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3 years ago

Find the product of 2x^4(3x^2 + 4x + 1)

Mathematics

1 answer:

lozanna [386]3 years ago

8 0

Answer:

$2 {x}^{4} (3 {x}^{2} + 4x + 1) \\=6{x}^{(4+2)}+8{x}^{(4+1)}+2{x}^{(4+0)}\\ = \boxed{6 {x}^{6} + 8 {x}^{5} + 2 {x}^{4} }$

<h3>6x⁶+8x⁵+2x⁴ is the right answer.</h3>

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A region is bounded by y=e−3x, the x-axis, the y-axis and the line x = 3. If the region is the base of a solid such that each cr

grigory [225]

Answer:

0.333 $\pi$ units³

Step-by-step explanation:

Think process:

The equation is given as y = $e^{-3x}$

Let, y = f (x)

Therefore, $f (x) = e^{-3x}$

We know that the limits are y-axis and x= 3

Y-axis: x= 0

then limits are given as x= 0 and x = 3

Integrating gives:

$\int\limits^3_0 {e^{-3x} } \, dx$ = $\frac{-1}{3}e^{-3x}$ + C

calculating from x= 0 to x = 3, we know volume is given by $\pi \int\limits^a_b {f(x)} \, dx$

= $\pi$ [ $\frac{-1}{3} e^{-9} - (\frac{-1}{3} e^{0})$ ]

= $\pi$ [0.000041136 + 1/3]

= 0.333 $\pi$ units³

8 0

3 years ago

What is the solution of the equation w/4 +3= w/3

bazaltina [42]

Answer:

Step-by-step explanation:

W====~~~

5 0

3 years ago

COLOR THEME Q ZOOM 1. The ratio of boys to girls at a dance was 9 to 5. How many girls were at the dance if there were 72 boys a

BabaBlast [244]

Answer:

72 boys=72:40

45 girls=81:45

90 girls=162:90

40 girls=72:40

etc.

Step-by-step explanation:

think of it as fractions

3 0

3 years ago

Find p and q for which the linear eqn has infinite solutions

jekas [21]

Answer:

p= 2.5

q= 7

Step-by-step explanation:

The lines should overlap to have infinite solutions, slopes should be same and y-intercepts should be same.

Equations in slope- intercept form:

6x-(2p-3)y-2q-3=0 ⇒ (2p-3)y= 6x -2q-3 ⇒ y= 6/(2p-3)x -(2q+3)/(2p-3)

12x-( 2p-1)y-5q+1=0 ⇒ (2p-1)y= 12x - 5q+1 ⇒ y=12/(2p-1)x - (5q-1)/(2p-1)

Slopes equal:

6/(2p-3)= 12/(2p-1)

6(2p-1)= 12(2p-3)

12p- 6= 24p - 36

12p= 30

p= 30/12

p= 2.5

y-intercepts equal:

(2q+3)/(2p-3)= (5q-1)/(2p-1)

(2q+3)/(2*2.5-3)= (5q-1)/(2*2.5-1)

(2q+3)/2= (5q-1)/4

4(2q+3)= 2(5q-1)

8q+12= 10q- 2

2q= 14

q= 7

7 0

3 years ago

Suppose that the distribution of typing speed in words per minute (wpm) for experienced typists using a new type of split keyboa

KengaRu [80]

Answer:

a. 0.5 or 50%

b. 0.496 or 49.6%

c. 0.8185 or 81.85%

d. Yes, it would be just 0.0013 or 0.13% of probability to find a typist whose speed exceeds 105 wpm

e. 0.0252 or 2.52%

f. The qualifying speed would be 47.4 wpm.

Step-by-step explanation:

a. Let's find the z-score this way:

μ = 60 σ= 15

z-score = (x - μ)/σ

z-score = (60 - 60)/15

z-score = 0

Now, let's calculate the p value for z-score = 0, using the z-table:

p (z=0) = 0.5 or 50%

b. z-score = (x - μ)/σ

z-score = (59.9 - 60)/15

z-score = -0.01

Now, let's calculate the p value for z-score = -.0.01, using the z-table:

p (z = -0.01) = 0.496 or 49.6%

If the question were less or equal than 60, a and b would have the same answer. But in this case, the question is "less than 60 wpm".

z-score = (x - μ)/σ

z-score = (45 - 60)/15

z-score = - 1

Now, let's calculate the p value for z-score = -1, using the z-table:

p (z = -1) = 0.1587

z-score = (x - μ)/σ

z-score = (90 - 60)/15

z-score = 2

Now, let's calculate the p value for z-score = 2, using the z-table:

p (z = 2) = 0.9772

In consequence,

p (-1 ≤ z ≤ 2) = 0.9772 - 0.1587 = 0.8185 or 81.85%

d. z-score = (x - μ)/σ

z-score = (105 - 60)/15

z-score = 3

Now, let's calculate the p value for z-score = 3, using the z-table:

p (z = 3) = 0.9987

In consequence,

p (z > 3) = 1 - 0.9987 = 0.0013

Yes, it would be just a 0.13% of probability to find a typist whose speed exceeds 105 wpm.

e. z-score = (x - μ)/σ

z-score = (75 - 60)/15

z-score = 1

Now, let's calculate the p value for z-score = 1, using the z-table:

p (z = 1) = 0.8413

In consequence,

p (z > 1) = 1 - 0.8413 = 0.1587

and if the two typists are independently selected, then

p = 0.1587 * 0.1587

p = 0.0252 or 2.52%

f. p = 0.2, using the z-table, the z-score is -0.84, then:

z-score = (x - μ)/σ

-0.84 = (x - 60)/15

-12.6 = x - 60

-x = -60 + 12.6

-x = - 47.4

x = 47.4

The qualifying speed would be 47.4 wpm.

8 0

3 years ago