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3 years ago

11

Darren has a wooden board that is Three-fifths of a meter long. He cuts the board into 3 equal parts. How long is each section o

f board?

1 answer:

Alik [6]3 years ago

8 0

Answer:

Each section of the board is 1/3 or 0.334(0.333333333333) of a meter

Step-by-step explanation:

3/5 divided by 3 is the equation we have to do.

3/5 divided by 3 is also equal to 3/5 times the reciprocal of 3 or 1/3

3/5 * 1/3

3*1 = 3

5*3 = 15

3/15 which can simplify to 1/3. (divide numerator and denominator by 3.)

Each section of the board is 1/3 or 0.334(0.333333333333) of a meter

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Please help me with average

Anvisha [2.4K]

Answer:

2x+1

Step-by-step explanation:

(3x-5)+(x+2)+(2x+6)=6x+3

6x+3/3=2x+1

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3 years ago

Read 2 more answers

Suppose x is a real number and epsilon > 0. Prove that (x - epsilon, x epsilon) is a neighborhood of each of its members; in

kaheart [24]

Answer:

See proof below

Step-by-step explanation:

We will use properties of inequalities during the proof.

Let $y\in (x-\epsilon,x+\epsilon)$ . then we have that $x-\epsilon$ . Hence, it makes sense to define the positive number delta as $\delta=\min\{x+\epsilon-y,y-(x-\epsilon)\}$ (the inequality guarantees that these numbers are positive).

Intuitively, delta is the shortest distance from y to the endpoints of the interval. Now, we claim that $(y-\delta,y+\delta)\subseteq (x-\epsilon,x+\epsilon)$ , and if we prove this, we are done. To prove it, let $z\in (y-\delta,y+\delta)$ , then $y-\delta$ . First, $\delta \leq y-(x-\epsilon)$ then $-\delta \geq -y+x-\epsilon$ hence $z>y-\delta \geq x-\epsilon$

On the other hand, $\delta \leq x+\epsilon-y$ then $z$ hence $z$ . Combining the inequalities, we have that $x-\epsilon$ , therefore $(y-\delta,y+\delta)\subseteq (x-\epsilon,x+\epsilon)$ as required.

3 0

4 years ago

Georgianna claims that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.

Allisa [31]

Answer:

The condition are

The Null hypothesis is $H_o : \mu = 5$

The Alternative hypothesis is $H_a : \mu < 5$

The check revealed that

There is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 5 \ year$

The sample size is n = 20

The sample mean is $\= x = 4.6 \ years$

The standard deviation is $\sigma = 2.2 \ years$

The Null hypothesis is $H_o : \mu = 5$

The Alternative hypothesis is $H_a : \mu < 5$

So i will be making use of $\alpha = 0.05$ level of significance to test this claim

The critical value of $\alpha$ from the normal distribution table is $Z_\alpha = 1.645$

Generally the test statistics is mathematically evaluated as

$t = \frac{\= x - \mu}{ \frac{\sigma }{\sqrt{n} } }$

substituting values

$t = \frac{ 4.6 - 5}{ \frac{2.2}{\sqrt{20} } }$

$t = -0.8131$

Looking at the value of t and $Z_{\alpha }$ we see that $t < Z_{\alpha }$ so we fail to reject the null hypothesis

This implies that there is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.

4 0

3 years ago

Write the equation in standard form for the circle with center (5,0) passing through (-1, 9/2)

andreev551 [17]

Answer:

(x - 5)^2 + y^2 = 225/4,

or you could write it as (x - 5)^2 + y^2 = 56.25.

Step-by-step explanation:

The factor form is

(x - h)^2 + (y - k)^2 = r^2 where the center is (h, k) and r = the radius.

So we have:

(x - 5)^2 + (y - 0)^2 = r^2

As the point (-1, 9/2) is on the line:

(-1 - 5)^2 + (9/2)^2 = r^2

r^2 = 36 + 81/4

r^2 = 225/4.

So substituting for r^2:

(x - 5)^2 + (y - 0)^2 = 225/4

(x - 5)^2 + y^2 = 225/4 is the standard form.

3 0

3 years ago

Robert can paint a room in 6 hours. Julio can paint a room in 8 hours.how long will it take for the two of them to paint a room

Llana [10]

Roberto paints 1/6 of a room in 1 hour.
Julio paints1/8 of a room in 1 hour.

Working together, they paint (1/6 + 1/8) = (4/24 + 3/24) = 7/24 room per hour.

The reciprocal unit rate is 24/7 hour per room = <em>3-3/7 hours</em> per room.

6 0

4 years ago