A sequence is defined recursively using the formula f(n + 1) = f(n) – 5 . Which sequence could be generated using this formula?

1, –5, 25, –125, ...
2, 10, 50, 250, ...
3, –2, –7, –12, ...
4, 9, 14, 19, ...

JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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Let the cost of the dining table is 100%

∵ It sells with a 30% markup

→ That means the selling price of the table will be 100% + 30%

∴ The selling price of the table = 130% of the cost price

∵ The cost price of the table = $130

∴ The selling price of the table = 130% x 130

→ Change the percentage to a decimal by divide it by 100

∴ The selling price of the table = 1.30 x 130 = 169

∴ The selling price of the dining table is $169

Valeria cannot cut any 23-foot pieces from the 9-foot ribbon. The length of the leftover piece of ribbon will be equal to the original length of the ribbon, which is 9 feet.

Valeria bought a 9-foot length of ribbon and wants to cut 23-foot pieces from it. We need to determine how many pieces she can cut and the length of the leftover piece of ribbon.

To find out how many 23-foot pieces Valeria can cut, we need to divide the length of the ribbon by the length of each piece. The calculation is as follows:

9 feet ÷ 23 feet = 0.39130434782

Since we can't have a fraction of a piece, Valeria can only cut 0 whole pieces. Therefore, she cannot cut any 23-foot pieces from the 9-foot ribbon.

As for the length of the leftover piece of ribbon, we need to subtract the total length of the cut pieces from the original length of the ribbon. In this case, since Valeria cannot cut any 23-foot pieces, the length of the leftover piece will be equal to the original length of the ribbon.

Hence, the length of the leftover piece of ribbon is 9 feet.

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Answer:

Step-by-step explanation:

\(\sf -3\left(33b+65\right)=-95b-6b-87\)

Combine like terms:

\(\sf -3\left(33b+65\right)=-101b-87\)

Expand:-

\(\sf -99b-195=-101b-87\)

Add 195 to both sides:-

\(\sf -99b-195+195=-101b-87+195\)

Simplify:-

\(\sf -99b=-101b+108\)

Add 101b to both sides:-

\(\sf -99b+101b=-101b+108+101b\)

Simplify:-

\(\sf 2b=108\)

Divide both sides by 2:-

\(\sf \cfrac{2b}{2}=\cfrac{108}{2}\)

Simplify:-

\(\sf b=54\)

Therefore, your answer is b = 54!!

___________________________

Hope this helps you!

Have a great day! :)

Answer:

-24

Step-by-step explanation:

The amount of money Rashon would need to invest is equal to $8,300.46.

Mathematically, the compound interest on an investment can be calculated by using this mathematical expression:

A(t) = P(1 + r/n)^{nt}

Where:

In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:

Quarterly interest rate = 0.069/4

Quarterly interest rate = 0.01725%

20,200 = P(1 + 0.01725)^{4 × 13}

20,200 = P(1.01725)^52

20,200 = 2.4336P

Principal, P = 20,200/2.4336

Principal, P = $8,300.46.

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Answer:

In this scenario, Rashon's investment is compounded quarterly at an interest rate of 6.9% as follows:

Quarterly interest rate = 0.069/4

Quarterly interest rate = 0.01725%

20,200 = P(1 + 0.01725)^{4 × 13}

20,200 = P(1.01725)^52

20,200 = 2.4336P

Principal, P = 20,200/2.4336

Principal, P = $8,300.46.

The minimum area of a poster that will contain 50 square inches of printed material and have 4-inch margins on the top and bottom and 2-inch margins on the left and right is 98 square inches.

