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svetoff [14.1K]

1 year ago

7

Students are measuring various objects around the classroom. A pencil measures 8 ⅜ inches while a pair of scissors measures 5 ½

inches. How much longer is the pencil than the pair of scissors?

1 answer:

Maslowich1 year ago

5 0

The pencil is longer than the pair of scissors by $2\frac{7}{8}$ inches.

A pencil measures $8\frac{3}{8}$ inches.

A pair of scissors measures $5\frac{1}{2}$ inches.

We need to find the difference between the measures of a pencil and the scissors.

We see that the pencil measure is greater than the pair of scissors.

<h3>What is a mix fraction?</h3>

A fraction is a part of a whole number. It has two parts - numerator and denominator.

Example: If you cut a cake into three slices each slice is 1/3.

Where 1 = numerator and 3 = denominator.

Four types of fractions:

Unit fraction - when the numerator is 1.

Proper fraction - When the numerator is less than the denominator.

Improper fraction - When the numerator is greater than the denominator.

Mixed fraction - When the fraction contains a whole number with a proper fraction.

Example: $3\frac{1}{3}$

The given measure of the pen and the pair of scissors is in mix fraction.

The pencil measure is longer than the pair of scissors measure so,

We will subtract the measure of the pair of scissors from the measure of the pen.

We have,

= $8\frac{3}{8} - 5\frac{1}{2}$

We can write the mix fraction into an improper fraction.

We multiply the denominator with the whole number and add this product with the numerator to get our numerator of the improper fraction. The denominator will remain the same as the mix fraction in the improper fraction.

So,

$8\frac{3}{8}=\frac{(8\times8)+3}{8}=\frac{64 + 3}{8} = \frac{67}{8}\\ 5\frac{1}{2} =\frac{(5\times2)+1}{2}= \frac{(10+1)}{2} = \frac{11}{2}$

= 67/8 - 11/2

= (67-44) / 8

= 23 / 8

Writing in mix fraction.

= $2\frac{7}{8}$

Thus the pencil is longer than the pair of scissors by $2\frac{7}{8}$ inches.

Learn more about mix fraction here:

brainly.com/question/13881046

#SPJ1

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Write an equation in slope-intercept form for the following line:<br> (-14.1) and (13,-2)

vesna_86 [32]

Answer:

$y=-\frac{1}{9}x-\frac{5}{9}$

Step-by-step explanation:

$(-14,1)(13,-2)$

Use the slope-intercept formula:

$y=mx+b$

m is the slope and b is the y-intercept. Use the slope formula first:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}$

Rise over run is the change in the y-axis over the change in the x-axis. Plug in the coordinates:

$(-14(x_{1}),1(y_{1}))\\(13(x_{2}),-2(y_{2}))$

$\frac{-2-1}{13-(-14)}$

Simplify parentheses (two negatives makes a positive):

$\frac{-2-1}{13+14}$

Simplify:

$\frac{-3}{27} =-\frac{3}{27}=-\frac{1}{9}$

The slope is $-\frac{1}{9}$ . Insert into the equation:

$y=-\frac{1}{9}x +b$

Now, to find the y-intercept, take one of the points and substitute for the x and y values of the equation:

$(13,-2)\\-2=-\frac{1}{9} (13)+b$

Solve for b, the y-intercept. Simplify parentheses:

$-\frac{1}{9}*\frac{13}{1}=-\frac{13}{9}$

$-2=-\frac{13}{9} +b$

Add $-\frac{13}{9}$ to both sides:

$-2+\frac{13}{9}=-\frac{13}{9} +\frac{13}{9} +b\\\\-2+\frac{13}{9} =b$

Simplify:

$-\frac{2}{1} +\frac{13}{9}\\\\-\frac{18}{9}+\frac{13}{9}\\ \\b=-\frac{5}{9}$

The y-intercept is $-\frac{5}{9}$ . Insert this into the equation:

$y=-\frac{1}{9} x-\frac{5}{9}$

Finito.

