Faith invested $1,100 in an account paying an interest rate of 5.1% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 18 years?

Answer: 1/3

Step-by-step explanation:

Half of the 14 brown eggs are cracked so there are 7 cracked eggs. There are 7+14=21 eggs in total so the probability of getting a cracked egg that is brown is 7/21=1/3

Answer:

1055.99 rad/min

Step-by-step explanation:

Given that,

The diameter of a bicycle, d = 24 inches

Radius, r = 12 inches

The bicycle is travelling at 12 mi/h.

We need to find the angular speed of the wheels in rad/min.

We know that,

1 mi/h = 0.0166667 mi/min

It means,

12 mi/h = 0.2 mi/min

Also,

12 inch = 0.000189394 miles

The angular speeds of the wheels is given by :

[tex]v=r\omega\\\\\omega=\dfrac{v}{r}\\\\\omega=\dfrac{0.2}{0.000189394}\\\\\omega=1055.99\ rad/min[/tex]

So, the angular speeds of the wheels is 1055.99 rad/min.

Answer: 2

bc 50+20=70

140 divided by 70 is 2

Step-by-step explanation:

Answer:

The solution is (0,4).

Step-by-step explanation:

We are given the following system of equations:

[tex]8x + 9y = 36[/tex]

[tex]3x + 4y = 16[/tex]

Solving by substitution.

In the first equation, we have that:

[tex]8x + 9y = 36[/tex]

[tex]8x = 36 - 9y[/tex]

[tex]x = \frac{36-9y}{8}[/tex]

Replacing in the second equation:

[tex]3x + 4y = 16[/tex]

[tex]3\frac{36-9y}{8} + 4y = 16[/tex]

Multiplying everything by 7

[tex]3(36 - 9y) + 32y = 128[/tex]

[tex]108 - 27y + 32y = 128[/tex]

[tex]5y = 20[/tex]

[tex]y = \frac{20}{5}[/tex]

[tex]y = 4[/tex]

Now, with y, we can find x.

[tex]x = \frac{36-9*4}{8} = 0[/tex]

So the solution is (0,4).

Answer:

Hope it help

Mark me as brainliest

Step-by-step explanation:

Recall the definition of absolute value:

• If x ≥ 0, then |x| = x

• If x < 0, then |x| = -x

(a) Splitting up f(x) = x |x| into similar cases, you have

• f(x) = x ² if x ≥ 0

• f(x) = -x ² if x < 0

Differentiating f, you get

• f '(x) = 2x if x > 0 (note the strict inequality now)

• f '(x) = -2x if x < 0

To get the derivative at x = 0, notice that f '(x) approaches 0 from either side, so f '(x) = 0 if x = 0.

The derivative exists on its entire domain, so f(x) is differentiable everywhere, i.e. over the interval (-∞, ∞).

(b) Similarly splitting up g(x) = x + |x| gives

• g(x) = 2x if x ≥ 0

• g(x) = 0 if x < 0

Differentiating gives

• g'(x) = 2 if x > 0

• g'(x) = 0 if x < 0

but this time the limits of g'(x) as x approaches 0 from either side do not match (the limit from the left is 0 while the limit from the right is 2), so g(x) is differentiable everywhere except x = 0, i.e. over the interval (-∞, 0) ∪ (0, ∞).

Answer:

7 yards

Step-by-step explanation:

sqrt(49)=7

The value of the x is 7 yards. The correct option is b.

Square is a polygon which has 4 sides. All four sides of the square are equal length and perpendicular to each other, that means the angle between two adjacent side is 90°.

Given shape is a square.

And side of the square is x yards.

The area inside the garden is 49 square yards.

Area is the amount of area occupied by an object's flat (2-D) surface or shape.

So, the area of the square = (side x side)

Substituting the values,

49 = (x)²

x = 7

Therefore, the side is 7 yards.

