You are starting a savings account for college. You put $1,000 in as your starting balance. You earn simple interest at 10% every year. You also must pay 30% income tax on the interest earned annually. Calculate the interest, balance, tax paid, and the overall balance of the account after taxes.

Note: your teacher may not want you to enter "feet" and instead may just want the number only.

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Work Shown:

tan(angle) = opposite/adjacent

tan(40) = h/20

20*tan(40) = h

h = 20*tan(40)

h = 16.7819926 which is approximate

h = 16.8

The streetlamp is approximately 16.8 ft tall.

When using your calculator, make sure it's in degree mode. One way to check is to compute something like tan(45) and you should get 1 as a result.

Answer:

All real numbers are solutions.

Step-by-step explanation:

3x-7=3(x-3)+2

3x-7=3x-7

subtract 7 from both sides

3x=3x

subtract 3x from both sides

0=0

All real numbers are solutions.

Answer:

1921.68 \(ft^{3}\)

Step-by-step explanation:

V = pi*r*r*h

= 3.14*6*6*17

= 1921.68

The simplified expression after simplification is ,

1) 4a

2) -12\(x^5\)

3) 27\(x^3\)

4) 3x-4

What is simplification of expression?

 The process of solving a math problem is simply known as simplifying an expression. In essence, you aim to write an expression as simply as you can when you simplify it. By the time you're done, you shouldn't have any more addition, subtraction, multiplication, or division to do. Making anything simpler is the definition of simplify. Reducing an expression, fraction, or mathematical problem to its simplest form is known as simplification. Using calculations and solving the problem makes it simple.

Here the given expressions are,

1) 5a-3a+2a

=> (5-3+2)a

=> 4a

2)-4\(x^2\).x.3\(x^2\)

=> -4*3\(x^(2+1+2)\)

=>-12\(x^5\)

3)\((3x^1)^3\)

=> \(3^3.x^3\)

=>27\(x^3\)

4)5-3(x+3)+6x

=>5-3x-9+6x

=>3x-4

There fore the simplified expressions are

1) 4a

2) -12\(x^5\)

3) 27\(x^3\)

4) 3x-4

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The equations that have graphs with the same y-intercept are:

To determine which equations have graphs with the same y-intercept, we need to look for equations that have the same constant term when written in the form y = mx + b, where m represents the slope and b represents the y-intercept.

The y-intercept is the value of y when x is equal to 0. In other words, it is the point where the graph intersects the y-axis.

Let's compare the equations and their constant terms:

y = 3x - 8 (Constant term: -8)

y = 3x - 9 (Constant term: -9)

y = 3x + 8 (Constant term: 8)

y = 5x - 8 (Constant term: -8)

y = 2x - 8 (Constant term: -8)

y = (1/3)x - 8 (Constant term: -8)

From the comparison, we can see that the equations y = 3x - 8, y = 5x - 8, y = 2x - 8, and y = (1/3)x - 8 all have the same constant term of -8. This means that their graphs will have the same y-intercept, which is -8.

Therefore, the equations that have graphs with the same y-intercept are:

y = 3x - 8

y = 5x - 8

y = 2x - 8

y = (1/3)x - 8

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Answer:

Step-by-step explanation:

59.89

Answer:

Step-by-step explanation:

We divide the number by 8 and write the remainder in reverse order to get the equivalent octal number.

Answer:

Let's write down the base of each one:

- Decimal is base 10 (0 to 9)

- Octal is base 8 (0 to 7)

So, if we want to convert decimal to octal, we need to divide the decimal number by 8 and hold onto the remainder.

Then once your quotient becomes 0, from the last remainder to the first, write your numbers.

For example here is 437 base 10.

437 / 8 = 54 R 5

54 / 8 = 6 R 6

6 / 8 = 0 R 6

So, the answer is 665 base 8.

Answer:

The answer is 8/15

hope it helps you

Answer:

Perpendicular H = 5.244 m (Approx)

Step-by-step explanation:

Given:

Hypotenuse = 9.4 m

Base = 7.8 m

Find:

Perpendicular H

Computation:

Perpendicular H = √Hypotenuse² - Base²

Perpendicular H = √9.4² - 7.8²

Perpendicular H = √Hypotenuse² - Base²

Perpendicular H = 5.244 m (Approx)

The  line at the coffee shop during rush hour is 15 people long.

Given:

- 5 people arrive at the coffee shop each minute.

- Each person has to wait for 3 minutes to be served.

Since 5 people arrive each minute,  the rate of people entering the line is 5 people/minute.

Now, Each person has to wait for 3 minutes to be served.

So, Average length of line = Rate of people entering * Time for a person to be served

Average length of line = 5 people/minute * 3 minutes

Average length of line = 15 people

Therefore, on average, the line at the coffee shop during rush hour is 15 people long.

