Find the nth term of the geometric sequence with given first term a and common ratio r.
a = 7/2, r = - 1/2
What is the fourth term?

Answer:

$1054

Step-by-step explanation:

simple interest = 4% of original amount each time

850/100 = 8.5 = 1%

8.5 x 4 = 34 = 4%

34 x 6 = 204

$850 + $204 = $1054

Answer:

Seems correct to me. I color coded the various terms.

Step-by-step explanation:

[13x³ came by adding 9x³ and 4x³]

Check the picture below.

\(\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =60 \end{cases} \\\\\\ A=\cfrac{8^2}{2}\left( ~~ \cfrac{\pi (60) }{180}-\sin(60^o ) ~~ \right)\implies A=32\left( ~~ \cfrac{\pi }{3}-\sin(60^o ) ~~ \right) \\\\\\ A=32\left( ~~ \cfrac{\pi }{3}-\cfrac{\sqrt{3}}{2} ~~ \right)\implies A=\cfrac{32\pi }{3}-16\sqrt{3}\implies A\approx 5.8~in^2\)

Answer:

40,000

Step by step explanation:

842,963

840,000

40,000

Answer:

a) 1.07, b) 0.1423

Step-by-step explanation:

Answer: An island nation with a strong navy is easier to defend.

Step-by-step explanation:

The fact that could be added to either column is that an island nation with a strong navy is easier to defend.

The information given is about facts concerning Great Britain and Japan.

Option A and D are incorrect as the information given wasn't stated. Option B is wrong because it stated a fact about South Africa.

The correct option is C.

Answer:

1,3, and 4

Step-by-step explanation:

got a hundo on the testo

Answer: Credit cards

Step-by-step explanation:

(you can search it up as well)

Answer:

x = 0 and y = 5

Step-by-step explanation:

y = 2x + 5

x + 2y = 10

Substitute y = 2x + 5 in x + 2y = 10

x + 2(2x + 5) = 10

x + 4x + 10 = 10

5x = 10 - 10

5x = 0

x = 0/5

x = 0

Substitute x = 0 in x + 2y = 10

0 + 2y = 10

2y = 10

y = 10/2

y = 5

a. The roots of function f(x) = x³ + x + 1 is strictly increasing according to differential calculus.

b. A Python program using the bisection method can be used to find the root of f(x) = x³ + x + 1 within the interval [-1, 0].

a. To prove that the function f(x) = x³ + x + 1 is strictly increasing using differential calculus, we need to show that the derivative of f(x) is positive for all x in its domain.

Let's find the derivative of f(x):

f'(x) = d/dx (x³ + x + 1)

= 3x² + 1

Since the coefficient of the quadratic term (3x²) is positive, the derivative is positive for all real values of x. This means that the function f(x) is increasing for all x in its domain.

b. To find the root of f(x) using a computer program, we can use the bisection method. This method relies on the intermediate value theorem to find a root within a given interval.

Here's an example of a Python program that uses the bisection method to find the root of f(x):

def f(x):

   return x**3 + x + 1

def bisection(a, b, tolerance):

   while abs(b - a) > tolerance:

       c = (a + b) / 2

       if f(a) * f(c) < 0:

           b = c

       else:

           a = c

   return (a + b) / 2

root = bisection(-1, 0, 1e-5)

print("Root:", root)

In this program, the f(x) function defines the cubic polynomial. The bisection function performs the bisection method to find the root within the interval [-1, 0] with a given tolerance of 1e-5. The result is then printed as the estimated root.

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Using an ideal gas equation to solve the problem. Then the original volume is 17.67 liters.

An ideal gas is a theoretical composed of a set of randomly moving gas particles that interact only through elastic collision.

Given

A balloon containing 0.500 mol at 0. 00°C and 65.0 kPa pressure are expanded by adding more argon.

Pressure (P) = 65 kPa

Mole (n) = 0.5 mol

Temperature (T) = 0 °C = 273.15 K

Universal gas constant (R) = 8.317 L.kPa/mol.K

We know the ideal gas equation

\(\rm PV =nRT\\\\V \ \ = \dfrac{nRT}{P}\)

Put the values, we have

\(\rm V = \dfrac{0.5*8.317*273.15}{65}\\\\V = 17.67\)

Thus, the original volume is 17.67 liters.

