Please help math problem

Answer:

This geometric series is convergent:

\( \frac{10}{1 - ( - \frac{1}{5}) } = \frac{10}{ \frac{6}{5} } = 10( \frac{5}{6} ) = \frac{25}{3} = 8 \frac{1}{3} \)

The geometric series 10 - 2 + 0.4 - 0.08 + ... is convergent.

To determine if the geometric series 10 - 2 + 0.4 - 0.08 + ... is convergent or divergent, we need to examine the common ratio (r) between consecutive terms.

The common ratio (r) can be found by dividing any term by its preceding term.

Let's calculate it:

r = (-2) ÷ 10 = -0.2

r = 0.4 ÷ (-2) = -0.2

r = (-0.08) ÷ 0.4 = -0.2

In this series, the common ratio (r) is -0.2.

For a geometric series to be convergent, the absolute value of the common ratio (|r|) must be less than 1. If |r| ≥ 1, the series is divergent.

In this case, |r| = |-0.2| = 0.2 < 1.

Since the absolute value of the common ratio is less than 1, the geometric series 10 - 2 + 0.4 - 0.08 + ... is convergent.

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In a linear equation, 9.14 does he save by paying off the loan when the next payment is due .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Jan  293  18  311  1,507 16.25%

Feb  296  15  311  1,212 32.67%

Mar 298           12  311   913 49.25%

Apr  301            9  311   612 66.00%

May  304    6  311  308 82.92%

Jun  308    3  311    0        100.00%

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Answer: 6

Step-by-step explanation:

Two negatives make a positive, -42/-7 would be 6. The same as a normal 42/7

The exponential form of ⁵√13³ is \(13^{3/5}\).

Hence, option D) is the correct answer.

This question is incomplete, the complete question is:

Which of the following is equivalent to 5 sqrt 13³ ?.

A) 13^2.

B)13^15.

C)13^(5/3).

D)13^(3/5)

Given the expression; 5 sqrt 13³

This can be represented as; ⁵√13³

To convert from radical form to exponential form, we use apply the radical rule;

\(\sqrt[n]{a^m} = a^{m/n}\)

Hence,

\(\sqrt[5]{13^3} = 13^{3/5}\)

The exponential form of ⁵√13³ is \(13^{3/5}\).

Hence, option D) is the correct answer.

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a. The categorical qualitative variables from the ones listed above are:

- MarketSize (small, medium, or large market)

- PromotionType (Promotion 1, 2, or 3)

- WeekNumber (Week 1, 2, 3, 4)

b. The numerical (quantitative) variables from the ones listed above are:

- Sales (in $1000)

- AgeOfStore (in years)

c. The level of measurement for each variable is as follows:

- MarketSize: Nominal level of measurement. The categories (small, medium, large) are mutually exclusive and there is no inherent order or numeric value associated with them.

- PromotionType: Nominal level of measurement. The promotions (Promotion 1, 2, 3) are distinct categories with no inherent order or numeric value.

- WeekNumber: Ordinal level of measurement. The weeks (Week 1, 2, 3, 4) have a natural order but the differences between them are not necessarily equal.

- Sales: Ratio level of measurement. The variable represents the actual sales in dollars, which has a meaningful zero point and allows for meaningful ratios and calculations.

- AgeOfStore: Ratio level of measurement. The variable represents the age of the store in years, which has a meaningful zero point and allows for meaningful ratios and calculations.

Understanding the level of measurement of variables is important for selecting appropriate statistical methods and understanding the nature of the data. In this case, we have identified the categorical qualitative variables (MarketSize, PromotionType, WeekNumber) and the numerical (quantitative) variables (Sales, AgeOfStore) and determined their respective levels of measurement.

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The values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

√15/(y + 2) = y/√15 {opposite/adjacent}

y(y + 2) = (√15)² {cross multiplication}

y² + 2y = 15

y² + 2y - 15 = 0

by factorization;

(y - 3)(y + 5) = 0

y = 3 or y = -5

by Pythagoras rule:

(√15)² = x² + y²

15 = x² + 3²

x = √(15 - 9)

x = √6

z² = (√6)² + 2²

z = √(6 + 4)

z = √10

Therefore, the values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

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The person needs to walk about 6.478 miles in a direction of approximately 19.11° north of east to head directly home.

