How long will it take 15 machines to complete a task given that it takes 9 days for 5 machines to complete the same task?

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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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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Answer:

Answer in image

Step-by-step explanation:

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:

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]

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 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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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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Answer: 840 ways

Step-by-step explanation:

[tex]\displaystyle\\C_{10}^1*C_9^3=\\\\\frac{10!}{(10-1)!1!} *\frac{9!}{(9-3)!3!}=\\\\\frac{9!10}{9!1} *\frac{6!*7*8*9}{6!*1*2*3}=\\\\10*\frac{7*8*9}{2*3} =\\\\10*84=\\\\840\ ways[/tex]

Answer: 840 ways

mark me BRAINLIEST

Step-by-step explanation:

a) The linear function that best represents the red line is given as follows: y = -4x + 4.

b) The linear function that best represents the blue line is given as follows: y = x - 2.

c) Two coordinates of the red line are given as follows: (0,4) and (1,0).

d) The coordinates of the blue line are given as follows: (0,-2) and (2,0).

The slope-intercept definition used to define a linear function from it's graph is given as follows:

y = mx + b.

In which the coefficients are listed as follows:

For the red line, two points are given as follows:

(0,4) and (1,0)

Hence the parameters are of:

Thus the equation is of:

y = -4x + 4.

For the blue line, the equation is of:

y = x - 2.

As:

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The non-real complex number is  [tex]\frac{8}{3} + \sqrt{-\frac{7}{3}}[/tex].

We have,

To find a non-real complex number,

What is not a real number?

Real numbers include rational numbers like positive and negative integers, fractions, and irrational numbers. Now, which numbers are not real numbers? The numbers that are neither rational nor irrational are non-real numbers, like, √-1, 2 + 3i, and -i.

A non-real complex number is an imaginary number containing negative numbers in the root.  

Here,

[tex]\frac{8}{3} + \sqrt{-\frac{7}{3}}[/tex]

In this option, it includes the negative term that is in the root so this is imaginary, therefore, the answer is "Option B".

Hence, the non-real complex number is  [tex]\frac{8}{3} + \sqrt{-\frac{7}{3}}[/tex].

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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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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.

We have "No Solutions" or "Infinite Solutions" case.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the unit cost of Craft paper be x.

let the unit cost of boxes of markers be y.

let the unit cost of glue sticks be z.

So, the system of equations are

2x+ 4y + 5z= 36

6x+ 4y +2 z = 32

3x+ 2y+ z= 16

Now, solving the above three equation we get using Matrix method

All determinants are zero we have "No Solutions" or "Infinite Solutions" case.

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Answer: Chloe is 12 years old

y + 2.5

y = 9.5

9.5 + 2.5 = 12

The value of m in the equation m=-(4+m)+2 is -1.

How are linear equations solved step-by-step?

One of the easiest methods for resolving a system of linear equations is graphing. Simply plot each equation as a line on a graph and identify the point or points where the lines converge to find the value. These equations are simple to graph because they are already expressed in slope-intercept form.

m = -(4+m)+2

m = -4 -m + 2

m = -2 - m

m + m = -2

2m = -2

m = -1

Hence, the value of m in equation m=-(4+m)+2 is -1.

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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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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

Solution set of the equation is -3,-1, and 2 by simplifying the equation we get m³+2m²-5m-6 = 0

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Mathematical algebraic equations typically have one or more variables.

Given equation is: (6/m)+2 = (m+3)(m-1)

multiply with m both sides,

⇒6+2m = m(m²+2m-3)    

⇒m³+2m²-3m = 6+2m

So we get,

m³+2m²-5m-6 = 0

Solving we get, m = -3, m = -1, m = 2 as solution of given equation.

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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 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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Hello, Elyna. ,

The formula would be:

200+200x=b

Step-by-step formula:

1.) x equals hours, whereas b equals bacteria.

2.) There are 24 hours in one day.

3.) 24*5= 120

4.) Connect it.

5.) 200+200(120)= 6.) 24200= 5 bacterium days

Hope I could help.

The required amount of $799.90 will reduce the amount by $842.

Given that,
The amount will reduce the amount due on an invoice of $ 9410.25 by $ 842 if the terms of the invoice are 5/10, n/30 and the payment was made during the discount period is to be determined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
For 5/10  and n /30
The discount would be 5% if paid in the 30-day span,
Amount = amount invoiced [1 - 5%/100]
Amount = $842[0.95]
Amount = $799.9

Thus, the required amount of $799.90 will reduce the amount by $842.

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Answer:

Below

Step-by-step explanation:

See image below:

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%.

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:

Step-by-step explanation:

The total tax Kala paid on the CDs was $1.30/CD * 6 CDs = $1.3*6=7.80.The total cost of the CDs before tax was $97.20 - $7.80 = $97.2-7.8=89.40.The price of each CD before tax was $89.40 / 6 CDs = $89.4/6=14.90/CD. Answer: 14.90.

Answer:

6.825 ounces

Step-by-step explanation:

9.75 x 0.3 = 2.925

9.75 - 2.925 = 6.825