12 Work out an expression for the nth term for each sequence.b,20,19.8,19.6,19.4​

By using exponent properties, we will find the equivalent expression:

[(2/3)^4*(2/3)^3]^2 = (2/3)^14

There are two exponent properties that we can use here, these are:

a^x*a^y = a^{x + y}

(a^x)^y = a^{x*y}

Now we have the expression:

[(2/3)^4 (2/3)^3]^2

If we use the first property, we can rewrite the expression as:

[(2/3)^4 (2/3)^3]^2 = [(2/3)^{4 + 3}]^2

[(2/3)^{4 + 3}]^2  =  [(2/3)^7]^2

Now we can use the second property to get:

[(2/3)^7]^2 = (2/3)^{7*2} = (2/3)^14

That is the equivalent expression.

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The values of a2 and a3 that satisfy the sequence [tex]a_{n+1}[/tex] = [tex]\sqrt{a_{n} ^{2} + 3 }[/tex] are [tex]\sqrt{7}[/tex] and [tex]\sqrt{10}[/tex]

What is a sequence?

A sequence is an arrangement of any objects or a set of numbers in a particular order followed by some rule. If a1, a2, a3, a4 etc. denote the terms of a sequence, then 1,2,3,4 denotes the position of the term.

the rule of the sequence is  [tex]a_{n+1}[/tex] = [tex]\sqrt{a_{n} ^{2} + 3 }[/tex] when  n = 1

[tex]a_{2}[/tex]  = [tex]\sqrt{a_{1} ^{2} + 3 }[/tex] but [tex]a_{1}[/tex] = 2

[tex]a_{2}[/tex] =  [tex]\sqrt{(2) ^{2} + 3 }[/tex]

[tex]a_{2}[/tex] = [tex]\sqrt{7}[/tex]

when n = 2

[tex]a_{3}[/tex] =  [tex]\sqrt{a_{2} ^{2} + 3 }[/tex]

[tex]a_{3}[/tex]  =  [tex]\sqrt{a_{2} ^{2} + 3 }[/tex] but [tex]a_{2}[/tex]  = [tex]\sqrt{7}[/tex]

[tex]a_{3}[/tex]  =  [tex]\sqrt{(\sqrt{7}) ^{2} + 3 }[/tex]

[tex]a_{3}[/tex] = [tex]\sqrt{7 + 3}[/tex]

[tex]a_{3}[/tex] = [tex]\sqrt{10}[/tex]

In conclusion [tex]a_{2}[/tex] and [tex]a_{3}[/tex] are [tex]\sqrt{7}[/tex] and [tex]\sqrt{10}[/tex] respectively.

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A minimum of 68% is the expected percentage in a normal distribution and 60% is lower than what is expected.

What is the standard deviation?

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

The given data is:

{8, 12, 27, 32, 45, 57, 61, 73, 82, 94}

Now find the mean of the given data would be

Mean = sum of all points/n

         = 491/10

         = 49.1

Standard deviation(s) = [tex]\sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]

Standard deviation(s) = 29.31988

Considering one standard deviation from the mean, the lower and upper limits are given by the following

[49.1-29.31988, 49.1+29.31988}

=[19.78012, 78.41988]

We can see that only 6 {27,32,45,57,61,73} out of the 10 points, which is 60%, confine to the interval of one standard deviation from the mean.

Hence, a minimum of 68% is the expected percentage in a normal distribution and 60% is lower than what is expected.

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Volume of sphere is 4186.67 ft³ with a radius 10 ft.

The capacity of a sphere is its volume. It is the area that the sphere occupies. Cubic measurements of a sphere's volume include m3, cm3, in3, etc. The sphere has a round, three-dimensional shape. Its shape is determined by three axes: the x, y, and z axes. A sphere's volume is equal to 4/3 r³, where r is the sphere's radius. Using Archimedes' principle, one may determine volume, a fixed quantity. In accordance with Archimedes, the amount of water displaced if a solid sphere is dropped into a container of water will be equal to the volume of the sphere.

Given

Radius of sphere = 10 ft

Volume of sphere

4/3πr³

4/3 × 3.14 × 10³

4/3 × 3.14 × 1000

4/3 × 3140

4186.67 ft³

Volume of sphere is 4186.67 ft³ with a radius 10 ft.

