given A(-2,1) and B(4,3), what is the midpoint of segment AB​

Answer:

Yes! When simplifying 15:60 by dividing each side by 3, you get 5:20, which is the same as 5:20.

Step-by-step explanation:

Hope this helps <3

The rate of change of cumulative sales in 2004 is approximately -$0.001 per year.

To calculate the rate of change of cumulative sales in 2004, we need to find the derivative of the given function, which represents the average surcharge as a function of years since 1998. The derivative will give us the rate of change of the function.

Given function: f(x) = \(0.004x^3 - 0.061x^2 + 0.299x + 0.899\)

To find the derivative, we differentiate the function with respect to x:

\(f'(x) = d/dx (0.004x^3 - 0.061x^2 + 0.299x + 0.899)\)

Differentiating each term:

\(f'(x) = 0.012x^2 - 0.122x + 0.299\)

Now that we have the derivative, we can calculate the rate of change of cumulative sales in 2004. To do this, we need to substitute the value x = 2004 - 1998 = 6 into the derivative function:

Rate of change in 2004 = \(f'(6) = 0.012(6)^2 - 0.122(6) + 0.299\)

Calculating:

Rate of change in 2004 = 0.432 - 0.732 + 0.299

Rate of change in 2004 ≈ -0.001 dollars per year

Therefore, the rate of change of cumulative sales in 2004 is approximately -$0.001 per year.

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The completed statements with regards to the compound interest of the amount in the account are;

If the account has a 5% interest rate and is compounded monthly, you have $101.655 million money after 2 years

If the account has a 5% interest rate compounded continuously, you would have $106.096 million money after 2 years

Compound interest is the interest calculated based on the initial amount and the accumulated interests accrued from the periods before the present.

The compound interest formula indicates that we get;

\(A = P\cdot (1 + \frac{r}{n}) ^{n\cdot t}\)

Where;

P = The principal amount invested = $92 million

r = The interest rate = 5% monthly

n = The number of times the interest is compounded per annum = 12

t = The number of years = 2 years

Therefore; \(A = 92\cdot (1 + \frac{0.05}{12}) ^{12\times 2}\approx 101.655\)

The amount in the account after 2 years is therefore about $101.655 million

The formula for the amount in the account if the principal is compounded continuously, we get;

A = \(P\cdot e^{(r\cdot t)}\)

Therefore, we get;

\(A = 96 \times e^{0.05 \times 2} \approx 106.096\)

The amount in the account after 2 years, compounded continuously therefore, is about $106.096 million

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The diver has to travel approximately 69.28 meters to reach the wreckage of the ship.

The problem involves finding the horizontal distance that a diver has to cover to reach the wreckage of a ship after a rescue boat detects the signal at an angle of depression of 30°. The diver descends 40 meters to the seafloor.

The concept of trigonometry is useful in solving the problem. Here are the steps to solve the problem:

Step 1: Draw a diagram that represents the problem.

Step 2: Let the horizontal distance that the diver has to travel be "d".

Step 3: Let the angle of depression be "θ". From the diagram, we can see that tan θ = d / 40m.

Step 4: Substitute the value of θ and solve for "d".tan 30° = d / 40m1 / √3 = d / 40m√3d = 40m√3d ≈ 69.28 meters

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1. True or False? If Z is a random variable from a standard normal distribution and if P(Z

It seems like the question is incomplete. Please provide the complete question to get an accurate answer.

2. True or False? If z is a random variable with a standard normal distribution and if a is a positive number and if P(z > a) = 0.15, then P(-a < z < a) = 0.7?

Answer: True

Explanation: Since z follows a standard normal distribution, it is symmetric around the mean (which is 0). So, P(z > a) = P(z < -a) = 0.15. To find the probability between -a and a, we can use the property P(-a < z < a) = 1 - P(z > a) - P(z < -a) = 1 - 0.15 - 0.15 = 0.7.

