The height of a coconut falling from a tree can be represented by the function h(t)=-16t^2 + 24, where h(t) is the height of the coconut, in feet, and t is time, in seconds.
What is the initial height, in feet, of the coconut?

Answer:

r = 1/2, -1

Step-by-step explanation:

First, you need to find the 1st and 2nd derivatives for the function y = e^rx:

y' = re^rx

y'' = r^2e^rx

Next, you substitute them into the differential equation 2y'' + y' - y = 0:

2(r^2e^rx) + re^rx - e^rx = 0

Factor e^rx out:

e^rx(2r^2 + r - 1) = 0

Divide both sides by e^rx:

2r^2 + r - 1 = 0

Factor the left side:

(2r - 1)(r + 1) = 0

Solving both of the equations, you get:

2r - 1 = 0

2r = 1

r = 1/2

r + 1 = 0

r = -1

Values: r = 1/2, -1

Answer:

option c

Step-by-step explanation:

because i said soooo

To solve the equation 3(4d) – 14 = 15 – 5d – 4d, we need to simplify the equation and isolate d. The value of d is 29/21.

To find the value of d in equation 3(4d) – 14 = 15 – 5d – 4d, we need to simplify the equation and isolate d on one side of the equation. Let's start:

Therefore, the value of d in the equation is 29/21.

To solve 3/4 - 3/8, convert 3/4 to 6/8 and then subtract 3/8 from 6/8. The result is 3/8.

To find the answer to 3/4 - 3/8, follow these steps:

So, 3/4 - 3/8 = 3/8.

The answer is $62.59

A rhombus becomes a square when all its angles are right angles, in addition to having equal length sides. Therefore, option B is the correct answer.

A rhombus is a type of parallelogram where all four sides are of equal length. Mind you, this doesn't automatically make it a square, which is also a kind of parallelogram but with a few extra properties. The key difference is that a square has all four angles as right angles, meaning they are 90 degrees. In a rhombus, this isn't necessarily the case.

Therefore, the correct answer to the question is 'option B) When its angles are right angles'. So a rhombus is a square only when not only all its sides are equal in length, but its angles are also all right angles.

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Answer

Find out the what is the minimum simple interest rate Maggie needs to reach her goal .

To proof

Formula

[tex]Simple\ interest = \frac{principle\times rate\times time}{100}[/tex]

As given

Maggie has $14,100 to invest, and wishes to gain $4,000 in interest over the next eight years.

put all the values in the formula

[tex]4000 = \frac{14100\times rate\times 8}{100}[/tex]

Solving

[tex]rate = \frac{4000\times 100}{14100\times8}[/tex]

solving the above

[tex]rate = \frac{400000}{112800}[/tex]

rate =3.55% (approx)

the minimum simple interest rate Maggie needs to reach her goal is 3.55% .

Option (b) is correct .

Hence proved

The linear equation to find the area of the carpet after applying Felix's $50 discount is 3.50 × A = 180, where A represents the area in square feet. After solving the equation, we find that the area is 51.43 square feet.

To find the area, A, of the carpet that Felix buys, we can set up a linear equation based on the total cost after the discount and the cost per square foot. The original price of the carpet is $230, but Felix has a coupon for a $50 discount, reducing the cost to $180. Since the cost per square foot of the carpet is $3.50, we can denote the area of the carpet as A, and set up the equation:

3.50 × A = 180

To solve for A, we divide both sides of the equation by 3.50:

A = 180 / 3.50

A = 51.43 square feet

Final answer:

One strategy for converting a rate measured in one pair of units to a rate measured in a different pair of units is to use unit analysis. The conversion from ounces per cup to pounds per gallon is 1 lb / 2 gal.

Explanation:

One strategy for converting a rate measured in one pair of units to a rate measured in a different pair of units is to use unit analysis. This involves setting up conversion factors to cancel out the unwanted units. Here's an example:

Therefore, the conversion from ounces per cup to pounds per gallon is 1 lb / 2 gal.

Answer:

C) Step 3

Step-by-step explanation:

We are given that

[tex]4x+5< 6x+1[/tex]

We have to find the mistake made by Mia in her solution.

Step 1:[tex]4x+5<6x+1[/tex]

Reason: Given

Step 2: [tex]4x-6x+5<+1[/tex]

[tex]-2x+5<1[/tex]

Reason: Subtraction property of inequality

Step 3: [tex]-2x <1-5[/tex]

[tex]-2x<-4[/tex]

Reason: Using subtraction property of inequality

Step 4:[tex]-x<-2[/tex]

[tex]x>2[/tex]

Reason: Division property of inequality

Mia did mistake in step 3 .She using addition property instead of subtraction property.

Option C is true.

Jamie made $2375 of sales on one week and earns 20% of it as a commission.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Jamie is a salesperson in a shoe store and earns $95 per week, plus 20% of her weekly sales.

Jamie makes $475 in one week which is 20% of the total sale assuming he made $x worth of sales.

∴ (20/100)×x = 475.

0.2x = 475.

x = 475/0.2.

x = $2375

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Final answer:

To solve for 'a' in the equation y = -1/2ax - 5 with a given slope of 5/2, we compare it to the standard linear equation format and find that 'a' is equal to -5.

Explanation:

To solve for a, we need to look at the equation y = -1/2ax - 5 given that the slope (m) is 5/2. In a linear equation of the form y = mx + b, m represents the slope. Comparing it to the given equation, we can see -1/2a is the slope in our case. Therefore, to find a, we set -1/2a equal to the given slope of 5/2 and solve:

-1/2a = 5/2

To isolate a, we first multiply both sides by -2:

a = -2(5/2)

Multiplying this out, we find:

a = -5

Thus, in the context of a linear equation and assuming the slope m provided is indeed intended to be the value of the direct variation component, the value for a is -5.

