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Liono4ka [1.6K]
3 years ago
10

Dirk plants 12 seedlings in 8 min.

Mathematics
2 answers:
Slav-nsk [51]3 years ago
8 0
The answer would be b 105
Luda [366]3 years ago
4 0
This is a proportion question 
in 8 minutes he plants 12 seedlings
so in 1 minute he plants 12/8 seedlings

In 70 minutes he plants    (12 * 70) / 8 = 105 seedlings.
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JulsSmile [24]

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6 0
2 years ago
A 6.50% coupon bond with 18 years left to maturity is offered for sale at $1,035.25. What yield to maturity [interest rate] is t
Basile [38]

Answer:

The yield to maturity is 6.3974%

Step-by-step explanation:

The computation of the yield to maturity is as follows

Given that

NPER = 18 × 2 = 36

PMT = $1,035.25 × 6.50% ÷ 2 = $33.65

PV = $1,035.25

FV = $1,000

The formula is shown below:

=RATE(NPER;PMT;-PV;FV;TYPE)

The present value comes in negative

AFter applying the above formula, the yield to maturity is

= 3.1987% × 2

= 6.3974%

Hence, the yield to maturity is 6.3974%

7 0
3 years ago
If a = 5^x, b = 5^y and a^y×b^x = 25 then prove that: xy =1​
avanturin [10]

a =  {5}^{x}  \\ b =  {5}^{y}  \\  {a}^{y}  \times  {b}^{y}  = 25 \\ prove \: ( {5}^{x} )^{y}  \times ( {5}^{y} ) ^{x}  = 25 \\  {5}^{xy}  \times  {5}^{yx}  = {5}^{2} \\  {5 }^{xy + yx}  = 5^{2}  \\ 5^{2xy}  =  {5}^{2} \\ is \:  \: 2xy = 2 \\ xy =  \frac{2}{2}  \\ xy = 1

3 0
3 years ago
For what value of c is the function defined below continuous on (-\infty,\infty)?
kozerog [31]
f(x)= \left \{ {{x^2-c^2,x \ \textless \  4} \atop {cx+20},x \geq 4} \right&#10;

It's clear that for x not equal to 4 this function is continuous. So the only question is what happens at 4.
<span>A function, f, is continuous at x = 4 if 
</span><span>\lim_{x \rightarrow 4} \  f(x) = f(4)

</span><span>In notation we write respectively
</span>\lim_{x \rightarrow 4-} f(x) \ \ \ \text{ and } \ \ \ \lim_{x \rightarrow 4+} f(x)

Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just <span>4c + 20.
</span>
On the other hand, for x < 4, f(x) = x^2 - c^2. Hence 
\lim_{x \rightarrow 4-} f(x) = \lim_{x \rightarrow 4-} (x^2 - c^2) = 16 - c^2

Thus these two limits, the one from above and below are equal if and only if
 4c + 20 = 16 - c²<span> 
 Or in other words, the limit as x --> 4 of f(x) exists if and only if
 4c + 20 = 16 - c</span>²

c^2+4c+4=0&#10;\\(c+2)^2=0&#10;\\c=-2

That is to say, if c = -2, f(x) is continuous at x = 4. 

Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers (-\infty, +\infty)

4 0
3 years ago
The base of a pentagonal prism is regular with an apothem of 4 cm. The height of the prism is 16 cm. Find the volume of the pris
Georgia [21]

Answer:

volume ≈ 930 cm³ (nearest cubic cm)

Step-by-step explanation:

The base of the prism which is a pentagon is regular. The apothem which is a line drawn from the center to any side of the pentagon is 4 cm. The height of the prism is 16 cm.

The volume of a prism = Bh

where

B = base area

h = height of the prism

The base of the prism can be divided into 5 congruent triangles.But the base of the triangles is unknown.

The sum of interior angle of a pentagon is 540°. That means each angle is 108° . The triangle divide the angle into 2. Making the 2 base angle as 54° each. The last angle of the triangle at the center is 72°(remember sum of angle in a triangle is 180° which is 54° + 54° + 72° = 180°) .

The angle form the center can be divided by the line of height of the triangles. The angle will then be 36°. Using tangential ratio half of the length of the base of the triangle can be known. Therefore,

tan 36° = opposite/adjacent

tan 36° = opposite/4

opposite = 4 tan 36°

The full base of the triangles = 2(4 tan 36°)

area of each triangle = 1/2 × 2(4 tan 36°) × 4 = 16 tan 36°

Base area of the prism(pentagon) = 5 × 16 tan 36° = 80 tan 36°

Volume of the prism = Bh

where

h = 16 cm

B = 80 tan 36°

volume =  80 tan 36° × 16 = 1280  tan 36° = 1280  × 0.726542528

volume = 929.974435847  cm³

volume ≈ 930 cm³ (nearest cubic cm)

5 0
3 years ago
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