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2 years ago

Simplify.

Mathematics

1 answer:

inn [45]2 years ago

8 0

Answer:

$1. \frac{3y - 2}{5} = \frac{3y}{5} - \frac{2}{5} \\ \\ 2. \frac{6x - 3}{3} = \frac{6x}{3} - \frac{3}{3} \\ = 2x - 1 \\ \\ 3. \frac{4}{2} = 2$

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Caroline, Colin & Sarah share some money.

krek1111 [17]

Answer:

2/9

Step-by-step explanation:

After Caroline's share,

1 - 1/9 = 8/9 is left

Sarah gets:

1/(1+3) of 8/9

1/4 × 8/9

2/9

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3 years ago

A reasonable estimate of the

lyudmila [28]

Answer:

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2 years ago

Megan shaded 2/8 of the circle what is another way she could write this fraction

lidiya [134]

Answer:

Step-by-step explanation:

2/8 = 1/4

2/8 = 200/800

and so on.

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5 0

2 years ago

Read 2 more answers

The pulse rates of 174 randomly selected adult males vary from a low of 39 bpm to a high of 111 bpm. Find the minimum sample siz

Daniel [21]

Answer:

a. The sample size is approximately 97 adults

Step-by-step explanation:

The given parameters are;

The number of adults surveyed, n = 174

The lowest value of the pulse rate = 39 bpm

The highest value of the pulse rate = 111 bpm

The level of confidence used for determining the sample size = 90%

The given sample mean = 3 pm of the population mean

a. The range rule of thumb states that the standard deviation is approximately one quarter (1/4) of the range

The range = 111 bpm - 39 bpm = 72 bpm

Therefore, the standard deviation, σ = 72 bpm/4 = 18 bpm

The sample size, 'N', is given as follows;

$N = \dfrac{z^2 \cdot p \cdot q}{e^2}$

Where;

N = The sample size

z = The confidence level, 90% (z-score at 90% = 1.645)

p·q = σ² = 18² = 324

e² = 3² = 9

$N = \dfrac{1.645^2 \times 324}{3^2} = 97.4169$

Therefore the appropriate sample size, N ≈ 97 adults.

8 0

3 years ago

Find an equation of a line that is tangent to the graph of f and parallel to the given line. Please see picture

ivanzaharov [21]

Answer:

y = 3x - 2 (smaller y-intercept)

y = 3x + 2 (larger y-intercept)

Step-by-step explanation:

First let's write the generic equation of a line:

y = ax + b

This line needs to be parallel to the line 3x - y + 5 = 0, so it needs to have the same slope of this line.

The line 3x - y + 5 = 0 has a slope of 3, so our line has a = 3:

y = 3x + b

Now we need to find the values of b that make this line tangent to the function f(x) = x^3

Let's first find the derivative of f(x) in relation to x:

df(x)/dx = 3x^2

This derivative is the slope of the tangent line to the function for any value of x. We need a slope of 3, so:

3x^2 = 3

x^2 = 1

x = ±1

Now, to find the y-values, we have:

f(1) = 1^3 = 1

f(-1) = (-1)^3 = -1

So, using the points (1,1) and (-1,-1) in our parallel line, we have:

first line using (1,1) : 1 = 3*1 + b

b = -2

second line using (-1,-1) : -1 = -3*1 + b

b = 2

The value of b is the y-intercept of the line, so the line with smaller y-intercept is y = 3x - 2, and the line with larger y-intercept is y = 3x + 2

8 0

3 years ago