The correct answer is:

Row 15.

Explanation:

Each row of Pascal's triangle corresponds with the exponent of a binomial. The first row is a binomial to the first power; the second row, to the second power; the third row, to the third power; etc.

For the 15th power, we would want the 15th row of the triangle.

The probability that the rifleman will hit the target exactly 3 out of 4 shots is 0.4096, or 40.96%.

The student asked about the probability of a rifleman who averages 8 hits out of 10 shots to hit the target in 3 out of 4 shots. To solve this, we use the binomial probability formula, which is used when each shot is independent of the others.

The probability of hitting the target is given as 0.8 (8 out of 10). The probability of missing is 1 - 0.8 = 0.2. The formula for the exact outcome of 3 hits out of 4 is:
  P(X = 3) = (4 choose 3)
  (0.8)^3
  (0.2)^1

We need to calculate the binomial coefficient (4 choose 3) which is 4, multiply it by the probability of hitting the target three times (0.8)^3, and multiply the result by the probability of missing once (0.2)^1.

So, P(X = 3) = 4
  (0.512)
  (0.2) = 4
  0.1024 = 0.4096

Therefore, the probability that the rifleman will hit the target exactly 3 out of 4 shots is 0.4096, or 40.96%.

To compare 77% and 3/5, we convert them to the same format. 77% is equivalent to 77/100 and 3/5 is equivalent to 60/100, or 60%. Therefore, 77% is greater than 3/5.

In order to compare 77% and 3/5, you should convert them both to the same format. Percentages are a way of expressing a number as a fraction of 100. Hence, 77% can be written as 77/100.

Similarly, the fraction 3/5 remains as is, which is equivalent to 60/100, or 60% when converted into a percentage.

Comparing these values, it is clear that 77% is greater than 3/5, or 60%.

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Final answer:

After converting 3/5 to a percent (60%), we can see that 77% is greater than 60%, making 77% the greater value.

Explanation:

To determine which is greater, 77% or 3/5, we need to compare them either as percentages or as decimals. First, let's convert 3/5 to a percent. To do this, we divide the numerator by the denominator to get the decimal: 3 ÷ 5 = 0.6. Then, we convert the decimal to a percent by multiplying by 100: 0.6 × 100 = 60%.

Now that we have both numbers as percentages, we can easily compare them: 77% is greater than 60%. Therefore, 77% is greater than 3/5.

To simplify the expression (9x^8y^3)^1/2, distribute the 1/2 exponent to the numerical coefficient and to the variables, resulting in 3x^4y^(3/2).

To simplify the expression (9x^8y^3)^1/2, we will apply the rule that states when you have an exponent (in this case the 1/2, which denotes a square root) outside the parentheses, you distribute it to both the numerical coefficient and the variables inside the parentheses. Using this rule:

Thus, the simplified form of the expression will be 3x^4y^(3/2).

The expression (9x^8y^3)^(1/2) can be simplified as 3x^4y^(3/2).

To simplify the expression, we need to understand the properties of exponents. When we have a number or variable raised to a fractional exponent, it means taking the corresponding root of the number or variable.

In this case, we are taking the square root (1/2 exponent) of each term within the parentheses: 9, x^8, and y^3.

The square root of 9 is 3 because 3^2 = 9.

The square root of x^8 is x^(8/2) = x^4 because (x^4)^2 = x^8.

The square root of y^3 is y^(3/2) because (y^(3/2))^2 = y^3.

Combining these simplified terms, we get 3x^4y^(3/2).

Therefore, the expression (9x^8y^3)^(1/2) simplifies to 3x^4y^(3/2).

The answer is  

x ≥ 4

x + y ≤ 10

y ≥ 0

First, rearrange the equation so that only zero will be on the right side:

x^2 + 14x +24 = 0

Let the coefficients be:

a = 1

b = 14

c = 24

To complete the square, add (b/2)^2 to both sides of the equation:

(b/2)^2 = 49

x^2 + 14x + 49 + 24 = 49

x^2 + 14x + 49 = 25

(x+7)^2 = 25

Therefore, the solution set of the equation is {-12, -2}

The solution set of the quadratic equation x² + 14x = −24 is [-12, -2] option (a) is correct.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic equation:

x² + 14x = −24

It is required to solve the equation by completing the square.

First, arrange the quadratic equation

x² + 14x + 24 = 0

x² + 14x + 7² - 7² + 24 = 0

(x + 7)² -25 = 0

(x + 7)²  = 25

x + 7 = ±5

Taking positive sign:

x + 7 = 5

x = -2

Taking negative sign:

x + 7 = -5

x = -12

The solution set is [-12, -2]

Thus, the solution set of the quadratic equation x² + 14x = −24 is [-12, -2] option (a) is correct.

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SOS

Answer:

[tex]\frac{3}{20}-\frac{1}{20}i[/tex]

Step-by-step explanation:

Find the multiplicative inverse of a complex number using the process described below:

The inverse is found by reciprocating the original complex number. The reciprocal of the complex number (6+2i) is [tex]\frac{1}{6+2i}[/tex]. Multiply the numerator and denominator of the reciprocal by conjugate of the denominator and simplify:

[tex]\frac{1}{6+2i}*\frac{6-2i}{6-2i}[/tex]

You get: [tex]\frac{3}{20}-\frac{1}{20}i[/tex]

Hope this helps!!