A quantity with an initial value of 200 grows continuously at a rate of 4% per second.
What is the value of the quantity after 1.55 minutes, to the nearest hundredth?

Answer:

Step-by-step explanation:

Remark

The first step is the key step. You have to get the xs on one side and the numbers on the other.

Solution

4 + 6x = 16                  Subtract 4 from both sides

4-4+6x = 16 - 4           Combine

6x = 12                        Divide both sides by 6. You want x by itself.

6x/6 = 12/6

Answer: x = 2

If the two cylinders are similar, that means that the ratio between the diameter and the height will be the same in both solids.

In the bottom cylinder, we have a ratio of 3ft to 12ft. This is a ratio of 3:12, or 1:4, where the 1 is the height and 4 is the diameter.

The top cylinder has a height of 8 inches, meaning that the 8 corresponds to the 1 in the ratio. Thus, we can set up the equation like this:

[tex]\frac{1}{4} =\frac{8}{x}[/tex]

To get from 1 to 8, we have to multiply by 8. But because we don't want to change the ratio, we have to multiply the denominator by 8 as well:

[tex]\frac{1}{4}*\frac{8}{8}=\frac{8}{32}[/tex]

That means the top cylinder has a diameter of 32. But we can't forget our units. Because we used 8 inches in our ratio, that means the diameter is 32 inches.

The multiplicative inverse for √2-i = 1/(√2+1) and  The multiplicative inverse is √2+1 = 1/(√2-1)

Given Data

For√2+i

the real part is  is √2 and the imaginary part is i

The multiplicative inverse is √2+1 = 1/(√2-1)

rationalising the denominator we have

= 1/√2-1 * √2-1/√2-1

= √2-1/(√2-1)*(√2-1)

= √2-1/(2-√2-√2+1)

= √2-1/(-2√2+3)

For√2-i

the real part is  is √2 and the imaginary part is -i

The multiplicative inverse is √2-1 = 1/(√2+1)

Rationalising the denominator we have

= 1/√2+1 * √2+1/√2+1

= √2+1/(√2+1)*(√2+1)

= √2+1/(2+√2+√2+1)

= √2+1/(2√2+3)

Learn more about complex Numbers here

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Answer:

c. It is a reflection around the x-axis and a reflection around the y-axis

Step-by-step explanation:

The total amount accrued, principal plus interest, with compound interest on a principal of $3,000.00 at a rate of 6% per year compounded 1 times per year over 3 years is $3,573.05.

Given Data

A = P + I where

P (principal) = $3,000.00

I (interest) = $573.05

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 6/100

r = 0.06 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 3,000.00(1 + 0.06/1)^(1)(3)

A = 3,000.00(1 + 0.06)^(3)

A = $3,573.05

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The measurements that show equal length is 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft

An equation is an expression that shows the relationship between two or more numbers and variables.

1 ft = 12 in; 1 yd = 3 ft and 1 yd = 36 in.

Hence:

15 yd = 15 yd * 36 in per yd = 540 in

195 ft = 195 ft * 12 in per ft = 2340 in

5280 yd = 5280 yd * 3 ft per yd = 15840 ft

The measurements that show equal length is 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft

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Answer:

The answer is J.

Step-by-step explanation:

Because y= 2x-3 as shown on the graph and on the chart it shows y=-x+3

Answer:

See the explanation

Step-by-step explanation:

Please see the photo

Answer:

$3.50

Step-by-step explanation:

For this question, you just take the price paid and divide it by the number of gallons.  In this case, you get $3.50 per gallon.

Answer:

34

Step-by-step explanation:

Sum of two numbers = 7

1+6

2+5

3+4

34+9=43

[tex]===============================[/tex]

Let's find the square root of

[tex]\bold{\displaystyle\frac{144}{169}}[/tex]

So what number times itself equals [tex]\bf{\displaystyle\frac{144}{169}}[/tex]?

Take the square root of both the numerator (144) and the denominator (169)

[tex]\bold{\sqrt{\displaystyle\frac{144}{169} }}[/tex]

The square root of 144 is 12 (12 times itself equals 144), and the square root of 169 is 13 (13 times itself equals 169)

[tex]\bold{\displaystyle\frac{12}{13}}[/tex]

This number times itself equals [tex]\bf{\displaystyle\frac{144}{169}}[/tex].

[tex]==================================[/tex]

Answered by:

[tex]^\star^\bigstar^\circ\tt{An~Emotional~Helper!~:D}}^\circ^\bigstar[/tex]

Answer:

multiplication, so d, 2 x 3

Step-by-step explanation:

remember... PEMDAS!!

Answer:

#10=462

#11=240

Step-by-step explanation:

22x21=462

16x15=240

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$420\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &7 \end{cases} \\\\\\ 420 = (P)(0.06)(7)\implies \cfrac{420}{(0.06)(7)}=P\implies 1000=P[/tex]

Answer:

90

Step-by-step explanation:

im not sure but im pretty sure it would be 90 dont come at me if it not:(

Answer:

360°/3=120°

 which is the size of each exterior angle.

Step-by-step explanation:

An equilateral triangle has 3 lines of symmetry, but of more importance in this case, it has rotational symmetry of order 3. This means that in a rotation of 360° the same image appears 3 times.

