Danny opened a savings account and deposited $100.00. The account earns 2% interest,
compounded annually. If he wants to use the money to buy a new bicycle in 3 years, how
much will he be able to spend on the bike?
nt
P(1 + 1)^²₁. where A is the balance (final amount), P is the principal
Use the formula A = P 1 +
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.

Answer:

22 servings

Step-by-step explanation:

4+7=11 cups

11 divided by 1/2=22

Answer:

Answer: 27:8

Step-by-step explanation:

There are 24 + 16 + 14 = 24+16+14= 54

54 marbles in total.

The ratio of total marbles to red marbles is 54 : 16, which simplifies to 27 : 8.

Answer: 27:8

\(Answer:\ f(x)=-\sqrt{x-2}+3\)

Step-by-step explanation:

The work done by f in moving a particle once counterclockwise around the given curve is -15π.

The problem requires us to calculate the work done by the vector field f along a closed curve C, which is a circle centered at (5,5) with a radius of 5. To do this, we can use the line integral of f along C, which is given by:

∫C f · dr = ∫C (f(x,y) · T) ds

where T is the unit tangent vector to C and ds is the arc length element along C.

To parameterize the curve C, we can use the parametric equations:

x = 5 + 5cos(t)

y = 5 + 5sin(t)

with 0 ≤ t ≤ 2π. Then, the unit tangent vector T is given by:

T = (-sin(t), cos(t))

and the arc length element ds is given by:

ds = √(x'(t)² + y'(t)²) dt = 5 dt

Using these expressions, we can compute the line integral as:

∫C f · dr = ∫C [(x-3y)i + (3x-y)j] · (-sin(t)i + cos(t)j) 5 dt

After some algebraic manipulation, we obtain:

∫C f · dr = -15π

Therefore, the total work done by f in moving the particle once around the given curve counterclockwise is -15π.

Learn more about work done

brainly.com/question/31655489

#SPJ11

The work done by f in moving a particle once counterclockwise around the given curve is zero.

To find the work done by a vector field f in moving a particle along a curve C, we use the line integral formula. The line integral of a vector field f along a curve C is given by the formula ∫C f · dr, where dr is the differential of the position vector r(t) of the curve C. In this case, the vector field is f = (x - 3y)i + (3x - y)j and the curve is the circle (x - 5)² + (y - 5)² = 25 centered at (5,5) with radius 5. To evaluate the line integral, we need to parameterize the curve. Since the curve is a circle, we can use the parametrization r(t) = 5cos(t)i + 5sin(t)j, where t ranges from 0 to 2π. Then, dr = -5sin(t)dt i + 5cos(t)dt j.

Evaluating the line integral, we get ∫C f · dr = ∫0^2π f(r(t)) · dr/dt dt = ∫0^2π (-15sin²(t) + 15cos²(t))dt = 0. Therefore, the work done by f in moving a particle once counterclockwise around the given curve is zero.

You can learn more about work done at

https://brainly.com/question/25573309

#SPJ11

Recall that the volume of a cube equals (side)^3. We can create an equation to model this.

1728 in^3 = (side)^3

We can get the cube root of both sides.

12 in = side

Each side is 12 inches long.

The pivot for the Partition(numbers, 0, 6) operation is 54. The low partition consists of 56, 38, 41, 32, 45, and 31. The high partition consists  87, 58, and 96. After the completion of Partition(numbers, 0, 6), the updated order of the numbers would be (56, 38, 41, 32, 45, 31, 54, 87, 58, 96).

In the given scenario, the quicksort algorithm chooses the element at the midpoint (index 5) of the given range (from 0 to 6) as the pivot. In this case, the element at index 5 is 54. The Partition operation then divides the numbers into two partitions based on their relationship to the pivot. All elements less than the pivot are placed in the low partition, while all elements greater than the pivot are placed in the high partition.

