1, 6, 36, 216, 1296...

Write the recursive form of the sequence above.

The required two other expression are d + 49d/100 and 149d/100.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

We have;

An art teacher enlarged the area of a copy of a painting by 49%. and d represent the area of the original painting.

Given expression is d+ 0.49d

New expressions are

1) d+ 0.49d

= d + 49d/100

2) d+ 0.49d

= d + 49d/100

= 149d/100

Thus, required two other expression are d + 49d/100 and 149d/100.

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The first 10 Pythagorean triples are: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), and (16, 63, 65).

Pythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The first 10 Pythagorean triples, listed in ascending order of their hypotenuse lengths, are (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), and (16, 63, 65). There are infinitely many Pythagorean triples, and they have important applications in mathematics, physics, and engineering.

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Using the concept of proportions and ratios, 684L of natural oil is required to produce 855L of Petrolyn oil.

Proportions are mathematical statements that express the equality of two ratios. A ratio is a comparison of two values, often written as a fraction. For example, if you have 5 apples and 2 bananas, the ratio of apples to bananas can be written as 5/2. A proportion is an equation that sets two ratios equal to each other, such as:

a/b = c/d

In this problem, we need to find the ratio or simply equate and calculate how many liters of natural oil are needed

4L of natural oil = 5L of synthetic oil

xL of natural oil = 855L

cross multiply both sides and solve for x

x = (855 * 4) / 5

x = 684L

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Answer:

Step-by-step explanation:

There are 12 months in a year, and 7 of them have more than 5 letters in their names (July, August, September, October, November, December, and January).

The complement of the event is drawing a month with 5 or fewer letters in its name. There are 5 months with 5 letters in their names (May, March, April, June, and August), and 2 months with 4 letters in their names (July and June). Therefore, there are 7 months with 5 or fewer letters in their names.

The probability of drawing a month with 5 or fewer letters in its name is 7/12. The probability of the complement of the event (drawing a month with more than 5 letters in its name) is 1 - 7/12 = 5/12.

Therefore, the probability of the complement of the event is 5/12.

If yall ain't gotta show work just put 5/12 that's the answer the person with the long paragraph

Answer:7/12

Step-by-step explanation:

1/3 = 4/12

1/4=3/12

3/12+4/12 = 7/12

7/12 is the answer

The value of 6½ - 1⅓ is 5 ⅙

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

To solve 6½ - 1⅓ ;

we make the mixed fraction improper fraction

= 13/2 - 4/3

= (39-8)/6

= 31/6

= 5 1/6

therefore The value of 6½ - 1⅓ = 5 1/6

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Step-by-step explanation:

[tex]6 \frac{1}{2} - 1\frac{1}{3} = 5 \frac{1}{6} [/tex]

Answer:y=-5x+6

Step-by-step explanation:

The 59th term of the given arithmetic sequence, is -496

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called the common difference of that arithmetic progression.

Given that, an arithmetic sequence 26, 17, 8, we are asked to find the 59th term,

nth term of an arithmetic sequence, is given by :-

aₙ = a₁+(n-1)d

Where n is the asked term, d is the common difference,

Here d = 17-26 = 8-17 = -9

Therefore,

a₅₉ = a₁+(59-1)(-9)

a₅₉ = 26+58×(-9)

a₅₉ = -496

Hence, the 59th term of the given arithmetic sequence, is -496

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Answer:

Grace can expect to rent an apartment with a size of approximately 710.32 square feet for $1,500 per month based on the given linear regression equation.

Step-by-step explanation:

The given linear regression equation is y=0.775x+950.25, where x represents the square footage of the apartment and y represents the monthly rental price. To find the size of the apartment Grace can expect to rent for $1,500 per month, we can substitute y with 1,500 in the equation and solve for x:

1,500 = 0.775x + 950.25

0.775x = 1,500 - 950.25

0.775x = 549.75

x = 710.32

Therefore, Grace can expect to rent an apartment with a size of approximately 710.32 square feet for $1,500 per month based on the given linear regression equation.