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Answer:

9

3

1

10

4

10

3/2

15

20/3

28

96/25

??

a) A department manager receiving an allocation of costs will care about management's methodology of overhead allocation because the overhead costs allocated to their department will have a direct impact on the department's profitability and cost efficiency.

b) The allocation base is the measure used to determine how much of the overhead costs should be allocated to a particular department or product, while the allocation rate is the amount of overhead costs allocated to each unit of the allocation base

c) Budgets are an important tool for cost planning, but their effectiveness depends on how well they are developed and implemented.

a) If the allocation method used by management is not accurate or fair, it could result in the department being burdened with more costs than they actually incur, which could affect their ability to meet their targets and objectives. It is, therefore, important for department managers to ensure that the allocation of costs is done fairly and accurately.

b) The allocation base and rate are important because they determine how the overhead costs are allocated to different departments or products.

Different allocation bases and rates can result in significantly different amounts of overhead costs being allocated to different departments or products, which can impact their profitability. While all of the overhead costs eventually make their way to the income statement, the allocation of these costs can have a significant impact on the accuracy of the income statement and the ability of the organization to make informed decisions.

c) Budgets can be helpful in providing a roadmap for achieving the organization's goals and objectives, but they need to be flexible enough to adapt to changing circumstances and priorities.

The budget(s) that are most important to the organization's success will depend on the nature of the organization and its objectives. However, typically the operating budget, capital budget, and cash budget are the most important budgets for most organizations.

The government's budget process is similar to the operating budgeting process described in the chapter in that it involves the development of a budget to allocate resources and achieve goals. However, the government's budget process is more complex and involves additional considerations such as political priorities and public opinion. Additionally, the government's budget process involves a more detailed review and approval process than the operating budgeting process.

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a) The fire is out of the reach of helicopter 1.

b) Only helicopter 3 can be sent to stop the fire.

We have both the location of the fire and the initial position of the three helicopters set on a Cartesian plane. The locations are listed below:

The distance is found by the straight line distance formula, an application of Pythagorean theorem:

a) \(d = \sqrt{[1 - (- 3)]^{2}+[4-(-5)]^{2}}\)

\(d = \sqrt{4^{2}+9^{2}}\)

\(d = \sqrt{97}\)

d ≈ 9.849

The fire is out of the reach of helicopter 1.

b) Helicopter 2

\(d = \sqrt{[- 2 - (- 3)]^{2}+[3 - (- 5)]^{2}}\)

\(d = \sqrt{1^{2}+8^{2}}\)

\(d = \sqrt{65}\)

d ≈ 8.062

Helicopter 3

\(d = \sqrt{[4 - (- 3)]^{2}+ [- 2 - (-5)]^{2}}\)

\(d = \sqrt{7^{2}+3^{2}}\)

\(d = \sqrt{58}\)

d ≈ 7.616

Only helicopter 3 can be sent to stop the fire.

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Answer:

\(8<\sqrt{66}<9\)

Step-by-step explanation:

\(64<66<81 \implies 8<\sqrt{66}<9\)

Answer:

Step-by-step explanation:

7(i)

\(\displaystyle\\\frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=\frac{dx}{dx} *(3x-5)^\frac{5}{3}+x*\frac{d}{dx} \{(3x-5)^\frac{5}{3} \}\\\\ \frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=1*(3x-5)^\frac{5}{3} +x*\frac{5}{3}*(3x-5)^{\frac{5}{3} -1}*\frac{d}{dx} \{(3x-5)\}\\\\ \frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=(3x-5)^\frac{5}{3} +\frac{x*5*(3x-5)^{\frac{2}{3}}*3 }{3} \\\\\frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=(3x-5)^\frac{5}{3} +5x*(3x-5)^\frac{2}{3} \\\\\)

\(\displaystyle\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3}*((3x-5)^{\frac{5}{3}-\frac{2}{3}} + 5x)\\\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3} *(3x-5)^\frac{3}{3}+5x) \\\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3} *(3x-5+5x)\\\ \frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(8x-5)*(3x-5)^\frac{2}{3}\)

7(ii)