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Answer:

answer in picture

Step-by-step explanation:

The figure B has the perimeter of 34ft.

We have four figures as shown in the figure.

We have to determine which figure has a perimeter of 34 feet.

The perimeter of -

Rectangle = 2(L + B)

Square = 4a         [a is the side of square]

According to the question -

Fig (a) -    Perimeter = 2(10 + 8) = 2 x 18 = 36ft

Fig (b) -    Perimeter = 2(12 + 5) = 2 x 17 = 34ft

Fig (c) -    Perimeter = 4 x 7 = 28ft

Fig (d) -    Perimeter =  4 x 9 = 36ft

Hence, the figure B has the perimeter of 34ft.

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The figure B has the perimeter of 34ft.

There are four figures given

As shown in the figure.

We have to determine which figure has a perimeter of 34 feet.

Since we know that,

Perimeter of:

Rectangle = 2(L + B)

Square = 4a         [a is the side of square]

Now

For Figure ( a):

Perimeter = 2(10 + 8) = 2 x 18 = 36ft

For Fig (b):

Perimeter = 2(12 + 5) = 2 x 17 = 34ft

For Fig (c):

Perimeter = 4 x 7 = 28ft

For Fig (d):

Perimeter =  4 x 9 = 36ft

Hence, the figure B has the perimeter of 34ft.

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Answer:

Step-by-step explanation:

From the expression xy = 4, y = 4/x

Substituting y = 4/x into the expression  y(x-4)(x+2) and expanding;

=  y(x-4)(x+2)

= 4/x(x-4)(x+2)

On expansion;

= (4-16/x)(x+2)

= 4x+4(2)-(16/x)x-(16/x)2

= 4x+8-16-32/x

= 4x-8-32/x

The equivalent expression is 4x - 8 - 32/x

Answer:

E

Step-by-step explanation:

Here, we want to find the area of the shaded portion on the graph.

That would be P(-1.2<z<0.85)

we complete this by checking these values on the standard score table as follows;

P( z< 0.85) - P(z<-1.2) = 0.68727

It is impossible to construct an equilateral triangle with three vertices with integer coordinates.

Suppose ABC is an equilateral triangle with integer coordinates.

Then its area by the formula \(\frac{1}{2} (x_{1} (y_{2} -y_{3})+x_{2}(y_{3} -y_{1})+x_{3} (y_{1} -y_{2}))\) is an integer.

Let a be the length of a side. Then \(a^{2}\) is a positive integer. The area of the equilateral triangle is \(\sqrt{\frac{3}{4} } a^{2}\) which is irrational.

Hence we get a contradiction.

Therefore an equilateral triangle cannot have all its vertices integer coordinates.

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It is impossible to construct an equilateral triangle with three vertices with integer coordinates because the distance between any two points with integer coordinates is also an integer. In an equilateral triangle, all three sides must have equal length. However, if the distance between two points with integer coordinates is an integer, then the distance between the third point and either of the first two points will not be an integer in most cases. This means that it is not possible to find three points with integer coordinates that are equidistant from each other.

The distance between two points with integer coordinates can be calculated using the Pythagorean theorem. If we consider two points with coordinates (x1, y1) and (x2, y2), the distance between them is √((x2-x1)²+(y2-y1)²). If the distance between two points is an integer, it means that the difference between the x-coordinates and the y-coordinates is also an integer. In an equilateral triangle, the distance between any two points must be the same. However, it is impossible to find three points with integer coordinates that are equidistant from each other.

In conclusion, it is not possible to construct an equilateral triangle with three vertices with integer coordinates because the distance between any two points with integer coordinates is also an integer. In an equilateral triangle, all three sides must have equal length. However, if the distance between two points with integer coordinates is an integer, then the distance between the third point and either of the first two points will not be an integer in most cases. This means that it is not possible to find three points with integer coordinates that are equidistant from each other.

