MATHEMATICS HIGH SCHOOL

A candy store owner has chocolate candies worth $2.50 per pound and sour candies worth $0.90 per pound. How much of each kind of candies should she combine to get 60 lb of mixed candies worth $1.70 per pound? (Include units with your numerical answers.)

Answers

Answer 1

Answer:

Weight of chocolate candies = 30lbs

Weight of sour candies = 30lbs

Step-by-step explanation:

We are told in the question that :

Chocolate candies worth $2.50 per pound

Sour candies worth $0.90 per pound. How much of each kind of candies should she combine to get 60 lb of mixed candies worth $1.70 per pound?

Let x represent the number of pounds of chocolate candies

Let 60 - x represent the number of pounds of sour candies

Hence, we have the equation

x × $2.50 + (60 - x) × $0.90 = 60 × $1.70

= 2.5x + 54 - 0.9x = 102

Collect like terms

2.5x - 0.9x = 102 - 54

= 1.6x = 48

x = 48/1.6

x = 30 lbs

x represent the number of pounds of chocolate candies,

60 - x represent the number of pounds of sour candies

= 60 - 30

= 30lbs

Weight of chocolate candies = 30lbs

Weight of sour candies = 30lbs

Therefore, she should combine 30lbs of chocolate candies and 30lbs of sour candies to get 60 lb of mixed candies worth $1.70 per pound.

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A circle has all three types of symmetry.
a. True
b. False

Answers

Answer:

The answer is TRUE

Step-by-step explanation:

Given a statement that

"A circle has all three types of symmetry"

we have to tell the above statement is true or false

The circle possesses the symmetry which are:

(i) Linear symmetry possess infinite lines of symmetry of order 4

(ii) Point symmetry possess point symmetry about the centre O

(iii)Rotational symmetry possess rotational symmetry of an infinite order.

Hence given statement is TRUE

A circle has all three types of symmetry

True, because a circle will always have the same points when your rotate it.

Joey is buying plants for his garden. He wants to have at least twice as many flowering plants as nonflowering plants and a minimum of 36 plants in his garden. Flowering plants sell for $8, and nonflowering plants sell for $5. Joey wants to purchase a combination of plants that minimizes cost. Let x represent the number of flowering plants and y represent the number of nonflowering plants. What are the vertices of the feasible region for this problem?
(0, 0), (0, 36), (24, 12)
(0, 36), (24, 12)
(0, 36), (24, 12), (36, 0)
(24, 12), (36, 0)

Answers

(24, 12) and (36, 0). The least amount of flowering plants occurs when x=2y, and the largest amount occurs when y=0. These two points satisfy both conditions and both sum to 36.

Answer: (24, 12), (36, 0)

Step-by-step explanation:

Let x be the number of flowering plants and y be the number of non- flowering plants.

According to the question, we need to minimize the cost of plants.

$Minimize:8x+5y$

Subject to the constraints,

$2y\leq\ x\nx+y\geq36$

To find the feasible region find the points of the equation to plot it on graph.

For the first equation $2y=x$ , at x=0 y=0 and at x=4, y=2

For the second equation $x+y=36$ , at x=0 y=36 and at x=36, y=0

Thus points for eq (1) are (0,0) and (4,2) and points for equation (2) are (0,36) and (36,0).

Now, plot it on graph, we get the shaded feasible region as shown in the graph.

and we can see the vertices of the feasible region = (24, 12), (36, 0)

A shipping container is in the shape of a right rectangular prism with a length of 2 feet, a width of 14.5 feet, and a height of 14 feet. The container is completely filled with contents that weigh, on average, 0.9 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?

Answers

Answer:

1.8k AND 57k

Step-by-step explanation:

What's the value of log2 (1/8) ?

Answers

$log_aa^p=p\n------\n\nlog_2 ( (1)/(8) ) =log_28^(-1)=log_2(2^3)^(-1)=log_22^(-3)=-3\n\nAns.\ -3$

The correct answer for the value $log_(2)(1)/(8)$ is equal to -3.

What is Logarithm?

In mathematics, Logarithms are defined a way of expressing exponents. A logarithm is defined as the power to which a number must be raised to get some other values.

The expression for logarithm of a number is written as ㏒ₓb = y.

Properties of Logarithm:

$log_(x) (x^n) = n$

The value of $log_(2)(1)/(8)$ can be calculated by recognizing that $(1)/(8)$ is equal to 2 raised to the power of -3.

$log_(2)(1)/(8)$ = $log_(2)(2^(-3))$

From the property of logarithm:

$log_(2)(2^(-3))$

= -3

The value of $log_(2)(1)/(8)$ is -3.

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The graph shows the cost of parking, y , per hour, x , at a parking garage. The graph is titled Parking Rates. The X-axis is labeled Number of Hours and goes from zero to four by a scale of one. The y-axis is labeled Cost in dollars and goes from zero to eighteen by a scale of two. Five points are shown on the graph. Zero hours, zero dollars. One hour, four dollars. Two hours, eight dollars. Three hours, twelve dollars. Four hours, sixteen dollars. Which equation represents the relationship shown in the graph?

Answers

The relationship shown in the graph represents a linear equation because the cost of parking increases at a constant rate per hour. To find the equation that represents this relationship, we can use the slope-intercept form of a linear equation:

\[y = mx + b\]

Where:
- $y$ is the cost in dollars (the dependent variable).
- $x$ is the number of hours (the independent variable).
- $m$ is the slope, which represents the rate of change.
- $b$ is the y-intercept, which represents the initial cost when $x$ is zero.

Based on the points provided in the graph:

Point 1: (0 hours, 0 dollars) gives us the y-intercept, so $b = 0$.

Point 2: (1 hour, 4 dollars) allows us to find the slope ($m$) as follows:

So, the equation that represents the relationship shown in the graph is:

\[y = 4x\]

This equation represents a linear relationship where the cost ($y$) is directly proportional to the number of hours ($x$) at a rate of $4 per hour.

What is the equation of the line that passes through the point (5,-1)(5,−1) and has a slope of \frac{1}{5} 5 1

Answers

Answer:

This is easy how do I send my work like a photo

Step-by-step explanation:

Final answer:

The equation of the line is y = 1/5x - 2.

Explanation:

The equation of a line can be written as y = mx + b, where m is the slope of the line and b is the y-intercept.

Given that the line passes through the point (5,-1) and has a slope of 1/5, we can substitute these values into the equation to find b.

Using the point-slope formula, we have y - y1 = m(x - x1).

Plugging in the values for (x1, y1) as (5, -1) and m as 1/5, we can simplify the equation to y + 1 = 1/5(x - 5).

Rearranging the equation gives us y = 1/5x - 10/5, which can be simplified to y = 1/5x - 2.

Therefore, the equation of the line that passes through the point (5,-1) and has a slope of 1/5 is y = 1/5x - 2.

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