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2 years ago

Write 0.00658 in standard form

Mathematics

1 answer:

Svetllana [295]2 years ago

5 0

Answer:

0.00658 = 6.58 * 10^-3

Step-by-step explanation:

The standard form is a way of writing numbers easily in powers of 10.

To write a number in standard form, we have to move the decimal point to the front of the first non zero number.

Depending on the position of the decimal point to the first non zero number, movement can be towards the right or towards the left. When we move towards the right, our power of 10 will be negative, when we move in the left direction, our power of 10 will be positive

In this question, we shall be moving towards the right. Thus, our power of 10 is negative. We shall be moving towards the right 3 three times

Thus our power would be 10^-3

Thus our standard form will be 6.58 * 10^-3

Kindly note that another pointer is, if the value of our number to be written in standard form is less than zero, then the standard form will come in negative powers of 10. If the value of the number is greater or equal to 1 at least, then then the standard form will be in positive powers of 10

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A researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of th

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Answer:

a. The sample has more than 30 grade-point averages.

Step-by-step explanation:

Given that a researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample

We are asked to find the conditions under which that sample mean can be treated as a value from a population having a normal distribution

Recall central limit theorem here

The central limit theorem states that the mean of all sample means will follow a normal distribution irrespective of the original distribution to which the data belonged to provided that

i) the samples are drawn at random

ii) The sample size should be atleast 30

Hence here we find that the correct conditions is a.

Only option a is right

a. The sample has more than 30 grade-point averages.

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1 year ago

Gavin has 460 baseball players in his collection of baseball cards,and %15 of the players are pitchers.How many pitchers are in

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460 times 0.15
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1 year ago

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Which transformation will map an isosceles trapezoid onto itself? rotation by 180° about its center, reflection across a diagona

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Answer:

The correct option is 4.

Step-by-step explanation:

The non parallel sides of an isosceles trapezoid are congruent.

The image of an isosceles trapezoid is same as the preimage of isosceles trapezoid if

1. Reflection across a line joining the midpoints of parallel sides.

2. Rotation by 360° about its center.

3. Rotation by 360° about origin.

If we rotate the trapezoid by 180° about its center, then the parallel sides will interchanged.

If we reflect the trapezoid across a diagonal, then the resultant figure will be a parallelogram.

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After rotation by 360° about the center, we always get an onto figure.

Therefore option 4 is correct.

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A student club holds a meeting. The predicate M(x) denotes whether person x came to the meeting on time. The predicate O(x) refe

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Answer:

a) $\exists \, x \in C : O(x) = 0$

b) $\{ x \in C : O(x) = 1 \} \subseteq \{ x \in C : M(x) = 1 \}$

c) $\{ x \in C: M(x) = 1 \} = C$

d) $\{ x \in C : D(x) = 1 \} \, \cup \, \{x \in C : M(x) = 1 \} = C$

e) $\exists \, x \in C : M(x) = 1 \, \wedge D(x) = 1$

f) $\exists \, x \in C : O(x) = 1 \, \wedge M(x) = 0$

Step-by-step explanation:

M(x) = 1 if the person x came to the meeting, and 0 otherwise.

O(x) = 1 if the person is an officer of the club and 0 otherwise.

D(x) = 1 if the person has paid hid/her club dues and 0 otherwise.

Lets also call C the set given by the members of the club. C is the domain of the functions M, O and D.

a) If someone is not an officer, the there should be at least one value x such that O(x) = 0. This can be expressed by logic expressions this way

$\exists \, x \in C : O(x) = 0$

b) If all the officers came on time to the meeting, then for a value x such that O(x) = 1, we also have that M(x) = 1. Thus, the set of officers of the Club is contained on the set of persons which came to the meeting on time, this can be written mathematically this way:

$\{ x \in C : O(x) = 1 \} \subseteq \{ x \in C : M(x) = 1 \}$

c) If everyone was in time for the meeting, then C is equal to the set of persons who came to the meeting on time, or, equivalently, the values x such that M(x) = 1. We can write that this way:

$\{ x \in C: M(x) = 1 \} = C$

d) If everyone paid their dues or came on time to the meeting, then if we take the set of persons who came to the meeting on time and the set of the persons who paid their dues, then the union of the two sets should be the entire domain C, because otherwise there should be a person that didnt pay nor was it on time. This can be expressed logically this way:

$\{ x \in C : D(x) = 1 \} \, \cup \, \{x \in C : M(x) = 1 \} = C$

e) If at least one person paid their dues on time and came on time to the meeting, then there should be a value x on C such that M(x) and D(x) are both equal to 1. Therefore

$\exists \, x \in C : M(x) = 1 \, \wedge D(x) = 1$

f) If there is an officer who did not come on time for the meeting, then there should be a value x in C such that O(x) = 1 (x is an officer), and M(x) = 0. As a result, we have

$\exists \, x \in C : O(x) = 1 \, \wedge M(x) = 0$

I hope that works for you!

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2 years ago

The same student (as in the previous question) realizes that he has forgotten to zero the balance before measurements of data se

seraphim [82]

Answer:

The average value of the second set of measurements obtained with the properly zeroed balance is 550g.

Step-by-step explanation:

The average value of a set is the sum of all the elements of the set divided by the cardinality(number of elements) of the set.

Here, our set of data with the properly zeroed balance is as follows:

547 g, 554 g, 546 g, 554 g, 548 g, 545 g, 546 g, 555 g, 553 g, 552

There are 10 values in this set, to the average value is:

$A = \frac{547 g + 554 g + 546 + 554 g + 548 g + 545 g + 546 g + 555 g + 553 g + 552g }{10}$

$A = \frac{5500}{10}$

$A = 550g$

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