To find the distance and direction the person needs to walk to head directly home, we can use the Pythagorean theorem and some trigonometry.
1. First, break the southwest walk into west and south components. Since it's a 3-mile walk at a 45-degree angle, the west and south components are equal: 3 * cos(45°) = 3 * 0.7071 ≈ 2.121 miles for both west and south components.

2. Calculate the total west and south distances. The total west distance is the sum of the initial westward walk and the west component of the southwest walk: 4 miles + 2.121 miles ≈ 6.121 miles. The total south distance is just the south component of the southwest walk: 2.121 miles.

3. Use the Pythagorean theorem to find the straight-line distance back home: √((6.121 miles)^2 + (2.121 miles)^2) ≈ 6.478 miles, which is the correct distance.

4. Determine the angle between the eastward direction and the straight-line path back home. Use the inverse tangent function: angle = atan(south distance / west distance) = atan(2.121 miles / 6.121 miles) ≈ 19.11° north of east, which is the correct direction.

So, the person needs to walk about 6.478 miles in a direction of approximately 19.11° north of east to head directly home.

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Okay so our starting point is - 1,260 feet

Now it is descending (-) 5 ft per minute for 12 minutes

So we multiply -5 (negative because it is descending) by 12

-5 x 12 = -60

So now we add -60 to -1,260

This would be -1,320

So the submarine's new position in relation to the sea level is -1,320

Hope this helped. Have a great day!

that would be -1260 + 12(-5) = -1260 - 60 = -1320 feet

The sine of angle V is 97/72. The length of side VW is 65 units.

To find the sine of angle V, we need to use the ratio of the length of the side opposite angle V to the length of the hypotenuse. In this case, side VU is opposite angle V, and hypotenuse UW is the longest side of the right triangle.

Using the Pythagorean Theorem, we can find the length of side VW:

VW² = UW² - VU²

VW² = 72² - 97²

VW² = 5184 - 9409

VW² = 4225

VW = 65

Now we can use the sine ratio:

sin(V) = opposite/hypotenuse = VU/UW

sin(V) = 97/72

Therefore, the ratio that represents the sine of ∠V is 97/72.

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Answer:

The correct answer is 3/5.

Step-by-step explanation:

Let's assume that the total number of passengers on the train initially are '100x'.

Now, it is given that 1/5 of them get off at station A. So, the number of passengers who get off at station A are -

1/5*100x = 20x

Hence, the passengers left on the train will be - 100x - 20x = 80x

Now, it is given that a quarter of the remaining passengers are dropped off at station B. So, the passengers being dropped off at station B are -

1/4*80x = 20x

So, after the drop off at station B the remaining passengers in the train will be - 80x - 20x = 60x

Therefore, the fraction of passengers who remained on the train after station B will be - 60x/100x = 3/5

Answer:

Step-by-step explanation:

MIXED NUMBER: Convert to a mixed number by placing the numbers to the right of the decimal over 10.Reduce the fraction

8 4/5

SIMPLFIED FRACTION: Convert to a mixed number by placing the numbers to the right of the decimal over 10.Reduce the fraction. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number and adding the numerator to get the new numerator. Place this new numerator over the original denominator.

44/5

The statement "D. Given any two distinct lines in the Cartesian plane, the two lines will either be parallel or perpendicular" is NOT true.

A. The statement is true. The ratios of the vertical rise to the horizontal run, also known as the slopes, of any two distinct nonvertical parallel lines are equal. This is one of the properties of parallel lines.

B. The statement is true. If two distinct nonvertical lines are parallel, then they have the same slope. Parallel lines have the same steepness or rate of change.

C. The statement is true. Given two distinct lines in the Cartesian plane, the two lines will either intersect at a point or they will be parallel and never intersect. These are the two possible scenarios for distinct lines in the Cartesian plane.

D. The statement is NOT true. Given any two distinct lines in the Cartesian plane, they may or may not be parallel or perpendicular. It is possible for two distinct lines to have neither parallel nor perpendicular relationship. For example, two lines that have different slopes and do not intersect or two lines that intersect but are not perpendicular to each other.