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The inequality that shows how long the temperature in Austin will remain colder than that in San Antonio is 33.5 + 2.5t < 37.5 + 1.5t and the time is less than 4 hours

From the question, we have the following parameters that can be used in our computation:

Austin

Initial temperature = 33.5 degrees Fahrenheit

Rate of increment = 2.5 degrees Fahrenheit

San Antonio

Initial temperature = 37.5 degrees Fahrenheit

Rate of increment = 1.5 degrees Fahrenheit

The above parameters mean that

Current temperature = Initial temperature + Rate of increment x Number of hours

Austin: A(t) = 33.5 + 2.5t

an Antonio: B(t) = 37.5 + 1.5t

When Austin is colder than San Antonio, we have

Substitute the known values in the above equation, so, we have the following representation

33.5 + 2.5t < 37.5 + 1.5t

Divide both sides by 1

t < 4

Hence, the interval is less than 4 hours

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The level of the sand in the box when the box is placed at the largest face will be 3 inches.

Volume is the scalar quantity of any object that specified occupied space in 3D.

Volume has units of cube example meter³,cm³, etc.

The volume of the cube = side³.

The volume of sand when placed on a small face (4 x 12) will be as follows,

Volume = 4 x 12 x (16 - 4) = 4 x 12 x 12

When the box was kept at the largest face (16 x 12) the volume was still the same.

Let's say it goes up to h.

h x 16 x 12 = 4 x 12 x 12

h = 12/4 = 3 inches

Hence "The level of the sand in the box when the box is placed at the largest face will be 3 inches".

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Expressing the probability as a decimal rounded to 4 decimal places the value of p ( z < 0.74 ) is 0.7704.

Given :

for a standard normal distribution, find: p(z < 0.74) express the probability as a decimal rounded to 4 decimal places.

Standard normal distribution :

The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.

Probability :

Probability is a branch of mathematics that deals with the occurrence of a random event.

From z - score table :

the test statistic follows the standard normal distribution N(0,1).

the probability p = 0.7704

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The box plot indicates that the interquartile range (IQR) of the data 0, 25, 50, 75, and 100 is 100.

Find the median (middle value) of the bottom half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3). The IQR represents the variation between Q3 and Q1. We use the median to summarize a typical value rather than the mean when a data collection contains outliers or extreme values. The interquartile range, which is the difference between the first and third quartiles, is a statistic that is frequently used to summarize variability in data sets with outliers.

Here,

The first and third quartiles would need to be located initially. Then, to obtain the IQR, you would divide the third quartile by the first.

IQR, in my opinion, is 100.

The interquartile range (IQR) of the data 0, 25, 50, 75, 100 will be 100 by the given box plot.

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The percentage of occupancy for the month of December is 86.5%.

What is percentage?

Percentage is a fundamental concept in mathematics that describes a portion or proportion of a whole number. It is expressed as a fraction or ratio of two numbers and is typically represented with a percent symbol (%). This concept is frequently used in business, finance, and other fields to compare and analyze data. For example, a company might use a percentage to track the success of a marketing campaign or to compare the amount of sales between two different stores. Percentage can also be used to calculate discounts, taxes, and other types of fees.

Given: Community Hospital December, 20XX

PCU Inpatient Service Days Bed Count Percentage of Occupancy

⇒ Med/Surg 1876, 70 = (1,876 x 100)/ (70 x 31)

= 187,600/ 2,170 = 86.45 = 86.5%

⇒ ICU 300, 10 (300 x 100)/ (10 x 31)

= 30,000/ 310 = 96.77 = 96.8%

⇒ CCU 240, 8 (240 x 100)/ (8 x 31)

= 24,000/ 248 = 96.77 = 96.8%

⇒ Rehabilitation 300, 12 (300 x 100)/ (12 x 31)

= 30,000/372 = 80.6%

⇒ Burn 75, 5 (75 x 100)/ (5 x 31)

= 7,500/ 155 = 48.38 = 48.4%

⇒ Psychiatry 200, 15 (200 x 100)/(15 x 31)

= 20,000/465 = 43.0%

⇒ Pediatric 870, 30 (870 x 100)/ (30 x 31)

= 87,000/ 930 = 93.5%

⇒ Total for patient care 3861, 150 (3,861 x 100)/ (150 x 31)

= 386,100/ 4,650 = 83.0%

⇒ Nursery 280, 10 (280 x 100)/ (910 x 31)

= 28,000/ 310 = 90.3%

For example, Med/Surg has 1,876 inpatient service days and 70 beds in the month of December (31 days). The percentage of occupancy is therefore the inpatient service days multiplied by 100 and divided by the product of the number of beds (70) and the number of days (31) to get 86.5%

⇒ (1,876 x 100)/ (70 x 31)

= 187,600/ 2,170 = 86.45 = 86.5%

Hence, the percentage is 86.5%.

