What is the equivalent ratio for 19:7?

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

The sum of the interior angles of a regular polygon with 9 sides will be 1260°. The correct option is A.

An angle is defined in mathematics as the figure formed by joining two rays at their common endpoint. An interior angle is an angle that exists within a shape. Polygons are closed shapes with sides and vertices. All of the interior angles of a regular polygon are equal.

Given that the number of the sides of the polygon is 9. The sum of the interior angles of the polygons will be calculated as,

Sum = ( n - 2 ) 180°

Sum = ( 9 - 2 ) 180

Sum = 7 x 180

Sum = 1260°

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Answer:

A) (2x − 7) (4x² + 14x + 49)

C) (3x + 5) (9x² − 15x + 25)

Step-by-step explanation:

Sums and differences of cubes factor as:

a³ + b³ = (a + b) (a² − ab + b²)

a³ − b³ = (a − b) (a² + ab + b²)

8x³ − 343 is a difference of cubes.

(2x)³ − 7³

(2x − 7) (4x² + 14x + 49)

27x³ + 125 is a sum of cubes.

(3x)³ + 5³

(3x + 5) (9x² − 15x + 25)

Answer:

y=-15x+b

Step-by-step explanation:

Just move it around and use a calucator

Answer:

table 3 and table 12 show a proportional relationship

The coordinate points in the table D shows proportional relationship.  Therefore, option D is the correct answer.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

A) Slope= (3-2)/(4.5-3) =1/1.5

Slope= (8-4)/(12-8) = 4/4 =1

B) Slope= (60-15)/(4-1)

= 45/5

= 15

Slope= (120-70)/10-5)

= 50/5

= 10

C) Slope= (3-2)/(12-8)

= 1/4

Slope= (5-4)/(16-14

= 1/2

D) Slope= (10-5)/(2-1)

= 5

Slope= (35-25)/(7-5)

= 10/2

= 5

Therefore, option D is the correct answer.

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Irene has 49 Books, and Alejandro has 24 books.

Let's assume that Irene has x books, and Alejandro has y books. According to the given information, we can form the following equations:

1. Irene has twice as many books as Alejandro plus 1:

  x = 2y + 1

2. The total number of books between Irene and Alejandro is 73:

  x + y = 73

We can now solve this system of equations to find the values of x and y.

Substituting the value of x from equation (1) into equation (2), we have:

(2y + 1) + y = 73

3y + 1 = 73

3y = 72

y = 24

Now, we can substitute the value of y into equation (1) to find x:

x = 2(24) + 1

x = 49

Therefore, Irene has 49 books, and Alejandro has 24 books.

To verify our solution, we can check if the sum of their books equals 73:

49 + 24 = 7

So, our solution is correct.

In conclusion, Irene has 49 books, and Alejandro has 24 books.

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Answer:

Can you add more context?

Step-by-step explanation:

Answer:

F

Step-by-step explanation:

Answer: The ratio of their heights is 1/2 .

Let the radius of one cone be 'r'

and its height be 'h'

therefore, its perimeter of circular base will be 2 π r

and its volume will be given as  1 /3 π \(r^{2}\) h

Let the radius of second cone be 'R'

and the height be 'H'

therefore its perimeter of circular base will be given as 2 π R

and its volume will be given as  1 /3 π \(R^{2}\) H

ratio of their perimeters = 3 : 4

                         →         \(\frac{2 \pi r}{2 \pi R}\)  =  \(\frac{3}{4}\)

                          →         \(\frac{r}{R}\)  =  \(\frac{3}{4}\)

and ratio of their volume = 9 : 32

                          →      \(\frac{\frac{1}{3} \pi r^{2} h}{\frac{1}{3} \pi R^{2} H}\)  =    \(\frac{9}{32}\)

                          →      \((\frac{r}{R} )^{2}\) * \(\frac{h}{H}\) =  \(\frac{9}{32}\)

now put the value of  \(\frac{r}{R}\)  in the above equation we get

                          →        \((\frac{3}{4}) ^{2}\)  *  \(\frac{h}{H}\)  =  \(\frac{9}{32}\)

solving it we will get

                    →        \(\frac{h}{H}\) = \(\frac{1}{2}\)  

therefore the ratio of their heights will be    \(\frac{1}{2}\) .

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Answer:

50/100×30

15..........

The period of oscillation is 3 seconds

A Oscillation is the periodic change of a measure around a central value or between two or more states, usually in time.

The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle. It is measured in seconds

Oscillation can also be vibration or revolution or cycle.

Therefore, using the graph to determine the period. Then the wave particle made a complete oscillation at 3 second.

This means that the period of the particle is 3 seconds.

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The population of the animal found in 2006 was 3109.

For the given data in the question.

Population count of animals in 2007 is found as 2817.

The population count in 2007 is less than 292 than the population count in 2006.

Thus,

2007 population = 2006 population - 292.

2006 population = 2007 population + 292

2006 population = 2817 + 292

2006 population = 3109.

Therefore, the population count for the animals in 2006 is found to be 3109.

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Answer:

$79,618

Step-by-step explanation:

7 years x 3% = 21%

$65,800 x 21% = $13,818

$65,800 + $13, 818 = $79,618

The pressure needed to pump water up to the restaurant on the top floor is 4018000 N/m².

Pressure can be defined as the ratio of force to area of an object.

To calculate the pressure needed, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the pressure needed to pump water up to the restaurant on the top floor is 4018000 N/m².

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Answer:

Average time per day = 1.2 hours per day
Average time per day = 72 minutes per day

Step-by-step explanation:

To find Clarence's average time per day, we need to divide the total time he takes to walk the 15.5 miles by the number of days he walks, which is five.