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Answer:

The student completed 13 courses worth 3 credits

Step-by-step explanation:

System of Equations

Let's assign the following variables:

x = number of courses worth 3 credits

y = number of courses worth 4 credits

Some student completed 18 courses thus:

x + y = 18      [1]

The student earned a total of 59 credits:

3x + 4y = 59       [2]

From [1]:

y = 18 - x

Substituting in [2]:

3x + 4(18 - x) = 59

Operating:

3x + 72 - 4x = 59

Simplifying:

-x = 59 - 72 = -13

x = 13

The student completed 13 courses worth 3 credits

Answer:

48

Step-by-step explanation:

If EG=8, OE=4

x/12=4

x=4(12)

x=48

Answer:

3

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

5x3=15 and 3x9=27 so it’s 3.

9514 1404 393

Answer:

  y = 1/2x - 4

Step-by-step explanation:

The point-slope form of the equation for a line is a useful starting place when slope and point are given.

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

  y -(-2) = 1/2(x -4) . . . . line with slope 1/2 through point (4, -2)

  y = 1/2x - 4 . . . . . . . . eliminate parentheses, subtract 2

Answer:

(-6,4) hope that helps you it's that in the y there is two 4

Answer:

f(x) = (1/10)x²

Step-by-step explanation:

This is the answer that  I think it is but I am not sure if it is right...

Hope this helps!

Answer:

C or D

Step-by-step explanation:

Answer:

I think option D 3 times y divided by 8

the answer for the question is 24

.

Answer:

0.2

Step-by-step explanation:

2/10 or 1/5

Answer:

0.2

Step-by-step explanation:

Answer:

4(x - 9)^2 - 17

Step-by-step explanation:

A horizontal shift to the right by 9 changes x^2 to (x - 9)^2.

A vertical shift down by 1 changes - 16 to -17.

Therefore, the new equation is:

4(x - 9)^2 - 17

The options that are true are (1), (3) and false ones are (2), (4).

The basis of all mathematical operations are the arithmetic operations. These operations include addition, subtraction, multiplication, and division.

The given options can be examined one by one as follows,

(1) The given number 20 may be expressed as a mathematical operation as follows:

20 = 10 × 2

Which implies it is two times that of 10.

Thus, it is true.

(2) The given number 10 may be expressed as a mathematical operation as follows:

10 = 20 ÷ 2

Which implies it is half of 20.

Thus, it is false.

(3) The given number 30 may be expressed as a mathematical operation as follows:

30 = 15 × 2

Which implies it is two times that of 15.

Thus, it is true.

(4) The given number 15 may be expressed as a mathematical operation as follows:

15 = 30 ÷ 2

Which implies it is half of 30.

Thus, it is false.

Hence, the true and false options are (1), (3) and (2), (4) respectively.

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Work Shown:

Let's say there are 28 cards in a full stack.

6/7 = 24/28 after multiplying top and bottom by 4

Since he has 24/28 of a stack left, this means he has 24 cards left.

He wants to arrange the remaining cards into piles so that each pile consists of 3/28 of a full stack. In other words, he wants each pile to have 3 cards.

So this must mean he will get 24/3 = 8 piles

(8 piles)*(3 cards per pile) = 8*3 = 24 cards total

A fraction is a way to describe a part of a whole. The number of stacks that Peter has left into stacks that are each 3/28 of a pack of the left cards is 8.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

Given that Peter has 6/7 of a stack of baseball cards left. Also, he makes small stacks from the left cards of size 3/28. Therefore, the number of stacks Peter made,

[tex]\text{Number of stacks Peter made} = \dfrac{\text{Stack of baseball cards left}}{\text{Size of small stack of cards}}\\\\\\\text{Number of stacks Peter made} = \dfrac{\frac{6}{7}}{\frac{3}{28}}\\\\\\\text{Number of stacks Peter made} = \dfrac{6 \times 28}{7 \times 3} = 8[/tex]

Hence, the number of stacks that Peter has left into stacks that are each 3/28 of a pack of the left cards is 8.

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Answer:

1.5

Step-by-step explanation:

4:6 = 1:1.5

Answer:

[tex]105m^3/min[/tex]

Step-by-step explanation:

We are given that

Base side of square pyramid, a=3 m

Height of square pyramid, h=9m

[tex]\frac{da}{dt}=6m/min[/tex]

[tex]\frac{dh}{dt}=-1/min[/tex]

We have to find  the rate of change of the volume of the pyramid at that instant.