In the given numbers, the elements less than 54 are 56, 38, 41, 32, 45, and 31, which form the low partition. The elements greater than 54 are 87, 58, and 96, which form the high partition. After the completion of the Partition operation, the numbers are rearranged so that the low partition comes before the pivot and the high partition comes after the pivot. Therefore, the updated order of the numbers becomes (56, 38, 41, 32, 45, 31, 54, 87, 58, 96).

Learn more about numbers here: brainly.com/question/13045235

#SPJ11

We can expect most pregnancies in this village to fall within the range of 229.71 to 294.29 days.

To find the range that would contain the middle 98% of most pregnancies, we need to use the concept of the standard normal distribution.

First, we can convert the given mean and standard deviation to the standard normal distribution using the formula:

z = (x - mu) / sigma

where x is the value we are interested in, mu is the mean, sigma is the standard deviation, and z is the corresponding z-score in the standard normal distribution.

For the lower bound of the range containing the middle 98%, we need to find the z-score that corresponds to the lower 1% of the distribution. Since the normal distribution is symmetric, the upper bound will be the same z-score but with a negative sign.

Using a standard normal distribution table or a calculator, we can find that the z-score for the lower 1% is -2.33. Therefore, the lower bound of the range containing the middle 98% can be found by solving for x in the z-score formula:

-2.33 = (x - 262) / 13

-2.33 ×13 + 262 = x

x = 229.71

Similarly, the upper bound of the range containing the middle 98% can be found by using a z-score of +2.33:

2.33 = (x - 262) / 13

2.33 ×13 + 262 = x

x = 294.29

for such more question on range

https://brainly.com/question/16444481

#SPJ11

Answer:

573440 Kg

Step-by-step explanation:

\(\boxed{\bf Mass = density * volume}\)

Find the volume of the solid cube

          Volume of solid cube = side³

                                              = 4 * 4 * 4

                                              = 64 m³

\(\sf Mass = 8960* 64\\\)

        = 573440 Kg

Step-by-step explanation:

X = 50+45 = 95 exterior angle

y =95 + 52 = 147 exterior angle

Z = 180 Straight angle

I think the answer is 3$ because if you divide each item by the price you get 1 3 and 5 3 is more likely to be the middle so that would be your average price the unit rate of each of the items is dividing the price by the number of items to get the price of one item or your unit rate.

The dependent variable in this case would be the total number of hot dogs needed for the cookout.

In mathematics, a variable is a symbol, usually a letter, used to represent a quantity in an equation or in a mathematical expression. It can be thought of as a placeholder that can take on different values in a given equation or expression. Variables are essential for mathematics because they allow us to explore different scenarios and solve problems.

This is dependent on the number of guests attending, which is the independent variable. Depending on how many people show up, the individual will need to adjust the amount of hot dogs to accommodate the guests.

To know more about variables click-
https://brainly.com/question/25223322
#SPJ4

Answer:

Here you are...

Step-by-step explanation:

If you double one of the dimensions, say change one side from 2 to 4 it doubles the volume. if you were to do this to any side, say double it, it would double the volume. ... It will make the volume 4 times as much also. the volume would go from 30 to 120.

Answer: mmm

Step-by-step explanation:

mmm

Answer:

\( \sqrt{7y} ( \sqrt{27y} + 5 \sqrt{12y} )\)

\( \sqrt{7y} ( \sqrt{9} \sqrt{3y} + 5 \sqrt{4} \sqrt{3y} )\)

\( \sqrt{7y} (3 \sqrt{3y} + 10 \sqrt{3y} )\)

\(13 \sqrt{7y} \sqrt{3y} \)

\(13y \sqrt{21} \)

Answer:

The length of the piece of wood can be found using the Pythagorean theorem. The ramp is the hypotenuse of a right triangle with one leg being the height of the cinder block (30 cm) and the other leg being the distance from the block to where the ramp begins (72 cm). So, the length of the piece of wood is \(√(30² + 72²) = √(900 + 5184) = √(6084) = 78 cm.\)

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

when you distribute, the 6x on each side cancel out leaving there to be no solution to the problem. I attached a photo of my work as well.

