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2 years ago

A number, x, rounded to 2 significant figures is 1300Write down the error interval for x.

Mathematics

1 answer:

nikitadnepr [17]2 years ago

7 0

Answer:

$[1250,1350)$ .

Step-by-step explanation:

It is given that a number, x, rounded to 2 significant figures is 1300.

It is possible if,

1. The value of x is greater than of equal to 1250 and less than or equal to 1300.

i.e., $1250\leq x\leq 1300$ ...(1)

2. The value of x is greater than of equal to 1300 and less than 1350.

i.e., $1300\leq x$ ...(2)

On combining (1) and (2), we get

$1250\leq x < 1350$

1350 is not included in the error interval for x.

Interval notation is $[1250,1350)$ .

Therefore, the error interval for x is $[1250,1350)$ .

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2 years ago

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Darcie wants to crochet a minimum of 3 blankets blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a

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Answer:

The inequality to determine the number of days, $s$ , Darcie can skip crocheting and still meet her goal is:

$s\leq 15$

Thus, Darcie can skip a maximum of 15 days.

Step-by-step explanation:

Question

Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways. Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal.

Given:

Darcie has a target to crochet a minimum of 3 blankets.

Rate at which Darcie crochets = $\frac{1}{15}$ of a blanket per day.

Darcie has 60 days to crochet the blankets

To write an inequality to determine the number of days, $s$ , Darcie can skip crocheting and still meet her goal.

Solution:

The number of days Darcie can skip crocheting is represented by $s$

So, number of days left for Darcie to crochet = $60-s$

In 1 day Darcie crochets $\frac{1}{15}$ of a blanket.

So, in $(60-s)$ days she will crochet = $\frac{1}{15}(60-s)$ blankets.

Her aim is to crochet at least 3 blankets.

Thus, the inequality can be given as:

$\frac{1}{15}(60-s)\geq 3$

Solving for $s$

Multiplying both sides by 15 to remove fractions.

$15\times\frac{1}{15}(60-s)\geq 3\times 15$

$60-s\geq 45$

Subtracting both sides by 60.

$60-60-s\geq 45-60$

$-s\geq -15$

Dividing both sides by -1.

$\frac{-s}{-1}\leq \frac{-15}{-1}$ [ On dividing by negative number the sign of the inequality is reversed]

∴ $s\leq 15$

Thus, Darcie can skip a maximum of 15 days.

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1 year ago

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Find the quantity q that maximizes profit if the total revenue, R(q), and total cost, C(q) are given in dollars by R(q)=3q−0.002

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Answer:

The value of q that maximize the profit is q=200 units

Step-by-step explanation:

we know that

The profit is equal to the revenue minus the cost

we have

$R(q)=3q-0.002q^{2}$ ---> the revenue

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The profit P(q) is equal to

$P(q)=R(q)-C(q)$

substitute the given values

$P(q)=(3q-0.002q^{2})-(200+2.2q)$

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$P(q)=-0.002q^{2}+0.8q-200$

This is a vertical parabola open downward (because the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the value of q that maximize the profit

The y-coordinate of the vertex represent the maximum profit

using a graphing tool

Graph the quadratic equation

The vertex is the point (200,-120)

see the attached figure

therefore

The value of q that maximize the profit is q=200 units

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Answer:

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Step-by-step explanation:

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4. gym practice

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2 years ago

A number, x, rounded to 2 significant figures is 1300Write down the error interval for x.​

A number, x, rounded to 2 significant figures is 1300Write down the error interval for x.