8 0

3 years ago

What is the next odd number after 160 to which 9 would divide without a reminder

ale4655 [162]

Ok so one way is to list the multiplues of 9 close to thtat
first use a caltulator to find out how much more we need
160/9=17.777777
that is 17.7777 nine's
so round up
18
18 is even
odd times even=even
18 must be odd
18+1=19
9 times 19=171
the answer is 171

7 0

3 years ago

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posledela

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3 years ago

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Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of

jarptica [38.1K]

Answer:

The "probability that a given score is less than negative 0.84" is $\\ P(z$ .

Step-by-step explanation:

From the question, we have:

The random variable is <em>normally distributed</em> according to a <em>standard normal distribution</em>, that is, a normal distribution with $\\ \mu = 0$ and $\\ \sigma = 1$ .
We are provided with a <em>z-score</em> of -0.84 or $\\ z = -0.84$ .

Preliminaries

A z-score is a standardized value, i.e., one that we can obtain using the next formula:

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Where

<em>x</em> is the <em>raw value</em> coming from a normal distribution that we want to standardize.
And we already know that $\\ \mu$ and $\\ \sigma$ are the mean and the standard deviation, respectively, of the <em>normal distribution</em>.

A <em>z-score</em> represents the <em>distance</em> from $\\ \mu$ in <em>standard deviations</em> units. When the value for z is <em>negative</em>, it "tells us" that the raw score is <em>below</em> $\\ \mu$ . Conversely, when the z-score is <em>positive</em>, the standardized raw score, <em>x</em>, is <em>above</em> the mean, $\\ \mu$ .

Solving the question

We already know that $\\ z = -0.84$ or that the standardized value for a raw score, <em>x</em>, is <em>below</em> $\\ \mu$ in <em>0.84 standard deviations</em>.

The values for probabilities of the <em>standard normal distribution</em> are tabulated in the <em>standard normal table, </em>which is available in Statistics books or on the Internet and is generally in <em>cumulative probabilities</em> from <em>negative infinity</em>, - $\\ \infty$ , to the z-score of interest.

Well, to solve the question, we need to consult the <em>standard normal table </em>for $\\ z = -0.84$ . For this:

Find the <em>cumulative standard normal table.</em>
In the first column of the table, use -0.8 as an entry.
Then, using the first row of the table, find -0.04 (which determines the second decimal place for the z-score.)
The intersection of these two numbers "gives us" the cumulative probability for z or $\\ P(z$ .

Therefore, we obtain $\\ P(z$ for this z-score, or a slightly more than 20% (20.045%) for the "probability that a given score is less than negative 0.84".

This represent the area under the <em>standard normal distribution</em>, $\\ N(0,1)$ , at the <em>left</em> of <em>z = -0.84</em>.

To "draw a sketch of the region", we need to draw a normal distribution <em>(symmetrical bell-shaped distribution)</em>, with mean that equals 0 at the middle of the distribution, $\\ \mu = 0$ , and a standard deviation that equals 1, $\\ \sigma = 1$ .

Then, divide the abscissas axis (horizontal axis) into <em>equal parts</em> of <em>one standard deviation</em> from the mean to the left (negative z-scores), and from the mean to the right (positive z-scores).

Find the place where z = -0.84 (i.e, below the mean and near to negative one standard deviation, $\\ -\sigma$ , from it). All the area to the left of this value must be shaded because it represents $\\ P(z$ and that is it.

The below graph shows the shaded area (in blue) for $\\ P(z$ for $\\ N(0,1)$ .

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3 years ago

Henry can write 5 1/4 pages of his novel in 3 hours how many page can he write in 8 hours

ICE Princess25 [194]

If you would like to know how many pages can Henry write in 8 hours, you can calculate this using the following steps:

5 1/4 = 21/4 pages ... 3 hours
x pages = ? ... 8 hours

21/4 * 8 = 3 * x
21 * 2 = 3 * x
3 * x = 42
x = 42 / 3
x = 14 pages

Henry can write 14 pages of his novel in 8 hours.

8 0

3 years ago