Answer:

The answer is False meaning it's no solution

Step-by-step explanation:

1. Distribute 3 through the parentheses which will be 6x+12=6x+10

2.Cancel equal terms on both sides of the equation and you will get 12=10 which isn't a true statement.

The length of the line segment BP = 15 using the trigonometric ratio of sine for the angle P.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the right triangles formed by points at P, A and the tangent to the bigger circle with its radius as base;

radius r = 10 and hypotenuse AP = 30

sinP = 10/30 {opposite/hypotenuse}

sinP = 1/3

Also for the smaller circle, with right triangle formed by points at P, B and the tangent to the smaller circle with its radius as base;

radius r and hypotenuse BP = 20 - r

sinP = r/(20 - r)

1/3 = r/(20 - r)

3r = 20 - r {cross multiply}

3r + r = 20 {collect like terms}

4r = 20

r = 20/4 {divide through by 4}

r = 5

BP = 20 - 5

BP = 15

Therefore, length of the line segment BP is derived using the trigonometric ratio of sine as 15.

Know more about trigonometric ratios here: https://brainly.com/question/23130410

#SPJ1

Answer:

x= 50(3) 150 minutes

Step-by-step explanation:

Ruebens 3p.m nap is three times as long as his 10a.m nap

Answer:

80

Step-by-step explanation:

multiply the ratio 4:1 by 20

4:1

80:20

there are 20 sweet snacks. Meaning the other half are

salty snacks.

PS:

Can I have Brainliest?

a) Not possible to determine the percentage of the length of seashells collected by Jaya that were between 3.5 and 7 inches.

b) 25% of the length of seashells collected by Jaya were between 2 and 3.5 inches.

c) It is not possible to determine the percentage of the length of seashells collected by Jaya that were more than 5 inches based on the information provided.

d) The range of lengths of seashells collected by Jaya was = 4.2 inches.

In statistics, the range is the difference between the highest and lowest values for a particular data collection.

For instance, if the provided data set is 2,5,8,10,3, the range is 10 - 2 = 8.

As a result, the range may alternatively be defined as the difference between the highest and lowest observations.

a) It is not possible to determine the percentage of the length of seashells collected by Jaya that were between 3.5 and 7 inches based on the information provided.

b) 25% of the length of seashells collected by Jaya were between 2 and 3.5 inches.

c) It is not possible to determine the percentage of the length of seashells collected by Jaya that were more than 5 inches based on the information provided.

d) The range of lengths of seashells collected by Jaya was 6.2 - 2 = 4.2 inches.

For more questions on Range of data

https://brainly.com/question/15953457

#SPJ4

Answer:

t= i/pr

Hope this helps!!!!!!!!

Answer:

x = 27

Step-by-step explanation:

2/3x - 1/9x + 5 = 20

Subtract 5 from each side

2/3x - 1/9x + 5 -5= 20-5

2/3x - 1/9x  = 15

Get a common denominator on the left side

2/3 *3/3 x - 1/9x = 15

6/9x - 1/9x = 15

5/9 x = 15

Multiply each side by 9/5

9/5 * 5/9x = 15 * 9/5

x = 15/5 *9

x = 3*9

x = 27

Answer:

x=27

Step-by-step explanation:

2/3 x -1/9 x+5=20

2/3x -1/9 x=20-5 common denominator

(6x-1x)/9=15 multiply each side by 9

(5x)=135

5x=135

x=135/5=27

x=27

Answer:

24

Step-by-step explanation:

area = wl (6×4 = 24)

w width l length

Applying one of the properties of a parallelogram, the value of x is 10°, then 6x=60° and 12x=120°.

There are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, a parallelogram presents some properties that are presented below.

The figure of the exercise shows two adjacent angles. From the property: the adjacent angles are supplementary, you have:

6x+12x=180

18x=180

x=10°

Therefore, 6x= 6*10=60° and 12x=12*10=120°.

Read more about the parallelogram here:

brainly.com/question/20526916

#SPJ1

If E= Emily's homeroom class students, and S = Santiago's homeroom class students then