\(\int\limits {(x*(3x-5)^\frac{2}{3}) } \, dx \\Let\ \sqrt[3]{3x-5} =u\\Hence,\\(\sqrt[3]{3x-5})^3=u^3\\ 3x-5=u^3\\3x-5+5=u^3+5\\3x=u^3+5\\\)

Divide both parts of the equation by 3:

\(\displaystyle\\x=\frac{u^3+5}{3}\\\\dx=\frac{d}{du} \{\frac{u^3+5}{3}\} \\dx=\frac{3u^2}{3} du=\\\\dx=u^2du\\Hence,\\\\\int\limits {\frac{u^3+5}{3}* u^2*u^2} \, du =\\\\\int\limits {\frac{u^3+5}{3} *u^4} \, du =\\\\\int\limits {\frac{u^7+5u^4}{3} } \, du =\\\\\frac{1}{3} \int\limits {u^7} \, du +\frac{1}{3}\int\limits {5u^4} \, dxu =\\\\\)

Answer:

x = 15.3

x = 20.9

Step-by-step explanation:

sin(46) = 11/x

⇒ x = 11/sin(46) = 15.3

cos(55) = 12/x

⇒ x = 12/cos(55) = 20.9

Answer:373248

Step-by-step explanation:

72^3 = 373248

From the given question, the value of the height of the cone is given by 57.3 centimeters to the nearest 1 decimal place: Option B

We should note that a cone is a three-dimensional geometric figure with a flat and curved surface pointed towards the top.  It is formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base(which does not contain the apex)

The volume of the cone is given by the formula

Volume = 1/3πr²h

Where Volume = 1500 centimeters cube, radius = 5 cm, π = 22/7

1500 = 1/3*22/7*5*5*h

1500 = (22*5*5*h)/3*7

Simplifying the expression further we have

1500 = 550h/21

1500(21) = 550h

31500 = 550h

Making h the subject of the relation we have

h = 31500/550

h= 57.272727...

h= 57.3 to one decimal place

Therefore the height of the cone is 57.3 cm

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Answer:

\(\frac{1}{10} * \frac{1}{100} = \frac{1}{1000}\)

1000 times

Step-by-step explanation:

Answer:

0.1% = 1 spin then

100% = ( 100×1) ÷0.1 = 1000

we are using 100% because its a sure bet it will happen but not logically

the answer is 1000

The triangle does not exist, as the property, the sum of two sides of a triangle is greater than the third side length of the triangle does not hold true.

Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric forms is represented by the symbol △ and consists of three connected vertices. Triangles may be categorized into a number of different varieties according to their sides and angles.

It is a triangle's property that the sum of any two sides of a triangle is greater than the third side.

Here sides given are 3 m, 5 m, 9 m.

Let us add the sides length 3 m and 5 m

3 m + 5 m = 8 m

Compare this with the third-side length of the triangle

8 m < 9 m

So, the property does not hold true.

So, the triangle does not exist.

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Answer:

The answer final is : 11x  I'm very sure

Step-by-step explanation:

If you want me to expand on the equation leave me a comment

Answer:x=11.8

Step-by-step explanation:

Answer:

2.375

Step-by-step explanation:

Assuming you mean \(2\frac{3}{8}\)  (if you meant \(\frac{23}{8}\) ignore this answer):

The first part is just 2. That's pretty easy. 2 wholes is 2.0

The 2nd part is 3 eights. Let's figure out how much 1 eight is.

We know it's half of 1/4, which is 0.25

So 1/8 is 0.125

3/8 is thus 3 of those, or 3 * 0.125 = 0.375

Now let's add both parts together.