360°/3=120°   which is the size of each exterior angle.

The triangle rotates through the exterior angle so that the next vertex can be in the same position as the previous one.

IN the same way, a square will rotate through 360/4=90°

A pentagon will rotate through 360/5=72°

for the figure to map onto itself.

Answer:

Step-by-step explanation:

diameter = 6 in

r = 6/2 = 3 in

h = 8 in

[tex]\textbf{Area of cylinder = $2\pi r(r+h)$ }[/tex]

                              [tex]= 2*3.14*3*(3+8)\\\\= 2*3.14*3*11\\\\= 207.24 \ in^{2}[/tex]

The probability of getting no kings is 0.7826

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

The random experiment follows a hypergeometric distribution with,

N = 52 since there are 52 cards in a deck.

k = 4 since there are 4 kings in a deck.

n = 3 since we randomly select 3 cards from the deck.

x = 0 since we want no kings.

The probability of getting no kings is;

[tex]\rm = \dfrac{^4C_0 \times ^{48}C_3}{^{52}C_3}\\\\=\dfrac{1 \times 17296}{22100}\\\\= 0.78[/tex]

Hence, the probability of getting no kings is0.7826.

To know more about probability click the link given below.

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The speed of the river current if the speed of the motorboat in still water is 15 km/h is 3 km/h.

Let x be the speed of the current in km/h units

Speed of the boat traveling against the current= (15-x) km/h

Time spent traveling 36 miles against the current=36/15-x hours

Time spent rafting36miles (with the current) =35/x hours

Equation=36/x-36/15-x=9

Multiply both sides by x×(15-x)

36×(15-x) - 36x = 9x×(15-x)

540 - 36x - 36x=135x-9x²

9x²-207x+540=0

x²-23x+60=0

(x-3)×(x-30) = 0

Roots are x= 3 and  x= 30

Since 15-x must be positive, the only root x = 3 survives

Hence:

Speed =3 km/h

Inconclusion the speed of the river current if the speed of the motorboat in still water is 15 km/h is 3 km/h.

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Answer:

43

Step-by-step explanation:

equation= sqrt (x2-x1)^2 + (y2-y1)^2

The most likely equation for line P so the set of equations has infinitely many solutions is 2x + 2y = -2.

If a linear equation has the same variable term and the same constant value on both sides of the equation, it has infinitely many solutions.

Therefore, let's check for the equation with the same terms and constant with the equation :

x + y = -1

Hence, the most likely equation of line p is as follows:

2x + 2y = -2

divide both sides by 2

2x/ 2 + 2y / 2  = -2 / 2

x + y = - 1

The equation of the line will be 2x + 2y = -2

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#SPJ1

Answer:

   16.5 ≈ x

Step-by-step explanation:

We have a right triangle where we know 1 side, 1 angle and we need to find another side. We can use trigonometric functions to find the missing side.

The tangent function definition is

tan α = opposite side/ adjacent side

In our problem

   tan 70° = x/ 6, multiply both sides by 6 to isolate x

6 · tan 70° = x, use the calculator (make sure is set in degrees)

    16.4848 ≈ x , round to the nearest tenths

         16.5 ≈ x

Answer:

x is 6 degrees

Step-by-step explanation:

so its 90 degress, how do i know? because it is parrallel to the one with a half square (the 90 degrees) so we equal the angels to 90  because they are equal to 90 (sorry if it sounds confusing, if you want i can still explain more later)

7x + 8x = 90

15x = 90

x = 90/15

x = 6

Answer:

Explanation:

Both the angles lie inside a right angle, whose total sum is 90 degrees.

Solve:

Each of the angle:

Answer: m∠1 + m∠4 = 180°

Step-by-step explanation:

If angles 1 and 4 are supplementary, their measures must add to 180 degrees.

Answer:

24y

Step-by-step explanation:

Multiple 6x4 to get 24

and then put the y in to

get your answer

solution÷

6×4y

6×4y=0

multiply 6×4y

24y=0

now send 24 to the right side and divide

y=0÷24

therefore,y=0

Answer:

3.6.

Step-by-step explanation:

15% = 15/100 = 0.15

so the answer is 0.15 * 24

= 3.6

Answer:

3.60

Step-by-step explanation:

Note:

Of = Multiply

15% can also be written as .15 as decimal

Solve:

.15 × 24 = 3.60

 Or we can solve like this:

[tex]\frac{24}{x}=\frac{100\%}{15\%}[/tex]

[tex]\frac{x}{24}=\frac{15}{100}[/tex]

[tex]\Rightarrow x=3.6[/tex]

Therefore, 15% of  £24 is 3.60

~Lenvy~

Answer:

:))

Step-by-step explanation:

Answer:

Q1. 95 degrees  

Q2. 100 degrees

Step-by-step explanation:

When you create a triangle, all angle measures must equal 180 degrees.

So, using that information, take 180 and subtract both of the other values.

180 - 25 = 155

155 - 60 = 95

When two angles are supplementary, the sum of their angle measures equal 180, or a straight angle.

Using that information, take 180 and subtract 80.

180 - 80 = 100