To determine the minimum area of the poster, we need to consider the dimensions of the printed material and the margins. The printed material covers an area of 50 square inches. The margins on the top and bottom are each 4 inches, which means we need to add 8 inches to the height of the printed material. The margins on the left and right are each 2 inches, which means we need to add 4 inches to the width of the printed material.
To determine the minimum area of the poster, follow these steps:

1. Add the top and bottom margins to the height of the printed material:
  Height = Printed Height + Top Margin + Bottom Margin
  Height = 50 square inches (assuming printed material height is 1 inch) + 4 inches + 4 inches
  Height = 9 inches

2. Add the left and right margins to the width of the printed material:
  Width = Printed Width + Left Margin + Right Margin
  Width = 50 square inches / 1 inch (since printed material height is 1 inch) + 2 inches + 2 inches
  Width = 54 inches

So, the total height of the poster is the height of the printed material plus the top and bottom margins, which is 50/width + 8 inches. The total width of the poster is the width of the printed material plus the left and right margins, which is 50/height + 4 inches.
Therefore, the minimum area of the poster is 7 x 14 = 98 square inches.

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The mean (expected value) of the number of hits is 5/12.

The variance of the number of hits is 17/48.

Mean (Expected Value):

The mean, also known as the expected value, represents the average value of a dataset. It is calculated by summing all the values in the dataset and dividing by the total number of values.

The variance measures the spread or dispersion of a dataset. It quantifies the variability or how much the values differ from the mean. A high variance indicates that the values are more spread out, while a low variance indicates that the values are clustered closely around the mean.

To find the mean and variance of the number of hits, we can use the concept of a binomial distribution.

Let's define the following variables:

X = number of hits

p = probability of hitting the moving target on any given shot

q = probability of missing the moving target on any given shot

n = number of shots

Given information:

p(first shot) = 1/3

p(subsequent shots | previous hit) = 1/2

p(subsequent shots | previous miss) = 1/4

Mean (Expected Value):

The mean of a binomial distribution is calculated as:

Mean = n × p

For the first shot, the probability of hitting is 1/3.

For subsequent shots, the probability of hitting is:

p(subsequent shots)

= p(subsequent shots | previous hit) × p(previous hit) + p(subsequent shots | previous miss) × p(previous miss)

Mean = (1 × 1/3) + (2 × 1/2 × 1/3) + (3 × 1/2 × 1/2 × 1/3)

Mean = 1/3 + 1/3 + 1/12

Mean = 5/12

Therefore, The mean (expected value) of the number of hits is 5/12.

The variance of a binomial distribution is calculated as:

Variance = n × p × q

For subsequent shots, the probability of missing is:

q(subsequent shots) = 1 - p(subsequent shots)

Variance = (1 * 1/3 * 2/3) + (2 * 1/2 * 1/3 * 1/2) + (3 * 1/2 * 1/2 * 1/3 * 1/2)

Variance = 2/9 + 1/12 + 1/48

Variance = 17/48

Therefore, the variance of the number of hits is 17/48.

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The researcher needs to enroll at least 226 women over 40 years old to ensure that a 95% confidence interval estimate of the mean birth weight of their infants has a length not exceeding 100 grams.

To find the sample size required for a 95% confidence interval with a maximum width of 100 grams, we need to use the formula:

n = (z * σ / E)^2

where:

n = sample size

z = the z-score for the desired confidence level, which is 1.96 for a 95% confidence level

σ = the population standard deviation, which is 385 grams

E = the maximum margin of error, which is half of the desired maximum width of the confidence interval, or 50 grams (since 100 grams is the maximum width, and we want it to be divided equally on both sides of the mean)

Substituting these values into the formula, we get:

n = (1.96 * 385 / 50)^2

n = 225.44

We need to round up the sample size to the nearest whole number, which gives us a sample size of 226.

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Answer:

yes

Step-by-step explanation:

School is an educational building where you learn math and reading and it doesnt help you but it benifits you in jobs.

Answer:

well yes but no at the same time

Step-by-step explanation:

have a nice week. please mark as brainllest

[o]-[o]

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Answer:

7.5 square units

Step-by-step explanation:

3x5=15. 15/2=7.5. 7.5 is the area. PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS brainliest.

Answer:

7.5 sq units

Step-by-step explanation:

Let's list out all the points in the triangle.

