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3 years ago

Half a number is at least 2 units from 20. write the sentence as an absolute value inequality

Mathematics

2 answers:

Anuta_ua [19.1K]3 years ago

8 0

Answer:

|1/2x - 20| ≥ 2

Step-by-step explanation:

The number is half of two and at least two units away.

sammy [17]3 years ago

6 0

Answer:

$|20-\dfrac{x}{2}|\geq 2$

Step-by-step explanation:

Half a number is at least 2 units from 20.

Let number be x

Write phrase as inequality.

"Half a number" $\Rightarrow \dfrac{x}{2}$

"From 20" $\Rightarrow 20-\dfrac{x}{2}$

"at least 2" $\Rightarrow \geq2$

Absolute inequality:

$|20-\dfrac{x}{2}|\geq 2$

Hence, The absolute value inequality is $|20-\dfrac{x}{2}|\geq 2$

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Amazon is offering free shipping on orders that total at least $200. Isabella already has $45 worth of goods in her cart, and fi

kari74 [83]

Answer:

She needs at least 11 pieces of accessories.

Step-by-step explanation:

She needs $200 and she has $45

200 - 45 = 155

Now she needs $155 worth of accessories and each piece is worth $15

155/15 = 10.33

then you round up to find the answer of 11 pieces of accessories.

4 0

4 years ago

Read 2 more answers

The width of the rectangle is five feet less than the length. If the perimeter of the rectangle is 34 feet find both dimensions

Lyrx [107]

Answer:

length = 11 ft, width = 6 ft

Step-by-step explanation:

Let w be the width, l be the length and p the perimeter. You can write down the following equations:

1. w = l - 5

2. p = 2*(w + l)

Now you have two equations with two unknown.

Plugging eq.1 in eq.2:

p = 2*(l-5 + l)

p = 2*(2*l - 5)

p = 4*l - 10

Remember p = 34

34 = 4*l - 10

4*l = 44

l = 11

Using eq.1 to solve for w:

w = 11 - 5

w = 6

4 0

3 years ago

What can anika conclude about the scale factor and missing measurements ? Check all that apply

ki77a [65]

We can see the ratio of a side big figure and small figure is 60:15 or 60/15 = 1/4.

In decimal form we can write 1/4 as 0.25.

Therefore, scale factor is 0.25.

So, second option is applicable. Please check second option :

<h3>The scale factor is 0.25.</h3>

Now, let us find the side A by multiplying by scale factor 0.25 of the big figure.

The corresponding side of A is 35.

Therefore, A is 0.25 × 35 = 8.75 cm.

Therefore, other applicable option is 3rd option.

<h3>The length of side A is 8.75 cm.</h3>

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3 years ago

Hamburger sells for 3 pounds for 6$. If Samantha buys 10 pounds of hamburger, how much will she pay?

Afina-wow [57]

She will pay 20$ for 10 pounds of hamburger

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3 years ago

Read 2 more answers

Two different samples will be taken from the same population of test scores where the population mean and standard deviation are

Rom4ik [11]

Answer:

The sample consisting of 64 data values would give a greater precision.

Step-by-step explanation:

The width of a (1 - <em>α</em>)% confidence interval for population mean <em>μ</em> is:

$\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}$

So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (<em>n</em>).

That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.

Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.

The two sample sizes are:

<em>n</em>₁ = 25

<em>n</em>₂ = 64

The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.

Width for <em>n</em> = 25:

$\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\ [2\cdot z_{\alpha/2}\cdot \sigma]$

Width for <em>n</em> = 64:

$\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\ [2\cdot z_{\alpha/2}\cdot \sigma]$

Thus, the sample consisting of 64 data values would give a greater precision.

3 0

3 years ago