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cluponka [151]
3 years ago
8

In the cafeteria, 100 milk cartons were put out for breakfast. At the end of breakfast, 27 remained. 1.What is the ratio of milk

cartons taken to total milk cartons? 2.What is the ratio of milk cartons remaining to milk cartons taken?
Mathematics
1 answer:
goldenfox [79]3 years ago
7 0
<span>1. The r</span>atio of milk cartons taken to total milk cartons,
100 - 27 = 73 were taken
73/100 is the ratio of milk cartons taken to total milk cartons

2. The ratio of milk cartons remaining to milk cartons taken
27 / 73 is the ratio of milk cartons remaining to milk cartons taken
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Recall that Rn denotes the right-endpoint approximation using n rectangles, Ln denotes the left-endpoint approximation using n r
pogonyaev

Answer:

R_5=1.12

Step-by-step explanation:

We want to calculate the right-endpoint approximation (the right Riemann sum) for the function:

f(x)=x^2+x

On the interval [-1, 1] using five equal rectangles.

Find the width of each rectangle:

\displaystyle \Delta x=\frac{1-(-1)}{5}=\frac{2}{5}

List the <em>x-</em>coordinates starting with -1 and ending with 1 with increments of 2/5:

-1, -3/5, -1/5, 1/5, 3/5, 1.

Since we are find the right-hand approximation, we use the five coordinates on the right.

Evaluate the function for each value. This is shown in the table below.

Each area of each rectangle is its area (the <em>y-</em>value) times its width, which is a constant 2/5. Hence, the approximation for the area under the curve of the function <em>f(x)</em> over the interval [-1, 1] using five equal rectangles is:

\displaystyle R_5=\frac{2}{5}\left(-0.24+-0.16+0.24+0.96+2)= 1.12

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2 years ago
Kate father is 50 years old and kate is 24 years old now. How many years ago was kates father three times as old as her
patriot [66]

Answer:

11

Step-by-step explanation:

50-x=3(24-x)

50-x=72-3x

2x=22

x=11years ago when kate's father was 3 times as old as kate=11

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2 years ago
A quadratic equation is shown below: 2x2 − 10x − 8 = 0 Part A: Describe the solution(s) to the equation by just determining the
dangina [55]
PART A:

The given quadratic equation is 2x²-10x-8=0

The radicand is given by b²-4ac where a, b, and c are the constants in a quadratic form ax²+bx+c

From the given equation, we have
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b = -10
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Radicand b²-4ac = (-10)² - 4(2)(-8) = 100 + 64 = 164

The radicand is >0 hence the quadratic equation has two distinct roots

PART B:

4x²-12x+5 = 0

We can use the factorization method to solve the equation
Firstly, we multiply 4 by 5 to get 20
Then we find the pair of numbers that multiply gives 20 and sum gives -12

The pair of number is -2 and -10
Rewriting the equation 
4x²-2x-10x+5 = 0
2x(2x-1)-5(2x-1) = 0
(2x-1)(2x-5) = 0

2x-1 = 0 and 2x-5 = 0
x = 1/2 and x = 5/2
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