(0,4) (4,1) and (5,4)

Find the distance b/w each side

distance b/w (0,4) and (4,1) is

\(\sqrt{(1-4)^{2}+( 4-0)^{2} }\) =\(\sqrt{(-3)^{2}+16 } =\sqrt{9+16}=\sqrt{25} =5\)

distance b/w (4,1) and (5,4) is

\(\sqrt{(4-1)^{2}+(5-4)^{2} }=\sqrt{9+1}=\sqrt{ 10 }\)

distance b/w (5,4) and (0,4) is

\(\sqrt{(4-4)^2+(0-5)^2}=\sqrt{25} =5\)

So the given triangle is an isoscles triangle meaning 2 sides are equal.

So we can use the formula 1/2*base*height=

1/2*\(\sqrt{10}\)*5

=0.5*3.16*5=7.905

So the approximate answer would be 7.5 sq units

Answer:

  -20, -18, -16

Step-by-step explanation:

For consecutive integer problems, it often works well to let a variable represent the middle one (or their average value).

__

Here, we can let x represent the second integer. Then the first is (x-2), and the third is (x+2). The given relation can be written as ...

  (5 +x)(-7) = 11 +5(-(x+2))

  -35 -7x = 11 -5x -10 . . . . . . eliminate parentheses

  -36 = 2x . . . . . . . . . add 7x -1

  -18 = x . . . . . . . . divide by 2

The three integers are -20, -18, -16.

Alessia spent $5,408 on entertainment in 2021.

To determine how much Alessia spent on entertainment in 2021, we need to work backward from the given information about her salary in 2022.

Let's assume Alessia's salary in 2021 was the same as in 2022, which is $26,000 after tax.

Since Alessia spends 35% of her after-tax salary on rent, we can calculate her rent expenditure:

Rent = 35% × $26,000

= $9,100

The remaining amount is split between food, petrol, and entertainment in the ratio 6:11:8.

To determine the ratio's total parts, we sum the individual parts:

Total parts = 6 + 11 + 8 = 25

Next, we calculate the value of one part of the ratio:

One part = ($26,000 - $9,100) / 25

= $16,900 / 25

= $676

Now, we can calculate how much Alessia spent on entertainment in 2021, which is 8 parts of the ratio:

Entertainment expenditure = 8 × $676

= $5,408

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Answer:

4 seconds

Step-by-step explanation:

fish broke the water's surface in 1 second and went back into the water at 5 seconds

∴ it was out of the water for 4 seconds

Answer:

4

Step-by-step explanation:

Answer:

Graph (0,4), graph (6,7) then connect in a straight line.

Step-by-step explanation:

Answer: espero que esto ayude :)

La solución simplificada de la expresión dada es x = -28.

Dado que, para determinar la solución simplificada de la expresión  3(x-8)+4x=8x+4    

Step-by-step explanation:

What is simplification?

El proceso en matemáticas para operar e interpretar la función para hacer que la función o expresión sea simple o más comprensible se llama simplificación y el proceso se llama simplificación

Aquí,

3(x-8)+4x=8x+4

3x - 24 + 4x - 8x = 4

-x = 4 + 24

-x = 28

Given :-

To find :-

Solution :-

On writing equations mathematically ,

\(\red{\longrightarrow}\) x(5 + k) = 3

\(\red{\longrightarrow}\) x(3 - k) = 1

Divide these both equations ,

\(\red{\longrightarrow}\) 5 + k/ 3 -k = 3/1

Cross multiply ,

\(\red{\longrightarrow}\) 5 + k = 3(3 - k)

\(\red{\longrightarrow}\) 5 + k = 9 - 3k

\(\red{\longrightarrow}\) 4k = 4

\(\red{\longrightarrow}\) k = 4/4

\(\red{\longrightarrow}\) k = 1

On substituting the value of k ,

\(\red{\longrightarrow}\) x = 3/(5 + k)

\(\red{\longrightarrow}\) x = 3/ 5+1

\(\red{\longrightarrow}\) x = 3/6

\(\red{\longrightarrow}\) x = 1/2 = 0.5

Hence the required answer is 1/2.