2 + 0.375 = 2.375

Answer: 2.375

The solution set to the given inequality is

(-∞, -4) U (2,∞)

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

5(x – 2)(x + 4) > 0

First we solve for x, we replace the inequality sign by = sign

5(x – 2)(x + 4) = 0

Divide both sides by 5

(x – 2)(x + 4) = 0

Now we set each factor =0  and solve for x

x-2 =0 , so x= 2

x+4 =0, so x= -4

Now we use number line and make three intervals

First interval -infinity to -4

second interval -4 to 2

third interval 2 to infinity

Now we check each interval with our inequality

First interval -infinity to -4, pick a number in this interval and check with our inequality. lets pick -5

5(-5 – 2)(-5 + 4) > 0

35>0 is true

second interval -4 to 2, pick a number in this interval and check with our inequality. lets pick 0

5(0– 2)(0 + 4) > 0

-40>0 is false

Third interval 2 to infinity, pick a number in this interval and check with our inequality. lets pick 3

5(3 – 2)(3 + 4) > 0

35>0 is true

solution set are the intervals that make the inequalities true

(-∞, -4) U (2,∞)

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Question:

What is the solution set to the inequality 5(x – 2)(x + 4) > 0?

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

In the first sequence,

let's take ratio of the next term with its preceding term, so we will get the common ratio ~

\(\qquad \sf  \dashrightarrow \: \cfrac{4}{16} = \dfrac{1}{4} \)

So, we can imply that The next term of the sequence is 1/4 times the previous term.

hence, the unknown term will be 1/4 times of previous term.

Therefore, the next term here is 1

In the second sequence,

Do the same procedure as above, we will get common ratio as :

\(\qquad \sf  \dashrightarrow \: \cfrac{18}{6} = 3\)

So, the next term is 3 times the preceding term, that is :

Therefore, the next term is 162

Answer:

second one Step-by-step explanation:

Answer:

ratios, fractions, statistics, and percentage increase or decrease.

Step-by-step explanation:

Answer:

The answer is 5.05

Step-by-step explanation:

Let the number be x,

5/9 = 0.56

Now,

x × 11/100 = 5/9

x = 5 × 100 ÷ 9 × 11

x = 500/99

x = 5.05

Thus, The number is 5.05

-TheUnknownScientist 72

7.54 and 0.46 are the solutions to the given quadratic equations

Given the quadratic equation below:

x^2-18x+8=0

We need to determine the solutions to the given quadratic expression. Using the general formula below:

x = -b±√b²-4ac/2a

From the equation

a = 1

b = -18

c = 8

Substitute

x = 18±√18²-4(1)(8)/2(1)
x= 18±√324-32/2

x =18± 17.08/2

x = 35.08/2 and 0.92/2

x = 17.54 and 0.46

Hence the two solutions to the given quadratic equation are 17.54 and 0.46

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Answer:

I think it's graph C and graph D

Answer:

#1

#2

ΔCDE ~ ΔFGH by AA postulate

#16

Correct choice is D

Thomas can pack the items into a maximum of 20 bags, with each bag containing 24 items after calculated with greatest common divisor.

To find the maximum number of bags Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192. The GCD will represent the maximum number of items that can be packed into each bag.

To find the GCD, we can use the Euclidean algorithm. First, we find the GCD of 120 and 168:

168 = 1 * 120 + 48

120 = 2 * 48 + 24

48 = 2 * 24 + 0

Therefore, the GCD of 120 and 168 is 24.

Next, we find the GCD of 24 and 192:192 = 8 * 24 + 0

Therefore, the GCD of 120, 168, and 192 is 24.

So, Thomas can pack 24 items into each bag. To find the maximum number of bags he can get, we divide the total number of items by 24:

Total number of items = 120 + 168 + 192 = 480

Number of bags = 480 / 24 = 20

Therefore, Thomas can get a maximum of 20 bags.

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Answer: Your welcome!

Step-by-step explanation:

a) In 5 years' time, there are expected to be 136 beetles in the area of rainforest (20 * 1.66^5 ≈ 135.9, rounded to 136).

b) In 20 years' time, there are expected to be 8,000 beetles in the area of rainforest (20 * 1.66^20 ≈ 8,002.2, rounded to 8,000).

Steps to solve:

-7x - 5y = -68 when x = -6

~Substitute and simplify

-7(-6) - 5y = -68

42 - 5y = -68

~Subtract 42 to both sides

-5y = -110

~Divide -5 to both sides

y = 22

Best of Luck!