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x/2 + 4 is  an equivalent expression .

What is an expression in maths?

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

                          This mathematical operation may be addition, subtraction, multiplication, or division. An expression's structure is as follows: Number/variable, Math Operator, Number/Variable is an expression.

                            An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases.

= 1/2(X+8)

= x/2 + 8/2

= x/2 + 4

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Answer:

If you need the answer as f by simplifying both sides of the equation and then isolating the variable, the answer would be:

[tex]xf=\frac{3x^2}{5}-\frac{f(x)}{5}[/tex]

Or, if you need to evaluate the function itself, the answer would be:

[tex]f(x)=3x^2-5xf[/tex]

Answer:

6 shirts you can buy and still have $14 dollars for lunch.

Step-by-step explanation:

So let's do 89-14=75. So since we just took out the cost of the lunch it should be a lot easier to solve now.

s=shirts

So 75=12.50s

75/12.50=6

So Corey can buy 6 shirts.

I hope this helps!!!

Answer:

—4—

_x+1_/4x+3

-(4x+4)

———–––

-1

#4x+3/x+1=4-1/x+1

Answer:

Answer in image

Step-by-step explanation:

221643611 ways of 6 numbers can be​ chosen

An arrangement of objects where the order in which the objects are selected does not matter.

Given,

A certain lottery requires players to select 6 different​ numbers in any​ order, from 1 to 53 inclusive.

We need to find different sets of 6 numbers can be​ chosen

Total=53

Numbers=6

The first number can be any of the 53 numbers

The second number can be any of the 53 numbers

The third number can be any of the 53 numbers

The fourth number can be any of the 53 numbers

And so on

Hence, number of selections is:

53×53×53×53×53×53

53⁶

221643611 ways

Hence, 221643611 ways of 6 numbers can be​ chosen

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domain of (f.g)(x) is {x l x ≠ 13} i.e option (c) where f(x) = x+7 and g(x) = 1/(x-13)

Domain of a function is defined as all those values of x that can be substituted in function for which function is defined.

Given: f(x) = x+7

g(x) = 1/(x-13)

First we need to find (f.g)(x) i.e multiplication of  f(x) and g(x)

(f.g)(x) = (x+7) ×1/(x-13) = [tex]\frac{x+7}{x-13}[/tex]

Domain of function is values of x over which function is defined

For (f.g)(x) it is defined at all values of x except when x-13=0 as at this point denominator will be zero and function will become infinite that is not defined.

So,  x - 13 ≠ 0

Adding 13 on both sides, we get

x ≠ 13

So domain of  (f.g)(x) is x∈R - {13} i.e {x | x≠ 13}

Hence, option (c) is correct answer.

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Answer:

6.825 ounces

Step-by-step explanation:

9.75 x 0.3 = 2.925

9.75 - 2.925 = 6.825

point A' is the contracted point of A. The coordinate of point A is (-4,4) and coordinate of point A' is (-2,4) as per the given question and available figure.

The extension or contraction of image or figure based on a scale factor is called dilation. In this way, an image is transformed from one position to another.

Scale factor is defined as the ratio of original image and transformed image.

As stated in the question, the polygon ABCDE is contracted and moved to a shape A'B'C'D'E'. The coordinate of point A is (-4,4) and point A' is (-2,4) as shown in figure. Angle A is equal to angle A' that means the shape of polygon was not changed.

hence, A'B'C'D'E' is the reflected image of ABCDE

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Step-by-step explanation:

greater than 6=0 cause no number on a dice is greater than six

an even number=1/2

less than 4=1/2

Answer:

x= -7

Step-by-step explanation:

the 2 x values are the same so it is an undefined slope so we set this equation x=-7

hopes this helps please mark brainliest

The number whose product of 5 and the difference between a number and 7 is 75 is, 22.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The given statement is The product of 5 and the difference

between a number and 7 is 75.

Let, The unknown number be 'n'.

