the required amount of water is 225 mililitres.

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The sum of 8.8 and 5.5 is 14.3

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

To find the sum of 8.8 and 5.5 without using pen and pencil:

First, we break the term in simple manner.

8.8 = 8 + 0.3 + 0.5

And 5.5 = 5 + 0.5

And now adding the terms one by one,

0.5 + 0.5 = 1.0

0.3 = 0.3

8 + 5 = 13

Addition,

13 + 1 + 0.3 = 14.3

Therefore, the value is 14.3

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The difference between the population means - 3.4 and -1.84 when calculated is found to be -2.62 years.

The 95% confidence interval for the difference in true mean ages of cars owned by students and faculty is between -3.4 and -1.84 years.

We know that the sample of 138 cars which belongs to the students have an average age of 5.13 years. The standard deviation = 3.45 years.

Then again,

A sample of 111 cars which belongs to the faculty have an average age of 7.75 years.  The standard deviation= 2.08 years.

So the difference between them will be , s - f

= 3.45 - 2.08 = 1. 37

and the mean will be , mean of students - mean of faculty =

-2.62.

This is the point of difference between their means.

The SD is found to be as 0.3961.

and MOE is 0.78

with these details now we will calculate the required intervals,

The lower end is found to be as  -2.62 - 0.78 = -3.4

The upper end is found to be as  -2.62 + 0.78 = -1.84

Therefore, the mean difference between the cars is - 3.4 and -1.84.

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The equation is (5 x 2) - (5 + 5) = 20

The given equation can be solved by performing the operations within the parentheses first.

First, 5 x 2 = 10, then 5 + 5 = 10.

Then, the next step is to subtract the second set of parentheses from the first set, 10 - 10 = 0.

Finally, we can see that 0 + 20 = 20.

In this equation, the operation of multiplication and addition are used and the final value is 20.

The equation is (5 x 2) - (5 + 5) = 20

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Complete Question is -

solve the following mathematical operation that involves parentheses, five numbers, two different operations and has a value of 20?

2(l+w) + 4a and 2l+2w + 2(2a) are two equivalent expressions which represent the total fencing material required to surround the playground and flower beds.

Mathematical expressions are a way of representing mathematical ideas, concepts, and operations using symbols and notation. They can take many forms, including numbers, variables, and operators. They can also be combined to create more complex expressions, equations, and formulas.

Explain:

The total fencing material required to surround the playground and flower beds would be the sum of the fencing material for the playground and the fencing material for the flower beds.

So, one possible expression for the total fencing material required to surround the playground and flower beds would be: 2(l+w) + 4a

Another possible expression for the total fencing material required to surround the playground and flower beds would be: 2l+2w + 2(2a)

Please note that these expressions are based on the information provided, and the actual total fencing material required will depend on the specific dimensions of the park and playground, and may differ from these expressions.

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The missing sides of the triangle can be found by applying the Pythagoras Theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that square of  hypotnuse (that is longest side) is equal to sum of the square of perpendicular and base .

that means : [tex]Hypotnuse^{2} = Perpendicular^{2} +Base^{2}[/tex]  ;

let missing side of the Right triangle be hypotnuse ;

So , missing side is written as : [tex]Hypotnuse = \sqrt{Perpendicular^{2} +Base^{2}}[/tex] .

For Example : Let a right triangle has sides lengths of perpendicular = 6 and hypotnuse = 10 .

let , the length of side "base" be unknown.

So ,  in order to find length of side b  (base) , we substitute the  known values into Pythagoras theorem:

[tex]10^{2} =6^{2} +Base^{2}[/tex] ;

[tex]Base = 100-36[/tex] ;

So , missing side "base" is = 8 ;

Therefore , the missing side can be found by using  the Pythagoras Theorem .

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multiple 5x 3 3/4 then change to an improper fraction

The domain is all values of x that makes the expression defined.

Set-Builder Notation: {x| x ≤ 3 }

Interval Notation: (-∞,3]

Given the function in the question;

y = 5√(6−2x)​

To find the domain, set the radicand greater than or equal zero and solve for x.

6 - 2x ≥ 0

Subtract 6 from both sides

6 - 6- 2x ≥ 0 - 6

-2x ≥ -6

Divide both sides by -2

-2x/-2 ≤ -6/-2

x ≤ -6/-2

x ≤ 3

Therefore, the domain is;

Set-Builder Notation: {x| x ≤ 3 }

Interval Notation: (-∞,3]

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The polynomial 5x³ 4x² 7x has three terms, with the highest degree being 3, which makes the degree of the polynomial 3. The polynomial can be written as 5x³ + 4x² + 7x.

1. Identify the polynomial: 5x³ + 4x² + 7x

2. Count the number of terms: 3

3. Find the highest degree (the largest exponent): 3

4. The degree of the polynomial is 3.

The degree of a polynomial is the highest degree of its terms. A polynomial is a mathematical expression consisting of one or more terms with coefficients and exponents. In this case, the polynomial is 5x³ + 4x² + 7x. This polynomial has three terms, and the highest degree is 3, which makes the degree of the polynomial 3. This means that the largest exponent of the terms is 3. To calculate the degree of a polynomial, simply count the number of terms and identify the highest degree, which is the largest exponent. If the polynomial has only one term, then the degree is the exponent of that term

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The distance in miles represented by a length on the map of 7 inches is 0.28

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

Given;

The scale of a map says that 2 inches represents 50 miles.

