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3 years ago

The diagram shows a trapezoid prism.

Mathematics

1 answer:

NikAS [45]3 years ago

8 0

Given:

The area of the cross-section is 55cm².

The volume of the prism is 330cm³.

To find:

The length of the prism.

Solution:

We have,

Area of the cross-section = Area of base = 55 cm²

Volume of the prism = 330cm³.

Let x be the length(height) of the prism.

We know that,

$\text{Volume of prism}=\text{Base area}\times height$

$330=55\times x$

$\dfrac{330}{55}=x$

$6=x$

Therefore, the length of the prism is 6 cm.

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tensa zangetsu [6.8K]

Answer: for 4 The 24 balloons cost are $40 and 9 balloons are $1.67

Step-by-step explanation:

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3 years ago

An instructor in a college class recently gave an exam that was worth a total of 100 points. The instructor inadvertently made t

solniwko [45]

Answer:

B) Method 2 will increase the standard deviation of the students' scores.

Step-by-step explanation:

Given that an instructor in a college class recently gave an exam that was worth a total of 100 points.

The average score for his students was 43 and the standard deviation of the scores was 5 points.

And now he is considering two different strategies for rescaling the exam results of which:

Method 1 = Add 17 points to everyone's score.

Method 2 = Multiply everyone's score by 1.7 .

And we have to check what will be the impact of these methods on the standard deviation of the students' scores.

For this let us consider a simple example to understand this:

Firstly, Formula for calculating Standard Deviation = $\sqrt{\frac{\sum (X-Xbar)^{2}}{n-1}}$

Suppose,

X X - Xbar $(X - Xbar)^{2}$

3 3 - 6 = -3 -3 * -3 = 9

5 5 - 6 = -1 -1 * -1 = 1

10 10 - 6 = 4 4 * 4 = 16

Mean of above data, Xbar = $\frac{3+ 5+10}{3}$ = 6

Standard Deviation of data = $\sqrt{\frac{26}{3-1} }$ = 3.6055

Now let us suppose that we multiply each value of above data with 2 so the new data will be:

X X - Xbar $(X - Xbar)^{2}$

3*2 = 6 6 - 12 = -6 -6 * -6 = 36

5*2 = 10 10 - 12 = -2 -2 * -2 = 4

10*2 =20 20 - 12 = 8 8 * 8 = 64

Mean of new data, Xbar = $\frac{6+ 10+20}{3}$ = 12

Standard Deviation of new data = $\sqrt{\frac{104}{3-1} }$ = 7.2111

Hence, we see that when we multiply any value to the data the standard deviation will increase and in other words it will multiplied by that value which value we multiplied with each data value i.e. when we multiply each data value with 2 the standard deviation also get multiplied by as

3.6055 * 2 = 7.2111

Therefore option B is correct that Method 2 will increase the standard deviation of the students' scores.

And on the other hand Similarly by adding any constant to the data the Standard Deviation will remain same. Therefore Method 1 will have no impact on standard deviation of the students' scores.

8 0

3 years ago

Answer for 6x-31=11x+64

PIT_PIT [208]

6x - 31 = 11x + 64
6x cancels out and you take 6x away from 11x
-31 = 5x + 64
64 cancels out and you take 64 away from -31
-95 = 5x
Divide both sides by 5
-19 = x

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3 years ago

Karen purchased a prepaid phone card for $30. Long distance calls cost 16 cents a minute using this card. Karen used her card on

Sedbober [7]

30-24.08=5.92, 5.92/.16=37 minutes

3 0

3 years ago

Help im behind my math class. pls

maks197457 [2]

Answer:

Please check the explanation.

Step-by-step explanation:

From the given diagram, we can observe that r and s are the two parallel lines intersected by the two transversal lines.

Therefore, the pairs of alternating interior angles formed by the two transversal lines are:

∠1 & ∠5

∠2 & ∠4

∠2 & ∠7

∠3 & ∠6

We know that alternating interior angles formed by a transversal line are congruent.

Thus,

∠1 = ∠5

∠2 = ∠4

∠2 = ∠7

∠3 = ∠6

Part a)

Given

m∠1 = 3x + 42

m∠5 = 8x - 8

∠1 = ∠5

3x + 42 = 8x - 8

flipe the equation

8x - 8 = 3x + 42

subtract 3x from both sides

8x - 8 - 3x = 3x + 42 - 3x

5x - 8 = 42

add 8 to both sides

5x - 8 + 8 = 42 + 8

5x = 50

divide both sides by 5

5x/5 = 50/5

x = 10.0000 (Rounded to four decimal places)

Thus, the value of x = 10.0000 (Rounded to four decimal places)

Part b)

Given

m∠6 = 12°

It is clear that angles ∠6 and angle ∠7 lie on a straight line.

Thus,

The sum of ∠6 and ∠7 is 180°.

∠6 + ∠7 = 180°

substituting m ∠ 6 = 12° in ∠6 + ∠7 = 180°

12° + ∠7 = 180°

subtract 12 from both sides

12° + ∠7 - 12° = 180° - 12°

∠7 = 168°

Thus, measure of angle ∠7 = 168°.

We already know that alternating interior angles formed by a transversal line are congruent.

∠7 and ∠2 are alternating interior angles.

Thus,

∠2 = ∠7

As ∠7 = 168°.

Therefore,

∠2 = 168°

Hence, we conclude that

∠2 = 168°

7 0

3 years ago