Answer:

  a = 1/2

Step-by-step explanation:

You want the solution to 3 +0.5(4a +8) = 9 −2a.

It usually works well to start by simplifying the equation. That is, you eliminate parentheses, combine like terms.

  3 +0.5(4a) +0.5(8) = 9 -2a

  3 + 2a +4 = 9 -2a

  7 +4a = 9 . . . . . . . . . add 2a

  4a = 2 . . . . . . . . . subtract 7

  a = 0.5 . . . . . . divide by 4

The value of a is 1/2.

__

Additional comment

The attached calculator output shows this value of 'a' satisfies the equation.

Answer:

Slope: [tex]\bf \boxed{-\dfrac{1}{3}}[/tex]

y-intercept: [tex]\boxed{-1}[/tex]

Equation: [tex]\boxed{\bf{y=-\dfrac{1}{3}x - 1}}[/tex]

The two boxes at the bottom are asking you to repeat the above information:

the slope is [tex]\bf \boxed{-\dfrac{1}{3}}[/tex]   the y-intercept is [tex]\boxed{-1}[/tex]

Step-by-step explanation:

Actually, you don't have to graph the equation since the graph is already provided

You have to answer the questions based on the provided graph

To find slope

1. Take any two well=defined points on the graph:

2. Find the difference in y-values between P2 - P1. This called rise

3. Find the corresponding difference in x-values: P2 - P. This is called run

4. The slope is computed as rise/run = - 1/3

To find y-intercept

Just note where the line crosses the y-axis and the y-value corresponding to that would be the y-intercept

This is also the y-value at which x = 0

Looking at the graph we see that the line crosses(intercepts) the y-axis at y = - 1
So y-intercept = - 1

To write the equation

The equation of the line is
y = mx + b

where

m = slope

b = y-intercept

So the equation of this particular line is

[tex]\bf{-\dfrac{1}{3}x - 1}[/tex]

Answer:

36

Step-by-step explanation:

3x+6= 8x-11

3x-8x= -11-6

-5x= -17x

x= 3  2/5

10x+2= 10(3  2/5)+2

         = 34+2

         = 36

" The value of the mean is always greater than the value of the standard deviation" is not a characteristic of the normal distribution

The curve of a normal distribution is known as the bell curve. The curve in statistical analysis represents the occurrence of some particular result as a product of the experiment. The normal curve is always symmetrical. This implies that the results of the trials will produce results near the mean value of the distribution.

Characteristics of a normal distribution involve:

1. The total area beneath the symmetric curve is 1: Since the area under the curve represents the chances of all the experiments; hence the summation must be 1.

2. The two tails of the curve extend indefinitely: The tails of the normal distribution never touch the horizontal axis; it is extended indefinitely.

4. The curve is symmetric about the mean: In a normal curve, the mean value of the distribution lies in the centre dividing the distribution curve into two symmetric parts.

Not a characteristic of a normal curve:

3. The value of the mean is always greater than the value of the standard deviation. The mean of the data can be negative as well as positive, but the value of the standard deviation is always positive. The small value of standard deviation implies the presence of more clustered data around the mean. The large value of the standard deviation indicates that the data is more spread out.

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Answer:

Step-by-step explanation:

First, we'll write the cost equations for each house, using the number of months since the initial purchase as the independent variable X:

For the house on Main Street:

Cost = 900X + 10,000

For the house on Empire Road:

Cost = 1050X + 4000

Next, we'll find the rate of change for each house by finding the slope of the respective cost equation:

The slope of the cost equation for the house on Main Street is 900. This means that for every month that passes, the cost of the house will increase by $900.

The slope of the cost equation for the house on Empire Road is 1050. This means that for every month that passes, the cost of the house will increase by $1050.