Answer:

B. X= 5 + 3i

5 + 3i

Step-by-step explanation:

We are given the quadratic equation

x² - 10x = -34

x² - 10x + 34 = 0

Using Almighty formula

x = -b ± √b² - 4ac/2a

When given equation: ax² + bx + c

Where: a = 1, b = -10 , c = 34

x = -10 ± √-10² - 4 × 1 × 34/2 × 1

x = 10 ± √100 - 136/2

x = 10 ± √-36 /2

x = 10/2 ±. √-36/2

x = 5 ± 6i /2

x = 5 ± 3i

Hence: the roots of the equation are:

x = 5 - 3i , x = 5 + 3i

Answer:

Step-by-step explanation

The tens digit of a certain two-digit number is 1/3 of the units digit. When the digits are reversed, the new number exceeds twice the original number by 2 more than the sum of the digits. Find the original number.

The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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The two tangent theorem can be used to find the required equations and  the lengths of the of the segments and tangents as follows;

4. 6x - 16 = 4x - 10

5. x = 13

6. 10y - 3 = 7y + 21

7. y = 8

8. GK = 139
9. GZ = 77

10. ZL = 62

The two tangent theorem states that intersecting tangent segments from the point of the intersection to the circle are congruent.

The two tangent theorem indicates;

PZ = GZ, and ZK = ZL

Therefore;

4. An equation that can be used to solve for x can be obtained from the equation formed using the two tangent theorem and plugging in the value of ZK and ZL in the equation; ZK = ZL

The equation is therefore; 6·x - 16 = 4·x + 10

5. 6·x - 16 = 4·x + 10

6·x - 4·x = 10 + 16 = 26

2·x = 26

x = 13

6. The equation that can be used to solve for y can be obtained from the equation PZ = GZ, by plugging in the values of PZ and GZ in the equation as follows;

10·y - 3 = 7·y + 21

7. 10·y - 3 = 7·y + 21

10·y - 7·y = 21 + 3 = 24

3·y = 24

y = 24/3 = 8

y = 8

8. GK = GZ + ZK

Therefore; GK = 7·y + 21 + 6·x - 16

GK = 7 × 8 + 21 + 6 × 13 - 16 = 139

GK = 139

9. GZ = 7·y + 21 = 7 × 8 + 21 = 77

GZ = 77

10. ZL = 4·x + 10

Therefore; ZL = 4 × 13 + 10 = 62

ZL = 62

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Answer:

B= 2

Step-by-step explanation:

At the water slides, there are a total of 37 temporary employees and 37 permanent employees. To determine the percentage of employees who are temporary,  50% of the employees at the water slides are temporary employees.

The total number of employees at the water slides is the sum of temporary and permanent employees: 37 temporary + 37 permanent = 74 employees.
To find the percentage of temporary employees, we divide the number of temporary employees by the total number of employees and multiply by 100:
Percentage of temporary employees = (Number of temporary employees / Total number of employees) * 100
Plugging in the values:
Percentage of temporary employees = (37 / 74) * 100
Calculating this expression gives us:
Percentage of temporary employees = 0.5 * 100 = 50%
Therefore, 50% of the employees at the water slides are temporary employees.

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Answer:

C)  started the practice and concept of microloans

Step-by-step explanation:

E d g e n u i t y 2020

The Grameen Bank of Bangladesh started the practice and concept of microloans.

Grameen Bank is a microfinance organisation and community development bank founded in Bangladesh.

The Grameen Bank of Bangladesh started the practice and concept of microloans, which are small loans given to individuals or groups, typically in developing countries, to help them start or expand small businesses.

The Grameen Bank is known for its focus on providing these loans to women, who are often excluded from traditional banking systems.

The bank has been widely praised for its success in reducing poverty and empowering women, and its model has been replicated in many other countries.

Hence, the Grameen Bank of Bangladesh started the practice and concept of microloans.

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The surface area of the pyramid is 72 m².

What is a pyramid?