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Answer: Independent events

Step-by-step explanation:

As the tree outcomes do not depend on previous branch

To apply the Laplace operator to the function h(x, y, z) = e^(-4x)sin(9y), we need to calculate the second partial derivatives with respect to each variable (x, y, z) and then sum them up. The Laplace operator is denoted as Δ or ∇^2 and is defined as the divergence of the gradient of a function.

Let's begin by calculating the partial derivatives:

∂h/∂x = -4e^(-4x)sin(9y)

∂²h/∂x² = (-4)^2e^(-4x)sin(9y) = 16e^(-4x)sin(9y)

∂h/∂y = e^(-4x)9cos(9y)

∂²h/∂y² = e^(-4x)9(-9)sin(9y) = -81e^(-4x)sin(9y)

∂h/∂z = 0

∂²h/∂z² = 0

Now, summing up the second partial derivatives:

Δh = ∂²h/∂x² + ∂²h/∂y² + ∂²h/∂z²

   = 16e^(-4x)sin(9y) - 81e^(-4x)sin(9y) + 0

   = (16 - 81)e^(-4x)sin(9y)

   = -65e^(-4x)sin(9y)

Therefore, the Laplacian of the function h(x, y, z) = e^(-4x)sin(9y) is given by -65e^(-4x)sin(9y).

The Laplacian operator is commonly used in various areas of mathematics and physics, such as differential equations and signal processing. It represents the sum of the second-order partial derivatives of a function and provides valuable information about the behavior of the function in the given domain. In this case, the Laplacian of h(x, y, z) describes the spatial variation of the function and indicates the rate at which the function changes at a specific point (x, y, z) in three-dimensional space.

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Answer: you could make 16 dozen cookies

Answer:

520

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

3.4+2(9.7-4.8x)=61.2

2(9.7-4.8x)=61.2-3.4

2(9.7-4.8x)=57.8

9.7-4.8x=57.8/2

9.7-4.8x=28.9

4.8x=9.7-28.9

4.8x=-19.2

x=-19.2/4.8

x=-4

Answer:

Step-by-step explanation:

B. Distribute 2 to 9.7 and −4.8x.

C. Combine 3.4 and 19.4.

E. Subtract 22.8 from both sides.

F. Divide both sides by −9.6.

To hypothesize that autism is a quantitative trait normally distributed in the population.

Hypothesis that autism is a quantitative trait normally distributed in the population is actually showing the assumption that we can calculate the level of autism in the population in numbers as well as it is present in everyone at some level just like weight.

There are two types of data:

• Quantitative: Any information that can be counted is referred to as quantitative data and is given a numerical value. You can find out “how many,” “how much,” or “how often” using quantitative variables.

• Qualitative: Qualitative information is descriptive in character and communicated verbally as opposed to numerically.

Hence, here they are assuming that we can measure the level of autism in the population.

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Since, 14 + 6 = 20

Therefore, 14 + 6 = 9 + 11

dont forget to like and mark me

Answer:

31

Step-by-step explanation:

Answer:

One solution

Step-by-step explanation:

Let's rewrite y = 6 - 3x as y = -3x + 6

Looking at these two equations, we can see they share a y-intercept

Making our solution 6

We know there is only one solution because the equations are not the exact same, if they were we'd have infinitely many solutions

We also know there aren't no solutions because the lines are not parallel (same slopes with difference y-intercepts)

Best of luck

A. The number of ways that disks can be selected so that none have bad sectors is 330. B. The number of ways that disks can be selected so that all have bad sectors is 5.  C. the number of ways to choose 4 disks that satisfy the given requirement is 550.

A. In how many ways can disks be selected so that none have bad sectors? The number of disks that are known to have bad sectors is 5, so the number of good disks is 16 - 5 = 11 disks.

The number of ways that 4 disks can be selected, without replacement and regard to order, is (11C4) = 330.

Therefore, the number of ways that disks can be selected so that none have bad sectors is 330.

B. In how many ways can disks be selected so that all have bad sectors? The number of disks that are known to have bad sectors is 5, so the number of ways that 4 disks can be selected, without replacement and regard to order, is (5C4) = 5.

Therefore, the number of ways that disks can be selected so that all have bad sectors is 5.

C. In how many ways can disks be selected so that exactly 2 do not have bad sectors? The total number of ways to choose 4 disks without respect to the order or replacement is (16C4) = 1820.5 disks are known to have bad sectors and the remaining 11 are good.

The total number of ways to choose 2 good disks out of 11 is (11C2) = 55.

The total number of ways to choose 2 bad disks out of 5 is (5C2) = 10.

Therefore, the total number of ways to choose 2 good disks and 2 bad disks is 55 × 10 = 550.

Therefore, the number of ways to choose 4 disks that satisfy the given requirement is 550.