Now that we have found the rate of change for each house, we can compare them to determine which house has the greater rate of change:

Since the slope of the cost equation for the house on Empire Road is greater than the slope of the cost equation for the house on Main Street (1050 > 900), the house on Empire Road has a greater rate of change.

Finally, we can compare the initial values of each house by comparing the y-intercepts of the respective cost equations:

The y-intercept of the cost equation for the house on Main Street is 10,000, which means that the initial cost of the house is $10,000.

The y-intercept of the cost equation for the house on Empire Road is 4000, which means that the initial cost of the house is $4,000.

Since the y-intercept of the cost equation for the house on Main Street is greater than the y-intercept of the cost equation for the house on Empire Road (10,000 > 4,000), the house on Main Street has a greater initial value.

$15 is the interest on the amount saved in a year

The formula for calculating simple interest is expressed according to the equation below:

I = PRT

where:

P is the principal = $300

R is the rate = 5% = 0.05

T is the time = 1 year

Substitute to have:

I = 300 * 0.05 * 1

I = $15

Hence the interest that she will earn in a year is $15

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The algebraic expression is 2x - 5 > 6

The given equation can be written in a verbal phrase as:

"Twice a number, decreased by five, is equal to a number greater than negative six."

When represented as an expression, we have

Hence, the expression is 2x - 5 > 6

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The exact value of a trig function can be found by using the unit circle, the trigonometric identities, tables or a calculator.

To find the exact value of a trigonometric function, there are several methods you can use. Below are a few:

1. Using the Unit Circle: The unit circle is a circle with radius 1 centered at the origin in the coordinate plane. The angles in the unit circle are measured in radians and the coordinates of points on the circle can be used to find the exact values of trigonometric functions. For example, given an angle θ in the unit circle, the x-coordinate of the point on the circle corresponding to θ is cos(θ) and the y-coordinate is sin(θ).

2. Using the Trigonometric Identities: There are several trigonometric identities that relate the values of the six trigonometric functions to one another. These identities can be used to find the exact value of a trigonometric function for certain angles. For example, the Pythagorean identity states that for any angle θ, sin²(θ) + cos²(θ) = 1.

3. Using Tables or a Calculator: Trigonometric tables or a scientific calculator can be used to find the exact values of trigonometric functions for certain angles. The values are often given in degrees, so it is important to convert the angle to radians if necessary.

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Answer:

Below

Step-by-step explanation:

Put ' - 3' into the equation where 'x' is and compute

6 ( 2(-3)^2 -5) =

6 ( 2*9   -5)

6 ( 18-5)

6(13) = 78

Answer: To graph the system of linear equations, you can plot the two lines on the same coordinate plane and look for the point where they intersect. If they intersect, that point represents the solution to the system.

The equation y = x - 6 can be written in slope-intercept form, y = mx + b, where m = 1 and b = -6. The equation of the line will be y = x - 6.

The equation y = -x - 2 can be written in slope-intercept form, y = mx + b, where m = -1 and b = -2. The equation of the line will be y = -x - 2.

Plotting these two lines on the same coordinate plane, we can see that they intersect at the point (2, -4). This means that there is one solution to the system of equations: (2, -4).

Step-by-step explanation:

Answer:

Step-by-step explanation:

$\frac{456.232}{4}$

Answer 15489 Rupees

Step-by-step explanation:

Total parts= 7+2=9 parts

total salary= 9x
taken salary for car repair= 2x/7
remaining salary= 15000 rupees

9x-2x/7= 15000
(63x-2x)/7=15000
61x/7=15000

61x=105000
x= 105000/61
x= 1721(approx)

Total salary= 9x
                   = 9*1721
                   =15489 rupees


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Answer:

b

Step-by-step explanation:

T2÷T1=r and T3÷T2=r and T4÷T3=r

The expanded form of 916.408 can be written as:

(9 x 100) + (1 x 10) + (6 x 1) + (4 x 0.1) + (8 x 0.01)

Expanded form is a way of writing a number that shows the place value of each digit in the number. In expanded form, a number is expressed as the sum of individual terms, each representing a digit in the number multiplied by its place value.