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The number A(t) of pounds of salt in the tank at time t is given by A(t) = 2000 (1 - [-5t]) pounds.

Initially, the tank contains 500 gallons of pure water, so V(0) = 500 gallons and C(0) = 0 pounds per gallon. As the brine is pumped into the tank at a rate of 5 gallons per minute, the volume of the solution in the tank increases by 5 gallons every minute. Therefore, we have the function:

V(t) = 500 + 5t

At the same time, the well-mixed solution is pumped out of the tank at a rate of 5 gallons per minute. This means that the volume of the solution in the tank decreases by 5 gallons every minute. Therefore, we have:

V'(t) = -5

Substituting the expressions we have derived for V(t), V'(t), and C(t), we obtain:

A(t) = 0 +  [(2 pounds/gallon) - (-5/V(u)) A(u)] du

Simplifying this expression, we get:

A'(t) = 2 - (5/V(t)) A(t)

This is a first-order differential equation, which we can solve using separation of variables:

A'(t)/(2 - (5/V(t)) A(t)) = 1

Integrating both sides with respect to t, we get:

ln|2 - (5/V(t)) A(t)| = t + C

where C is a constant of integration.

Solving for A(t), we obtain:

A(t) = (2/5) V(t) - (2/5) V(t) [-5(t-t⁰)]

where t₀ is the initial time, which we can set to 0 without loss of generality since we are interested in the amount of salt in the tank at any given time t.

Now we can substitute the expression we derived for V(t) into the equation for A(t) to obtain:

A(t) = (2/5) (500 + 5t) - (2/5) (500 + 5t) exp[-5t]

Simplifying this expression, we get:

A(t) = 2000 (1 - [-5t]) pounds

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Complete Question:

A large tank is filled to capacity with 500 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gal/min. The well-mixed solution is pumped out at the same rate. Find the number A(t) of pounds of salt in the tank at time t.

A(t) = ____ lb

To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the powers they possess, many rules of exponents are given.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The given value can be written as:

\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)

Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

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The ladder reaches approximately 5.196 meters up the wall, and the base of the ladder is approximately 5.196 meters from the wall. Calculated using trigonometric ratios.

To determine how far up the wall the ladder reaches and how far from the wall the base of the ladder is, we can use trigonometric ratios. In this case, we are given that the ladder makes an angle of 60° with the ground and is 6 meters long.

First, let's find the height the ladder reaches on the wall. We can use the sine ratio, which states that the sine of an angle is equal to the opposite side divided by the hypotenuse.

In this case, the opposite side is the height on the wall, and the hypotenuse is the length of the ladder.

Using the sine ratio, we have:

sin(60°) = height on the wall / 6 meters

To solve for the height on the wall, we can rearrange the equation:

height on the wall = sin(60°) * 6 meters

Using a calculator, we find that sin(60°) is approximately 0.866. Plugging this value into the equation, we have:

height on the wall = 0.866 * 6 meters

Calculating this, we find that the height on the wall is approximately 5.196 meters.

Next, let's find the distance from the wall to the base of the ladder. We can use the cosine ratio, which states that the cosine of an angle is equal to the adjacent side divided by the hypotenuse.

In this case, the adjacent side is the distance from the wall to the base of the ladder, and the hypotenuse is the length of the ladder.

Using the cosine ratio, we have:

cos(60°) = distance from wall / 6 meters

To solve for the distance from the wall, we can rearrange the equation:

distance from wall = cos(60°) * 6 meters

Using a calculator, we find that cos(60°) is also approximately 0.866. Plugging this value into the equation, we have:

distance from wall = 0.866 * 6 meters

Calculating this, we find that the distance from the wall to the base of the ladder is approximately 5.196 meters.

Therefore, the ladder reaches approximately 5.196 meters up the wall, and the base of the ladder is approximately 5.196 meters from the wall.

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Descriptive statistics is a branch of statistics that deals with the collection, analysis, interpretation, and presentation of data. It focuses on summarizing and describing the characteristics of a sample or population. The purpose of descriptive statistics is to provide a clear and concise summary of the data, including measures of central tendency, variability, and distribution.