Therefore, the statement "D. Given any two distinct lines in the Cartesian plane, the two lines will either be parallel or perpendicular" is the one that is NOT true.

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Answer:

B.X+2

Step-by-step explanation:

-2^3+12X-2^2+9X-2-22

-8+48-18-22

40-40=0

The following is a factor of the polynomial is x+2.

Factor theorem is a special kind of the polynomial remainder theorem that links the factors of a polynomial and its zeros.

The factor theorem removes all the known zeros from a given polynomial equation and leaves all the unknown zeros. The resultant polynomial has a lower degree in which the zeros can be easily found.

As per the factor theorem, (y – a) can be considered as a factor of the polynomial g(y) of degree n ≥ 1, if and only if g(a) = 0. Here, a is any real number. The formula of the factor theorem is g(y) = (y – a) q(y). It is important to note that all the following statements apply for any polynomial g(y):

Given:

f(x)=x³ + 12x² + 9x - 22

To the above equation (x + 2) is a factor of x³ + 12x² + 9x - 22.

As,

f(-2)= (-2)³ + 12(-2)² + 9(-2) - 22

f(x)= -8 + 48 -18 -22

f(x)= 40 -40

f(x) = 0

Hence, the factor of x+2

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Based on the observations, it is clear that an appropriate domain for the function is whole numbers (0, 1, 2, ...).

What is the domain of a function?

Functions assign outputs to inputs. The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

We have,

f(x) = 6x - 90

The interpret of the given function values and determine an appropriate domain for the function should be explained below:

The following information should be considered:

f(−6)= −126, meaning if the company sells -5 shirts, they would make a profit of -120 dollars. This interpretation does NOT make sense in the context of the problem.

f(6)= −44, meaning if the company sells 7 shirts, they would make a profit of −44 dollars. This interpretation makes sense in the context of the problem.

f(9.5)= -33, meaning if the company sells 9.5 shirts, they would make a profit of 5 dollars. This interpretation does NOT make sense in the context of the problem.

Based on the observations above, it is clear that an appropriate domain for the function is whole numbers (0, 1, 2, ...).

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Descriptive statistics summarize numbers and inferential statistics determine whether the results are significant.

What is statistics?

The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

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The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

What is derivative?

The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).

The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.

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Answer:

2 1 2 1

Step-by-step explanation:

Answer:

one eighth of a number b

Step-by-step explanation:

Answer:

one eighth of a number b

Step-by-step explanation:

Answer:

1st one is not a right triangle.

2nd one is not a right triangle.

3rd one is not a right triangle.

4th one is a right triangle.

Step-by-step explanation:

1, 2, and 3 could also be "not enough information".

Answer:   You can buy a 9-pound bag for $8.37.

Step-by-step explanation:

\(\frac{5lbs}{4.65} =\frac{p}{8.37}\)    

Then, we cross multiply, and we get:

5(8.37) = 4.65p

  41.85 = 4.65p   [We divided 4.65 by both sides]

         9 = p

Data

• Total phone calls: 154

• Second evening ( ,s ,): 10 more calls than the first evening ( ,f ,)

• Third evening ( ,t ,): 4 times as many calls as ,f

Procedure

We have to translate the given information into algebraic expressions.

• Maria received a total of 154 phone calls at the call center:

where f represents the first evening, s the second, and t the third.

• The second evening, she received 10 more calls than the first evening:

• The third evening, she received 4 times as many calls as the first evening:

As t and s can be used in terms of f, we will replace the second and third equations that we build in the first one:

Eliminating the parenthesis we get:

Solving for f:

Thus, the number of phone calls the first evening was 24.

Then, we have to replace this calculated value in the other equations to get s and t.

• Solving for ,s

• Solving for ,t

To prove our answers are correct, we can do the following:

Answer

• Number of phone calls the first evening: 24

• Number of phone calls the second evening: 34

• Number of phone calls the third evening: 96

The probability of guessing the correct answer for each question is 1/4, while the probability of guessing incorrectly is 3/4.

To calculate the probability of answering at most one correct answer, we need to consider two cases: answering zero correct answers and answering one correct answer.