2 inches = 50 miles

1 Mile = 2/50 inches

Hence, 7 Mile = 7 * 2/50 inches

7 Mile = 14/50 inches

7 Mile = 0.28 inches

Therefore, the scale factor of 7miles in the map will be 0.28inches

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The mean number of rooms = 6

We know that the formula for the mean.

mean = sum of all observations / total number of observations

First we find thr total number of rooms, from given frequency table.

Number of Rooms        Frequency          Total number of rooms

           4                             4                              16

           5                             7                              35

           6                             10                            60

           7                             12                             84

           8                             5                              40

           9                             2                               18

So, the total number of rooms of 40 houses in a town would be,

16 + 35 + 60 + 84 + 40 + 18 = 253

And the total number of houses = 40

Using above formula of mean,  the mean number of rooms would be,

x = 253/40

x = 6.325

Therefore, on an average there are 6 rooms in each house.

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The 5 ways to solve problems are identifying the problem, generating different solutions, choosing one solution, implementing the chosen solution and evaluating the result.

A problem is any type of disruption from normality that is impeding progress. A problem can be time-consuming and requires too much energy to solve it.

There are 5 different steps to solving a problem

Step 1. Identify the Problem

Step 2. Generate potential solutions

Step 3. Choose one solution

Step 4. Implement the solution you’ve chosen

Step 5. Evaluate results

Sometimes it is required to start the process entirely over. To make the problem-solving process easier, it’s best to facilitate the solution as much as possible. Try to concentrate on the solution instead of the problem. Finally, be in the correct psyche to want to change. This contains having the right mindset language, both are positive and open-minded. With sufficient practice, any problem can be solved.

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Answer:

15 lessons

Step-by-step explanation:

Answer: 75p

Step-by-step explanation:

So, if one kilogram of bacon is £1.50, then half a kilogram would cost half of that, so 75p

Answer:

x = -2/4 = -1/2

Step-by-step explanation:

The sum of 4 times a number and 5 is 3.

Let sum = +

times = *

is means =

a number = x

So, 4x + 5 = 3.  Then we solve it !

Subtract 5 to both sides to get 4x = - 2.

Next, we divide 4 to both sides to get x = -2/4 = -1/2

Answer:

The number is -8

Step-by-step explanation:

You can set up the question as (x/4)+5 = 3

x/4 = -2

x = -8

Answer: -120

6 less than is 6 - and 3 times a number 42 is 3 x 42 so...

6 - (3 x 42) = -120

The correct answer is option A. For P= -1/2 0 1/2 1/2 0 -1/2 0 0 1 D= 0 4 0 0 0 4 -1 0 0. The matrix can be diagonalized using the eigenvectors.

To diagonalize the matrix, the eigenvectors must be found first. The eigenvectors can be found by solving the characteristic equation and finding the eigenvalues. The eigenvalues of the matrix are 2 and -1. The eigenvectors associated with each eigenvalue are determined by solving the eigenvalue equation.

The eigenvectors for the matrix are [1, -2], [1, 2], [1, 0], and [0, 1]. After the eigenvectors are found, the matrix can be diagonalized by constructing the transformation matrix P. The transformation matrix P is composed of the normalized eigenvectors. The transformation matrix P is: P=[-1/2, 0, 1/2, 1/2, 0, -1/2, 0, 0, 1], and the diagonal matrix D is composed of the eigenvalues.

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The value of x using Pythagorean theorem is 14.05 units

An equation shows how two or more numbers and variables are related to each other.

Pythagoras theorem shows the relationship between the sides of a right angled triangle. It is given by:

hypotenuse² = adjacent² + opposite²

In the diagram, using Pythagoras theorem:

22² = (x + 1)² + (x + 2)²

484 = x² + 2x + 1 + (x² + 4x + 4)

2x² + 6x + 5 = 484

2x² + 6x - 479 = 0

x = 14.05

The value of x is 14.05 units

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Answer:

Step-by-step explanation:

3(23-2b) + 3b = 48

1. Use the distributive property and distribute the 3 before the parenthesis

             3(23-2b)   (make sure you read the (-) as part of the 2b so it's -2b

              69 - 6b

2. 69 - 6b +3b = 48   (combine like terms...the bs: -6b + 3b)

    69 -3b=48

3. 69 - 3b = 48         (subtract 69 from both sides)

   -69           -69

4. -3b = -21      (divide both sides by negative three...we want the b to be +

   /-3    /-3

Answer: b = 7

So, C is your answer

Answer:

Step-by-step explanation:

6

2/3

15

13

Hit

Miss

2/5

3

5

215

2

Not score

Score

Find the probability that Ryan misses the target and does not score a goal,

(2 marks)

The union of the intervals is (-∞,∞)
The intersection of the intervals is [0,2)

Hope this helped!