For example, the number 356 can be written in expanded form as:

3 x 100 + 5 x 10 + 6 x 1

Expanded form can be used to better understand the structure of numbers and how place value works.

So, the numbers should be placed as follows:

(9 x 1,000) + (1 x 100) + (6 x 10) + (4 x 1) + (8 x 0.1)

Therefore, the correct order is:

1000, 100, 10, 1, 0.1

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If we substitute so every tiny proportion with 0, 1, or 12, the approximate distinction among 7/8 and 6/11 is then equal to 0.

the end result of subtracting two numbers. the difference between two numbers. Example: Subtract five to get the difference between eight and three.

We can substitute each percentage with either a 0, 1, or 12 to calculate the difference between 7/8 and 6/11.

We can round up to one because we know that 7/8 is larger than 1/2 but much less over 1.

For 6/11, we can round up to 1 since we know it is larger than 1/2 but a little less than 1.

As a result, we can calculate the difference as follows:

7/8 - 6/11

= 1 - 1

= 0

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Answer:It is 45

Step-by-step explanation:Take 1,530 and divid it by 34 using a calculator.

The expression used to find the surface area of the rectangular prism is given as follows:

S = 2 x (1/2 x 3 x 4) + 4 x 2 + 3 x 2 + 5 x 2.

The prism is composed as follows:

The area of each component is given as follows:

The surface area is given by the addition of all these areas.

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Based on the simulation, we can say that, 95% of proportion of the 95 percent confidence intervals capture the population proportion of 0.3.

Confidence interval in statistics is defined as the certain range of values that you estimate for the unknown parameter lies within.

This means that, if you do your experiment more than once and do resampling, then this is the percentage that the parameters falls within a range.

If we say that the confidence interval is A% for a certain parameter like proportion, mean, standard deviation, etc. to be fall within a range of x and y, then this can be interpreted as that we are A% confident that the parameters fall within x and y.

In other words, A% of the intervals capture the parameters.

Therefore, here, we can say that, 95% of the 95% confidence intervals will capture the population proportion of 0.3.

Hence 95% of proportion of the 95 percent confidence intervals capture the given proportion.

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Answer:

Step-by-step explanation:

Given the radius of the base of the cone is 5 cm and the height of the cone is 12 cm, we can find the volume of the toy as follows:

Volume of the cone:

The volume of a cone can be found using the formula: V = (π * r^2 * h) / 3, where r is the radius and h is the height of the cone.

Plugging in the values, we get:

V = (π * 5^2 * 12) / 3 = 100π cm^3

Volume of the hemisphere:

The volume of a hemisphere can be found using the formula: V = (4/3) * π * r^3, where r is the radius of the hemisphere.

Plugging in the values, we get:

V = (4/3) * π * 5^3 = (4/3) * π * 125 = 500π / 3 cm^3

Total volume of the toy:

The total volume of the toy is equal to the sum of the volume of the cone and the volume of the hemisphere:

V = 100π + 500π / 3 = (100 + 500 / 3) * π = 600π / 3 cm^3

So, the total volume of the toy is 600π / 3 cubic centimeters.

The height of the cylinder having a volume of 471 cubic centimetres will be 6 cm. The correct option is D.

The volume of the cylinder is defined as the three-dimensional space occupied by the cylinder.

We can use the formula for the volume of a cylinder, which is given:

V = πr²h

Where V is the volume, r is the radius, and h is the height of the cylinder.

We are given that the cylinder is full at 471 cubic centimetres and that the radius is 5 centimetres. Therefore, we can plug in these values into the formula and solve for h:

471 = π(5²)h

471 = 25πh

h = 471 / (25π)

h ≈ 6 centimeters

Therefore, the height of the cylinder is approximately 6 centimetres.

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