∴ 5(n - 7) = 75.

Now, 5 will move from the numerator to the denominator.

n - 7 = 75/5.

n - 7 = 15.

Now, we'll move the constant to the other side such that the variable and the constants are on different sides for our further calculation.

n = 15 + 7.

n = 22.

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Answer:

Step-by-step explanation:

First factor the left expression to get

Then cancel out .[tex]\frac{(x+3)(x+2)}{(x+4)(x+2)}*\frac{x+4}{2x}\\ \\\frac{(x+3)}{2x}[/tex]

The x+2 cancel's as well as the x+4's.

Answer: A. 37.5%

Step-by-step explanation:

Technically, you can't even solve this, because you don't know how many athletes got exactly a 3.0 GPA.

Ignoring this major oversight, let's just say that no one received a 3.0 GPA. In that case, there would be 40 - 25 = 15 athletes who received a sub-3.0 GPA.

Therefore, the percentage of student athletes who received a sub-3.0 GPA is 15/40 = 3/8 = 37.5%.

Hence, the least square estimator is obtained when you substitute [tex]y_i[/tex] with [tex]Y_i[/tex] is

[tex]\beta _1=\frac{\sum_{i=1}^{n}x_iY_i}{\sum_{i=1}^{n}x_i^2}[/tex]

What is the line of regression?

A regression line indicates a linear relationship between the dependent variables on the y-axis and the independent variables on the x-axis.

Here given that,

Suppose an investigator has data on the amount of shelf space [tex]x[/tex] devoted to display of a particular product and sales revenue [tex]y[/tex] for that product.

The investigator may wish to fit a model for which the true regression line passes through [tex](0, 0)[/tex]. The appropriate model is [tex]Y=\beta x+E[/tex]

Assume that[tex](x_1, y_1), . . ., (x_n, y_n)[/tex] are observed pairs generated from this model, and derive the least squares estimator of [tex]b_1[/tex].

Here, our motive is to minimize the function

[tex]f(b_1)=[/tex][tex]\sum_{i=1}^{n}(y_i-b_1x_i)^2[/tex]

Now,

[tex]f`(b_1)=0\\\\f`(b_1)=2\sum{i=1}^{n}(y_i-b_1x_i).(-x_i)\\\\[/tex]

So, the least square estimate [tex]b_1[/tex] is

[tex]\sum_{i=1}^{n}x_iy_i=b_1\sum_{i=1}^{n}x_i^2[/tex]

Hence, the least square estimator is obtained when you substitute [tex]y_i[/tex] with [tex]Y_i[/tex] is

[tex]\beta _1=\frac{\sum_{i=1}^{n}x_iY_i}{\sum_{i=1}^{n}x_i^2}[/tex].

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The mean of the temperatures is 29°C, which corresponds to answer B.

For convenience reasons we are going to avoid the use of the Celsius symbol (°C) during the calculations.

[tex]19+22+30+45=116[/tex]

There are 4 values of temperature.

[tex]\frac{116}{4}=29[/tex]

The mean of the temperatures is 29°C, which corresponds to answer B.

The total cost to transport 12 tons of sugar is $9600.

From the information, Sugar Sweet company is going to transport its sugar to the market. It will cost $7500 to rent trucks, and it will cost an additional $175 for each ton of sugar transported.

Let C represent the total cost ( in dollars)

Let s represent the amount of sugar.

The equation to find the total cost to transport 12 tons of sugar will be:

C = 7500 + (175 × s)

C = 7500 + 175s

C = 7500 + (175 × 12)

C = 7500 + 2100

C = 9600

The cost is $9600.

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Answer: Chloe is 12 years old

y + 2.5

y = 9.5

9.5 + 2.5 = 12

To find the height of the column of water in the Fountain Hills fountain, we can use the tangent function and the information given in the problem. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can use the angle of elevation to the top of the fountain, the distance from the surveyor to the base of the fountain, and the height of the column of water to form a right triangle.

We can then use the tangent function to find the height of the column of water as follows:

tan(29.7°) = opposite/adjacent

opposite = tan(29.7°) * adjacent

opposite = tan(29.7°) * 980 feet

opposite = 0.56 * 980 feet

opposite = 548.8 feet

Therefore, the height of the column of water in the Fountain Hills fountain is approximately 549 feet. To the nearest 10 feet, this is 550 feet.