Thirty- eight percent of the animals in a dog and cat rescue center are cats. What percentage are dogs?

Fred and Frank play a game. Fred picks an even number X and asks Frank to add all even numbers between 0 and X (inclusive) as fa

TiliK225 [7]

Answer:

The even numbers between 0 and X represents an arithmetic sequence with a common difference of 2

The rule of arithmetic sequence = a + d(n - 1)

Where a is the first term and n is the number of terms

So, for the even numbers between 0 and X

The first term = a = 0

d = 2

So, we need to find n at the last term which is X

∴ X = 0 + 2 ( n -1 )

∴ n - 1 = X/2

∴ n = X/2 + 1

The sum of the arithmetic sequence = (n/2) × (2a + (n−1)d)

Substitute with a and d and X

So, the sum = (n/2) * (2*0 + (n−1)*2)

= (n/2) * ((n−1)*2)

= n(n-1)

= (X/2 + 1) * (X/2)

= X/2 by (X/2 + 1)

So, The quick way to add all even numbers between 0 and X always works.

8 0

2 years ago

Examine the fraction 3+2i4−2i. Which expression is the first step to simplify the fraction? 3+2i4−2i⋅3−2i3−2i

umka2103 [35]

Answer:

The correct answer is the last option.

Step-by-step explanation:

When you have a fraction with complex numbers, the first step to simplify is to multiply up and down the conjugate of the denominator, this will eliminate the complex part of the denominator, and in this way you can separate the expression in its real and complex part.

For the expression:

$\frac{3 + 2i}{4-2i
}$

The denominator conjugate is 4 + 2i

When multiplied, the denominator is:

$4 ^ 2 -4i ^ 2 = 16 -4 (-1) = 20$

4 0

2 years ago

Select the correct answer from each drop-down menu. the four vertices of an inscribed quadrilateral divide a circle in the ratio

AleksandrR [38]

The four angles of a quadrilateral are 30°, 60°, 150°, and 120° if the four vertices of an inscribed quadrilateral divide a circle in the ratio 1:2:5:4.

<h3>What is quadrilateral?</h3>

It is defined as the four-sided polygon in geometry having four edges and four corners.

We have the four vertices of an inscribed quadrilateral divide a circle in the ratio:

1:2:5:4

Let the sides of the quadrilateral be x, 2x, 5x, 4x.

We know the sum of all angles of quadrilateral = 360°

x+2x+5x+4x=360

12x = 360

First angle, x = 30°

Seconds angle, 2x = 2×30 ⇒ 60°

Third angle, 5x = 5×30 ⇒ 150°

Fourth angle, 4x = 4×30 ⇒ 120°

Thus, the four angles of a quadrilateral are 30°, 60°, 150°, and 120°

Learn more about the quadrilateral here:

brainly.com/question/6321910

3 0

1 year ago

Item 16 An indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumping it on the people b

nignag [31]

Answer:

3:16 P.M.
5:22 P.M.

Step-by-step explanation:

The two dump intervals have a greatest common factor (GCF) of 3, so their least common multiple (LCM) is ...

(18)(21)/3 = 126 . . . . minutes

This period is 2 hours 6 minutes. The last time both dumped was 1:10, so the next time both will dump is ...

1:10 +2:06 = 3:16 . . . P.M.

and the next time after that is ...

3:16 +2:06 = 5:22 . . . P.M.

4 0

2 years ago

The circular stream of water from a faucet is observed to taper from a diameter of 20 mm to 10 mm in a distance of 50 cm. Determ

steposvetlana [31]

Solution:

From Bernoulli equation

$\frac{1}{2}$ ρ $V_{1}^{2}$ + ρgh = $\frac{1}{2}$ ρ $V_{2}^{2}$ , where ρ is density of water, h – height difference and $V_{1}$ and $V_{2}$ are the velocities in upper and lower cross sections correspondingly. We take into account that the pressure in both cross-sections is the same and equal to the atmospheric one.

From the continuity and assuming water incompressible:

$\pi r_{1}^{2}$ $V_{1}$ = $\pi r_{2}^{2}$ $V_{2}$ , where $A_{1}$ and $A_{2}$ are the corresponding cross-sections. As the lower diameter is twice as low as the upper one, we can conclude that $V_{1} = \frac{V_{2}}{4}$

Inserting it back into Bernoulli equations produces:

$V_{1} = \sqrt{\frac{2}{15}gh} = 0.26m/s$ and the flow rate is

$\pi r_{1}^{2}V_{1} = \pi r_{2}^{2}V_{2} = 8.10^{-5} \frac{m^{3} }{s}$

6 0

2 years ago