The mixed number 3 2/3 comes between 3 and 4 on the number line.

How many 5 1/4 ounce glasses can be completely filled from a 33 1/2 ounce container of juice?

geniusboy [140]

You need to divide.
We are dividing the mixed numeral 33 1/21 by the mixed numeral 5 1/4.

(33 1/2 ) / (5 1/4) =

The first step is to change the two mixed numerals into improper fractions.
33 1/2 = 67/2, and 5 1/4 = 21/4

= (67/2) / (21/4)

Now we are dividing the fraction 67/2 by the fraction 21/4.
To divide a fraction by a fraction, rewrite the first fraction, change division intro multiplication, and flip the second fraction. To divide 67/2 by 21/4, we multiply 67/2 by 4/21.

= 67/2 * 4/21

To multiply fractions, multiply together the numerators, and multiply together the denominators. 67 * 4 = 268; 2 * 21 = 42

= 268/42

Using a calculator, 268/42 = 6.38095...

You can fill 6 full glasses.

5 0

3 years ago

I need help proving this ASAP

Ket [755]

Answer:

See explanation

Step-by-step explanation:

We want to show that:

$\tan(x + \frac{3\pi}{2} ) = - \cot \: x$

One way is to use the basic double angle formula:

$\frac{ \sin(x + \frac{3\pi}{2} ) }{\cos(x + \frac{3\pi}{2} )} = \frac{ \sin(x) \cos( \frac{3\pi}{2} ) + \cos(x) \sin( \frac{3\pi}{2}) }{\cos(x) \cos( \frac{3\pi}{2} ) - \sin(x) \sin( \frac{3\pi}{2}) }$

$\frac{ \sin(x + \frac{3\pi}{2} ) }{\cos(x + \frac{3\pi}{2} )} = \frac{ \sin(x) ( 0) + \cos(x) ( - 1) }{\cos(x) (0) - \sin(x) ( - 1) }$

We simplify further to get:

$\frac{ \sin(x + \frac{3\pi}{2} ) }{\cos(x + \frac{3\pi}{2} )} = \frac{ 0 - \cos(x) }{0 + \sin(x) }$

We simplify again to get;

$\frac{ \sin(x + \frac{3\pi}{2} ) }{\cos(x + \frac{3\pi}{2} )} = \frac{- \cos(x) }{ \sin(x) }$

This finally gives:

$\frac{ \sin(x + \frac{3\pi}{2} ) }{\cos(x + \frac{3\pi}{2} )} = - \cot(x)$

6 0

4 years ago

Make an equation that is equal to 2/3

wariber [46]

Answer:

Replace the 4 with a 3 to make the equation true

5 0

3 years ago

Read 2 more answers

Assume the sample variances to be continuous measurements. Find the probability that a random sample of 25observations, from a n

konstantin123 [22]

Answer:

a) $P(4S^2 > 4*9.1) = P(\chi^2_{24} >36.4) = 0.0502$

b) $P(13.848$ Step-by-step explanation:

Previous concepts

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

For this case we assume that the sample variance is given by $S^2$ and we select a random sample of size n from a normal population with a population variance $\sigma^2$ . And we define the following statistic:

$T = \frac{(n-1) S^2}{\sigma^2}$

And the distribution for this statistic is $T \sim \chi^2_{n-1}$

For this case we know that n =25 and $\sigma^2 = 6$ so then our statistic would be given by:

$\chi^2 = \frac{(n-1)S^2}{\sigma^2}=\frac{24 S^2}{6}= 4S^2$

With 25-1 =24 degrees of freedom.

Solution to the problem

Part a

For this case we want this probability:

$P(S^2 > 9.1)$

And we can multiply the inequality by 4 on both sides and we got:

$P(4S^2 > 4*9.1) = P(\chi^2_{24} >36.4) = 0.0502$

And we can use the following excel code to find it: "=1-CHISQ.DIST(36.4,24,TRUE)"

Part b

For this case we want this probability:

$P(3.462 < S^2$

If we multiply the inequality by 4 on all the terms we got:

$P(3.462*4 < 4S^2 < 4*10.745)= P(13.848< \chi^2$ And we can find this probability like this: $P(13.848$ And we use the following code to find the answer in excel: "=CHISQ.DIST(42.98,24,TRUE)-CHISQ.DIST(13.848,24,TRUE)"

8 0

3 years ago

Evaluate the expression.

EastWind [94]

Answer:

42

Step-by-step explanation:

We use (BODMAS) :

Brackets

Order/Index

Division

Multiplication

Addition

Subtraction

Now we do bracket first :

7(3²) = 7(9) = 63

Now we do division :

63÷3 = 21

Now we do multiplication :

2 × 21 = 42

Hope this helped and have a good day

4 0

2 years ago

Read 2 more answers