MATHEMATICS COLLEGE

You have a litre bottle of water and drink 375 millilitres.
How much is left?

Answers

Answer 1

Answer:

Answer:

625 ml

Step-by-step explanation:

1 litre is 1000 milliliters

1000 milliliters minus 375 milliliters is 625 milliliters

you have to subtract because you are looking for what is left

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Write 2 equivalent ratios for each ratio given:
2/7
3:3 1/2

2.5 to 6

Answers

Answer:

2/7 = 4/14

3:3 = 6:6

1/2 = 2/4

2.5:6 = 5:12

Step-by-step explanation:

For the first one, we can multiply the numerator and denominator of the fraction by 2 to get an equivalent fraction which is 4/14

For the second one we can multiply each side by 2 to get the ratio of 6:6

For the third one we can multiply the numerator and denominator by 2 to get 2/4

For the last one we can multiply each side by 2 to get 5:12

Find the angle between the vectors ????=????+???? and ????=−????+????. (Give an exact answer. Use symbolic notation and fractions where needed.)

Answers

Answer:

The angle between them is 60 degrees

Step-by-step explanation:

Given

$a = 2i + j -3k$

$b = 3i - 2j -k$

Required

The angle between them

The cosine of the angle between them is:

$\cos(\theta) = (a\cdot b)/(|a|\cdot |b|)$

First, calculate a.b

$a \cdot b =(2i + j -3k) \cdot (3i - 2j -k)$

Multiply the coefficients of like terms

$a \cdot b =2 * 3 - 1 * 2 - 3 * -1$

$a \cdot b =7$

Next, calculate |a| and |b|

$|a| = \sqrt{2^2 + 1^2 + (-3)^2$

$|a| = \sqrt{14$

$|b| = √(3^2 + (-2)^2 + (-1)^2)$

$|b| = √(14)$

Recall that:

$\cos(\theta) = (a\cdot b)/(|a|\cdot |b|)$

This gives:

$\cos(\theta) = (7)/(√(14) * √(14))$

$\cos(\theta) = (7)/(14)$

$\cos(\theta) = 0.5$

Take arccos of both sides

$\theta =\cos^(-1)(0.5)$

$\theta =60^o$

Add the numbers in the series 3+11+19+27+.....+395+403.

Answers

Answer:

10353

Step-by-step explanation:

The given series is in arithmetic progression since the common difference is same which is 8.

To find the sum of series we can simply apply the formula'

S= n/2( first term + last term)

S is the sum and n is the number of terms

we also need to find the number of terms n

n = (last term- first term)/2 + 1

$n= (403-3)/(8) + 1$

n= 51

$s= (51)/(2)(3+403)$

s= 10353

Evaluate k - m if k = 8, m = -7, and p = -10.

Answers

Answer:15

8-(-7)=8+ 7=15 BECAUSE -(-7) = +7

Step-by-step explanation:

BECAUSE -(-7) = +7 SO THE PROBLEM CHANGES TO 8+7=15

P=10 HAS NOTHING TO DO WITH THE FORMULA. K-M=?

A survey among students at a certain university revealed that the number of hours spent studying the week before final exams was approximately normally distributed with mean 25 and standard deviation 6. What proportion of students studied between 25 and 34 hours

Answers

Answer:

$P(25<X<34)=P((25-\mu)/(\sigma)<(X-\mu)/(\sigma)<(34-\mu)/(\sigma))=P((25-25)/(6)<Z<(34-25)/(6))=P(0<z<1.5)$

And we can find this probability with this difference:

$P(0<z<1.5)=P(z<1.5)-P(z<0)$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(0<z<1.5)=P(z<1.5)-P(z<0)=0.933-0.5=0.433$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem'

Let X the random variable that represent the hous spent studying the week before final exams of a population, and for this case we know the distribution for X is given by:

$X \sim N(25,6)$