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The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;

A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;

Solving the above inequality, we have;

2•x + 3 ≤ -3

2•x ≤ -3 - 3 = -6

2•x ≤ -6

Therefore;

x ≤ -6 ÷ 2 = -3

x ≤ -3

Which gives;

-∞ < x ≤ -3 in interval notation is (-∞, -3]

The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;

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Answer:

c)

subtract 5 times the second equation from 2 times the first equation

Step-by-step explanation:

subtract 5 times the second equation from 2 times the first equation

This will make the coefficient of the y variable 10

for both equations

10y - 10y = 0

leaving only x

Answer:

P(1,2)  m = 3    Since you are given a point and a slope, use the point-slope form for the equation of a line: y - y1 = m(x - x1)

y - 2 = 3(x - 1)

y - 2 = 3x - 3

y = 3x - 1 hope this helps

Step-by-step explanation:

Answer

y=3x+1

put in point slope form y-yone=m(x-x one)

y+2=3(x+1)

y+2=3x+3

y=3x+1

Answer:

8ft

Step-by-step explanation:

Pythagorean Theorem

\(a^2+b^2=c^2\\\\x^2+(x+7)^2=17^2\\x^2+(x+7)(x+7)=17^2\\x^2+(x^2+7x+7x+49)=289\\2x^2+14x+49-289=289-289\\2x^2+14x-240=0\\\)

Use Quadratic Formula to Solve

\(\frac{-b+-\sqrt{b^2-4ac} }{2a} \\\frac{-14+-\sqrt{14^2-4(2)(-240)} }{2(2)} \\\frac{-14+-\sqrt{2116} }{4}\\x=\frac{-14+46}{4}, x=\frac{-14-46}{4}\\x=8, -15\)

Ignore negative sign

Shorter side is 8ft and longer one is 15ft

The length of the shorter leg is 8 feet.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Let x be the length of the shorter leg.

Then according to question,

the other leg is x +7 feet.

And hypotenuse is 17 feet.

Using Pythagoras theorem

(x)² + (x+7)² = (17)²

2x²+14x+49-289 = 0

2x²+ 14x- 250 = 0

By solving further,

x = 8 , -15

Neglecting -15 because side is positive.

Therefore, shorter leg is 8 feet long.

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To find the equilibrium price and quantities, we need to set the demand and supply functions equal to each other. P and Q = 10 in this case.

Demand: P = 20 - Q

Supply: P = Q

Equating the two equations:

20 - Q = Q

Solving for Q:

2Q = 20

Q = 10

(a) Equilibrium price:

Substituting the equilibrium quantity (Q = 10) into either the demand or supply equation:

P = 10

Therefore, the equilibrium price is $10.

(b) Consumer surplus (CS):

To find consumer surplus, we need to calculate the area below the demand curve and above the equilibrium price.

Consumer surplus = 0.5 * (20 - 10) * 10 = $50

Producer surplus (PS):

To find producer surplus, we need to calculate the area below the equilibrium price and above the supply curve.

Producer surplus = 0.5 * 10 * 10 = $50

Total surplus (TS):

Total surplus is the sum of consumer surplus and producer surplus.

Total surplus = CS + PS = $50 + $50 = $100

Price ceiling:

(i) When a price ceiling of $14 is imposed, the quantity demanded and supplied will be the equilibrium quantity (Q = 10), as the price ceiling does not affect the equilibrium.

(ii) When a price ceiling of $10 is imposed, the quantity demanded will be 10, but the quantity supplied will be determined by the price ceiling of $10.

Price floor:

(1) When a price floor of $12 is imposed, the quantity demanded will be determined by the equilibrium quantity (Q = 10), but the quantity supplied will be 10, as the price floor does not allow prices to go below $12.

(2) When a price floor of $8 is imposed, the quantity demanded and supplied will be the equilibrium quantity (Q = 10), as the price floor does not affect the equilibrium.

Note: Since the inverse supply function is not provided, we assume that it is a linear function with a positive slope, which intersects the inverse demand function at the equilibrium price and quantity.

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Answer:

not sure

Step-by-step explanation:

I'm not sure how to do this guys I am very sorry for the inconvenience

Step-by-step explanation:

brother or sister whoever you are, please try to post the full question.

Answer:

15,999,999,995

Step-by-step explanation:

16 billion - 5 = 15,999,999,995

Answer:

im pretty sure it's 1,098

The dimensions of the rectangular garden are 8.5 meters and 7.5 meters.

Perimeter of a straight sided figures or objects is the total length of it's boundary.

The diagram is given below.

Given,

Perimeter of a rectangle = 2 (l + w), where l is the length and width.

Length of the rectangle = 4 + 3x

Width of rectangle = x + 6

Perimeter = 32 meters

Substituting,

2 (l + w) = 32

2(4 + 3x + x + 6) = 32

2(4x + 10) = 32

4x + 10 = 16

4x = 6

x = 6 / 4 = 3/2 = 1.5

Length = 4 + 3x = 8.5 meters

Width = x + 6 = 7.5 meters

Hence the length and width of the rectangle are 8.5 meters and 7.5 meters respectively.

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