True,This information can be used to make inferences about the population as a whole. Therefore, descriptive statistics helps statisticians to better understand and interpret the population data.

False, Descriptive statistics is a branch of statistics that focuses on summarizing and organizing data from a sample or population. It provides insights into the basic features of the data, such as the mean, median, and standard deviation, but does not make inferences about the population.

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Answer:

4

Step-by-step explanation:

As the picture shows, there are positives and negatives; adding a positive number with a negative number is the same as subtracting a positive from a positive.

So, 9 + (-5) would be the same as 9 - 5.

Hope I helped!

Given the function

First I'll rewrite it in terms of y

Next is to determine the values of y (range) for the given values of x

Now you can graph it:

The profit from selling 20 bags of rice is 61.67.e percentage profit from selling 20 bags of rice is approximately 10.54%.

To calculate the profit from selling 20 bags of rice, we need to determine the cost of the bags, the selling price, and subtract the cost from the selling price. Using the given cost equation c = 24x + 105 and the selling price equation s = 33x - x^2/30, we can calculate the profit expression and then determine the percentage profit.

Given that the cost equation is c = 24x + 105, we can substitute the value of x (which represents the number of bags) with 20 to find the cost of 20 bags.

c = 24(20) + 105

c = 480 + 105

c = 585

The cost of 20 bags of rice is 585.

Next, we use the selling price equation s = 33x - x^2/30 to find the selling price of 20 bags.

s = 33(20) - (20^2)/30

s = 660 - 400/30

s = 660 - 400/30

s = 660 - 13.33

s = 646.67

The selling price of 20 bags of rice is 646.67.

To calculate the profit, we subtract the cost from the selling price:

Profit = Selling Price - Cost

Profit = 646.67 - 585

Profit = 61.67

The profit from selling 20 bags of rice is 61.67.

To calculate the percentage profit, we divide the profit by the cost and multiply by 100:

Percentage Profit = (Profit / Cost) * 100

Percentage Profit = (61.67 / 585) * 100

Percentage Profit ≈ 10.54%

Therefore, the percentage profit from selling 20 bags of rice is approximately 10.54%.

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The circumstance that the score is located 5 points above the mean a central value, relatively close to the mean is when the population standard deviation is much greater than 5.

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Here, we have

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

Therefore, the correct option is D.

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Answer:

The expected gain (value) per job for the yard service owner on a given day can be calculated by taking a weighted average of the gains under each possible weather condition, where the weights are the probabilities of those conditions occurring.

If it does not rain, the yard service owner earns an average of $40 per job. If it rains, the owner earns $0 per job. The probability of rain on a given day is 25%. Therefore, the expected gain per job on that day is:

Expected gain per job = (probability of no rain) * (gain per job under no rain) + (probability of rain) * (gain per job under rain)

= (0.75) * (40) + (0.25) * (0)

= 30

Therefore, the expected gain (value) per job for the yard service owner on a given day is $30.

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Answer:

I don't think you can

Step-by-step explanation:

Answer:

p = 1

Step-by-step explanation:

Picture attached below for steps

help bye

Step-by-step explanation:

The correct inequality that describes the problem is 4x ≥ 40. Thus, the correct answer is A.

The answer is A because Ms. Wells is ordering 4 large cheese pizzas, and she expects to spend at least $40 on the pizzas. The inequality 4x ≥ 40 represents the total cost of the pizzas, which is 4 times the cost of each pizza (4x) and should be greater than or equal to $40. This inequality tells us that the total cost of the pizzas is at least $40, which is what Ms. Wells expects.

Option B, 4x > 40x, is incorrect because it doesn't make sense mathematically. The right side of the inequality is 40x, which is not related to the problem, and it also doesn't make sense that each pizza will cost 40 dollars.

Option C, 4x ≤ 40, is incorrect because it represents the total cost of the pizzas as less than or equal to $40, which doesn't match with Ms. Wells' expectation that she expects to spend at least $40 on the pizzas.

This question should be provided with answer choices, which are:

The correct answer is A.

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