For the case of answering zero correct answers, the probability can be calculated as (3/4)^5, as there are five independent attempts to answer incorrectly.

For the case of answering one correct answer, we have to consider the probability of guessing the correct answer on one question and incorrectly guessing the rest. Since there are five questions, the probability for this case is 5 * (1/4) * (3/4)^4.

To obtain the probability of answering at most one correct answer, we sum up the probabilities of the two cases:

Probability = (3/4)^5 + 5 * (1/4) * (3/4)^4.

Therefore, by calculating this expression, you can determine the probability of answering at most one correct answer among five questions when guessing randomly.

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The inverse of matrix C is a matrix with 2 rows and 2 columns. Row 1 is [-3, -2], and row 2 is [4, 2.5].

To determine the inverse of matrix C, we can use the formula for a 2x2 matrix inverse:

C^(-1) = (1/det(C)) * adj(C)

where det(C) is the determinant of matrix C and adj(C) is the adjugate of matrix C.

Given matrix C with row 1 as [5, -4] and row 2 as [-8, 6], we can calculate the determinant as:

det(C) = (5 * 6) - (-4 * -8) = 30 - 32 = -2

Next, we find the adjugate of matrix C by swapping the elements of the main diagonal and changing the signs of the other elements:

adj(C) = [6, 4]

        [-8, 5]

Finally, we can calculate the inverse matrix C^(-1) using the formula:

C^(-1) = (1/det(C)) * adj(C)

      = (1/-2) * [6, 4]

                 [-8, 5]

      = [-3, -2]

        [4, 2.5]

Therefore, the inverse of matrix C is a matrix with 2 rows and 2 columns. Row 1 is [-3, -2], and row 2 is [4, 2.5].

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Answer:

10

Step-by-step explanation:

Answer:

it's 100

Step-by-step explanation:

just divide 50,000 by 500 and you'll get 100 so 50000 Is 100 times as 500

Answer:

The answer is "Option B".

Step-by-step explanation:

The difference between most time and also the least spending time on Internet surfing is 3 hours. Since we do not have charts for tables etc., only 3 can be used we need. A range is defined as the difference between the largest and the smallest amounts. The range between both the largest as well as the smallest is unique. In this reply, it tells us that the gap between most time and the fewer hours invested surfing the web is 3 hours.

The answer is B

The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 3 hours.

This answer is proven 100% correct.

Hope this helps!

There are 1440 possible arrangements for the family wedding photo, considering the positions of the happy couple and the two youngest.

To find the number of possible arrangements for the family wedding photo, we need to consider the positions of the happy couple and the two youngest family members.

First, we place the happy couple in the middle position. This leaves eight family members to arrange on the remaining positions on either side of the couple.

For the two youngest family members, we have two options: placing the youngest on the left end and the second youngest on the right end, or vice versa.

Next, we arrange the remaining six family members on the remaining positions. Since there are six remaining family members, there are 6! (6 factorial) ways to arrange them.

Multiplying the number of options for the youngest family members (2) with the number of arrangements for the remaining family members (6!), we get:

\(2 * 6! = 2 * 720 = 1440.\)

Therefore, there are 1440 possible arrangements for the family wedding photo.

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happy with solution rate this

Step-by-step explanation:

A) distribute: 12x +16 = 0; 12x/12 = -16/12

x = -4/3

B) distribute: 420x +180 = 0; 420x/420 = -180/420

x = -3/7

Hope this helps! :)

0.0405 is the number that contain the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes, leading 0s are allowed.

According to collect from the data

Let us assume that the data as followed by

How many eight digit numbers contain the digit 2 exactly once, the digit 3 exactly twice, the digit 4 exactly thrice and more 5s than threes.

Let many eight digit numbers contain the digit 2 once, the digit 3 twice the digit 4 thrice and more 5s than threes.

2,3,3,4,4,4

now then:

= 8!/2!3!3!4!4!4!

= 8.7.6.5.4!/2×6×6×24×24×4!

= 35/864

Now 0.405 then the eight digit number contains the digit 2 once the digit 3 .

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Answer:

Is the answer not 361?

Step-by-step explanation:

Square 19.  

Im not sure what the question is.