A pyramid is a three-dimensional geometric shape that consists of a base polygon and a point called the apex. The base can be any polygon, such as a triangle, square, rectangle, or polygon with many sides, and the apex is directly above the center of the base. The height of the pyramid is the perpendicular distance from the apex to the base.

The rectangular pyramid has a rectangular base with dimensions 4 meters by 4 meters, and four triangular faces with a height of 7 meters. The area of the rectangular base is 4 * 4 = 16 square meters. Each of the triangular faces has a base of 4 meters and a height of 7 meters, so each face has an area of 1/2 * 4 * 7 = 14 square meters. Therefore, the total surface area of the pyramid is the sum of the area of the base and the four triangular faces, which is 16 + 4 * 14 = 72 square meters.

So the surface area of the pyramid is 72 m².

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Answer: Each person has 2 legs and each dog has 4 legs. So, the total number of legs is 2X + 4Y. We know that the total number of legs is 38. Therefore, we can write the equation:

2X + 4Y = 38

To solve for X and Y, we need another equation. We know that the total number of people and dogs in the park is X + Y. But we don't know the total number of people and dogs, so we can't use this equation directly. However, we do know that X and Y are both non-negative integers (since you can't have a negative number of people or dogs). So, we can try different values of X and Y until we find a solution that satisfies both equations.

Let's start by trying X = 1 and Y = 0. Plugging these values into the first equation, we get:

2(1) + 4(0) = 2

This is not equal to 38, so this is not the solution. Let's try X = 0 and Y = 1:

2(0) + 4(1) = 4

This is also not equal to 38. Let's keep trying different values of X and Y:

X = 1, Y = 1: 2(1) + 4(1) = 6

X = 2, Y = 1: 2(2) + 4(1) = 10

X = 3, Y = 1: 2(3) + 4(1) = 14

X = 4, Y = 1: 2(4) + 4(1) = 18

X = 5, Y = 1: 2(5) + 4(1) = 22

X = 6, Y = 1: 2(6) + 4(1) = 26

X = 7, Y = 1: 2(7) + 4(1) = 30

X = 8, Y = 1: 2(8) + 4(1) = 34

X = 9, Y = 1: 2(9) + 4(1) = 38

We have found a solution! When there are 9 people and 1 dog in the park, there are a total of 38 legs.

The margin of error for the survey, rounded to the nearest tenth, is approximately 4.0% when expressed as a percentage.

To determine the margin of error for a survey at the 95% confidence level, we need to calculate the standard error. The margin of error represents the range within which the true population proportion is likely to fall.

The formula for calculating the standard error is:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 64% (or 0.64) since 64% of the 1350 surveyed residents support the plan.

Plugging in the values:

Standard Error = \(\sqrt{(0.64 * (1 - 0.64)) / 1350)}\)

\(= \sqrt{(0.2304 / 1350)} \\= \sqrt{(0.0001707)}\)

≈ 0.0131

Now, to find the margin of error, we multiply the standard error by the appropriate critical value for a 95% confidence level. The critical value corresponds to the z-score, which is approximately 1.96 for a 95% confidence level.

Margin of Error = z * Standard Error

= 1.96 * 0.0131

≈ 0.0257

Finally, to express the margin of error as a percentage, we divide it by the sample proportion and multiply by 100:

Margin of Error as Percentage = (Margin of Error / Sample Proportion) * 100

= (0.0257 / 0.64) * 100

≈ 4.0%

Therefore, the margin of error for this survey, expressed as a percentage to the nearest tenth, is approximately 4.0%.

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Answer:

Option a. Y=3x

Step-by-step explanation:

Let us use cross multiplication method.

Let the cost of 1 magazine be x.

No. of copies                               Cost

1)50                                                $150

2)1                                                      x

50x=150 x 1               equation(1)

x=150/50

x=$3

Now see equation (1),

150=50x

150=50 x 3

Here let us represent the cost as y and no. of copies as x.

Y=3x

Therefore, a. Y=3x is the right answer.

Thank you!