Let's calculate his average time per day:

Average time per day = Total time / Number of days

Since Clarence takes a total of 6 hours to walk the 15.5 miles, we'll divide 6 by 5 to find his average time per day:

Average time per day = 6 hours / 5

Average time per day = 1.2 hours per day

To convert hours to minutes, we'll multiply the average time per day by 60:

Average time per day = 1.2 hours * 60 minutes

Average time per day = 72 minutes per day

Therefore, Clarence's average time per day is 72 minutes.

An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M

Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:

A = L x W

where A is the area of the logo, L is the length of the logo, and W is the width of the logo.

Substituting the given values, we get:

A = (7(1)/(5)) x M

or

A = (36/5) x M

Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:

A = X

Combining both equations, we get:

X = (36/5) x M

This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.

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Answer:

Log(x)

Step-by-step explanation:

Answer:

j = 139.99 + 139.99 * 0.08625

Answer:

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

I can do this so fast I know I am a high school

Answer:

c. $28

Step-by-step explanation:

If Emily only has $30 to spend and the sales tax is 5%, then we can set up an equation to solve for the maximum cost of the dress:

30 = x + 0.05x

where x is the cost of the dress.

Simplifying this equation gives:

30 = 1.05x

Dividing both sides by 1.05 gives:

x = 28.57

Therefore, the maximum cost of the dress is approximately $28.57.

So the answer is © $28.

Answer:

The correct operator for the exponential expression 3^5 ? 4^6 is > (greater than), because we can compare the values of the two exponents:

3^5 = 243

4^6 = 4096

Since 4096 is greater than 243, we can write:

3^5 < 4^6

or

4^6 > 3^5

Therefore, the correct operator for the exponential expression 3^5 ? 4^6 is > (greater than).

Given:

The polar coordinate is

The solution will be resolved graphically

where,

Let us now plot the coordinate using a graphing calculator

Hence, the correct option is Option 2.

Answer:

4  12/25

Step-by-step explanation:

4.48 can be written as 4 48/100

Simplify

4 24/50

Simplify some more

4 12/25

Hope this helped :)

(Didn't you just ask this question?)

Answer:

4 48/100 or 4 12/25

Step-by-step explanation:

the 48 in the hundredths place is obviously going to equal 48/100 and you can divide both the 48 and 100 by 4. 48÷4=12 100÷4=25

Answer:

The probability that the very first dam you designed will overtop during your anticipated 45-year career is 0.7985.

Step-by-step explanation:

The question is related to the reliability function.

The reliability of the dam built follows an Exponential distribution with mean time between failure as 200 years.

Then the parameter of the exponential distribution will be:

\(\lambda=\frac{1}{200}=0.005\)

The reliability function for the time in which the dam will overtop is given by:

\(R(t)=e^{-\lambda t}\)

Compute the probability that the very first dam you designed will overtop during your anticipated 45-year career as follows:

  \(R(t)=e^{-\lambda t}\)

\(R(45)=e^{-0.005\times 45}\)

         \(=e^{-0.225}\\=0.7985\)

Thus, the probability that the very first dam you designed will overtop during your anticipated 45-year career is 0.7985.

The table is a linear function, and the rule for the input/output table is f(x) = 1 + 3x

From the table, we can see that:

The output of the table  is 1 more than 3 times the input

If the input is x, then the output y is:

y = 1 +3 * x

Evaluate

y = 1 + 3x

Hence, the rule for the input/output table is f(x) = 1 + 3x

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Answer:

n = 19

Step-by-step explanation:

2n > 36 ( divide both sides by 2 )

n > 18

and

5n < 100 ( divide both sides by 5 )

n < 20

so n > 18 and n < 20

thus n = 19

The distance between -10 and 5 on a number line is 15

From the question, we are to determine the distance between the given points on a number line

The given points are -10 and 5

On a number line, the distance between any two points is the difference between the largest number and the smallest number

That is,

Distance between two points on a number line = Value of the largest number - Value of the smallest number

The given points are -10 and 5

The largest number is 5

and

The smallest number is -10

Thus,

Distance between -10 and 5 on a number line = 5 - -10

Distance between -10 and 5 on a number line = 5 + 10

Distance between -10 and 5 on a number line = 15

Hence, the distance between -10 and 5 on a number line is 15

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The answer and all work is shown in the provided screenshot! :)

Have a great day!

The required equation is g(x) = 10(3)x which is the correct answer would be an option (A).

The graph of g(x) is obtained by stretching the graph of f(x) vertically by a factor of 2.

Since the vertical stretch of a graph multiplies the y-coordinates of each point on the graph by a constant factor, the equation of g(x) must be obtained by multiplying the y-coordinate of each point on the graph of f(x) by 2.

In the given equation f(x) = 5(3)x, the y-coordinate of each point on the graph of f(x) is 5(3)x.

Thus, to stretch the graph of f(x) vertically by a factor of 2, we need to multiply this y-coordinate by 2 to get the y-coordinate of the corresponding point on the graph of g(x). This gives us the following equation for g(x):

⇒ g(x) = 2 × 5(3)x = 10(3)x

Therefore, the required equation is g(x) = 10(3)x.

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The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:

\(c^2 = a^2 + b^2 - 2ab*cos(C)\)

In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:

\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)

49 = 16 + 25 - 40*cos(C)

49 = 41 - 40*cos(C)

40*cos(C) = 41 - 49

40*cos(C) = -8

cos(C) = -8/40

cos(C) = -0.2

To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:

C = arccos(-0.2)

Using a calculator, we find that C ≈ 101.54 degrees.

Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

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