Volume of square pyramid, V=[tex]\frac{1}{3}a^2h[/tex]

Differentiate w.r.t t

[tex]\frac{dV}{dt}=\frac{1}{3}(2ah\frac{da}{dt}+a^2\frac{dh}{dt})[/tex]

Substitute the values

[tex]\frac{dV}{dt}=\frac{1}{3}(2(3)(9)(6)+(3^2)(-1)[/tex]

[tex]\frac{dV}{dt}=105m^3/min[/tex]

Hence, the rate of change of the volume of the pyramid at that instant=[tex]105m^3/min[/tex]

Answer:  Add 7+ [tex]\frac{2}{3}= \frac{7}{1} + \frac{2}{3} = \frac{7.3}{1.3} + \frac{2}{3} = \frac{21.2}{3} = \frac{23}{3}[/tex] For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(1, 3) = 3. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 3 = 3. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - seven plus two thirds = twenty-three thirds.

Multiple: 2 * [tex]\frac{3}{5} = \frac{2.3}{1.5} = \frac{6}{5}[/tex] Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(6, 5) = 1. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - two multiplied by three fifths = six fifths.

Subtract = [tex]\frac{23}{3} - \frac{6}{5} = \frac{23.5}{3.5} - \frac{6.3}{5.3} = \frac{115}{15} - \frac{18}{15} =\frac{115 - 18}{15}[/tex]For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(3, 5) = 15. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 5 = 15. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - twenty-three thirds minus six fifths = ninety-seven fifteenths.

Multiple: 4 Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(388, 15) = 1. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - four multiplied by ninety-seven fifteenths = three hundred eighty-eight fifteenths.

Step-by-step explanation:

hope this helps

Answer:10.14

Step-by-step explanation:

Answer:

the rate / speed of the boat is 10 miles per hour.

the rate / speed of the current is 2 miles per hour.

Step-by-step explanation:

r = rate of boat (speed of boat)

t = time

d = distance.

c = rate of current (speed of current)

with the current, the formula becomes (r + c) * t = d

against the current, the formula becomes (r - c) * t = d

going with the current, the boat takes 1 hour to travel 12 miles.

therefore:

(r + c) * t = d becomes (r + c) * 1 = 12

going against the current, the boat takes 1.5 hour to travel the same 12 miles.

therefore:

(r - c) * t = d becomes (r - c) * 1.5 = 12.

your two equations that need to be solved simultancously are:

(r + c) * 1 = 12

(r - c) * 1.5 = 12

divide both sides of the second equation by 1.5 and leave the first equaion as is to get:

r + c = 12

r - c = 8

add the equations together to get:

2 * r = 20

solve for r to get:

r = 20 / 2 = 10

(r + c) * 1 = 12 becomes (10 + c) * 1 = 12

simplify to get 10 + c = 12

solve for c to get c = 12 - 10 = 2

(r - c) * 1 = 8 becomes (10 - c) * 1 = 8

simplify to get 10 - c = 8

solve for c to get c = 10 - 8 = 2

you have:

r = 10

c = 2

that's your solution.

the rate / speed of the boat is 10 miles per hour.

the rate / speed of the current is 2 miles per hour.

Answer:

foot marker 320 at t=0

Step-by-step explanation:

8 sec x 85 ft/s =680 ft

1,000ft - 680 ft = 320 ft

At t = 0 seconds the car was at a foot marker of 320 feet.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A car is traveling along a test track in the desert at a constant rate of 85 feet per second.

After 8 seconds, the car is at foot marker 1000.

So, In those 8 seconds, the car has traveled (8×85) = 680 feet.

Therefore, Initially, the car was at (1000 - 680) feet.

= 320 feet.

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Answer:

Circle, angle, and line segment.

Answer:

x = 3

Step-by-step explanation:

Given that,

[tex]x=\sqrt[3]{27}[/tex]

We need to show work to solve it.

We know that,

27 = 3×3×3

or

27 = (3³)

So,

[tex]x=\sqrt[3]{3\times 3\times 3}\\\\=(3^3)^{\dfrac{1}{3}}\\\\x=3[/tex]

Hence, this is the required solution.

Answer:

910293012

Step-by-step explanation:

it is nine thousand four billion atoms in one partial.