Which ordered pair is a solution to the system of inequalities y >- 2 x/y 4?.

Using the formula of cubic structure,

a) Surface area of cube = 96 μM²

b) Volume of cube = 64 μM³

c) surface to voulme ratio = 1.5μM⁻¹

Cube Structure :

A cube is a three-dimensional solid shape with six faces. A cube is one of the simplest shapes in three-dimensional space. All six sides of a cube are square, a two-dimensional shape.

A cubic shape is sometimes considered a "cube". A cube can also be viewed as a block with equal length, width, and height. Also, there are 8 vertices and 12 edges, so 3 edges meet at the vertex.

Cube surface area = 6a² square units

where 'a' is a side of the cube

Cube volume = a³cubic units

We have given that

A six sided of each length 4 micrometer shape is known as cube.

that is side of cube (a) = 4 micrometer

Using the above formulae,

(a) Surface area of a cube= 6a²= 6x 4²

=96 μM²

(b)Volume of a cube= a³= 4x4x4=64 μM³

(c)surface to volume ratio is fraction of surface area of cube to the volume of cube .

= 96 μM²/64 μM³ = 1.5μM⁻¹

Larger cells will have decreased surface to volume ratio. It means, its surface area is too small to supply its raw materials to its volume.

Hence, the required volume is 64 μM³ and surface area of cube 96 μM².

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The first term of sequence is 120

Sequence is an arrangement of any objects or a set of numbers in a particular order followed by some rule.

A sequence can be defined based on the number of terms i.e. either finite sequence or infinite sequence.

Let the first term of the sequence is x

According to the question ,

The term-to-term rule for a different sequence is divide by 4 then add 6

So , the get the second term x will be divided by 4 and then added by 6

second term = (x/4) + 6 --------(2)

It is given that the second term of the sequence = 36

Using equation (1),

(x/4) + 6 = 36

Multiply by 4 both the sides,

=> x + 24 = 144

=> x = 144 - 24

=> x = 120

Hence , the first term of sequence is 120

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The following statements are TRUE about hypothesis testing ;

hypothesis testing is known as statistical inference type that uses data from a sample to develop inferences about a population parameter or population probability distribution. An educated guess is first made on the parameter or distribution.

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Answer:

-----------------------------

Distribute and regroup:

Substitute values:

Answer:

x = 15  and  y = -2

(x + 3)(y + 3) = 18

Step-by-step explanation:

Given equations:

[tex]\begin{cases}x+y=13\\xy=-30\end{cases}[/tex]

Rewrite the first equation to make y the subject:

[tex]\implies y=13-x[/tex]

Substitute the found expression for y into the second equation and solve for x:

[tex]\begin{aligned}xy&=-30\\y=13-x \implies x(13-x)&=-30\\13x-x^2&=-30\\-x^2+13x+30&=0\\x^2-13x-30&=0\\x^2+2x-15x-30&=0\\x(x+2)-15(x+2)&=0\\(x-15)(x+2)&=0\\\\\implies x-15&=0 \implies x=15\\\implies x+2&=0 \implies x=-2\end{aligned}[/tex]

[tex]\textsf{When}\;x=15 \implies y=-2[/tex]

[tex]\textsf{When}\;x=-2 \implies y=15[/tex]

As x > y then:

Substitute the found values of x and y into the equation:

[tex]\begin{aligned}\implies (x+3)(y+3)&=(15+3)(-2+3)\\&=18 \cdot 1\\&=18\end{aligned}[/tex]

Answer:

see explanation

Step-by-step explanation:

(i)

substitute x = g(x) into f(x) , that is

f(g(x))

= f(x² + 5)

= 2(x² + 5) - 1

= 2x² + 10 - 1

= 2x² + 9

--------------------------------------

(ii)

substitute x = f(x) into g(x) , that is

g(f(x))

= g(2x - 1)

= (2x - 1)² + 5 ← expand factor using FOIL

= 4x² - 4x + 1 + 5

= 4x² - 4x + 6

Answer:

The angle measurements will be the same, but the side length will be proportional to the original image but will be 3/2 times the length of the original sides.  

Step-by-step explanation:

In the calculation where Stan wants to make 60 cookies, then as per the given information, he will need 960 sprinkles to prepare the required number of cookies.

It has been given that the recipe for cookie by Stan requires 384 sprinkles for making 24 cookies. The calculation for the sprinkles required for making one cookie as per the given information will be

384/24 = 16 sprinkles per cookie

Stan wants to make 60 cookies, so the number of sprinkles required will be,

16 x 60 = 960 sprinkles.

Therefore, Stan will need 960 sprinkles to make 60 cookies.

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Complete question

Stan's cookie recipe makes 24 cookies and calls for exactly 384 sprinkles. He is wondering how many sprinkles (p) he will need to make 60 cookies. He assumes each cookie will have the same number of sprinkles.

How many sprinkles does Stan need to make 60 cookies?

The scale factor of B to A is 1/4

The size by which the shape is enlarged or reduced is called as its scale factor. It is used when we need to increase the size of a 2D shape, such as circle, triangle, square, rectangle, etc.

If A is an image and B is another image, scale factor A to B means figure B was enlarged 4 times the size of A.

So if Figure B is 4 times bigger than A, then figure A is 4 times smaller than B. which means if A is 1/4 times as small as B.

In conclusion, the scale factor of B to A is 1/4

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The distance of cheetah could run in 15 seconds is 1050ft.

What is the distance?

Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Here, we have

Given, A cheetah runs 420 feet in 6 seconds.

We have to determine Crystal wants to determine how far a cheetah could run in 15 seconds at this rate.

Speed of cheetah = 420/6ft/sec

= 70ft/sec

In 15 seconds cheetah could run

Distance = 15 × 70ft

= 1050ft

Hence,  the distance of cheetah could run in 15 seconds is 1050ft.

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The mass of the radioactive sample after 5 hours is 1471g.

since we know that an exponential function is the form of y = abˣ, where where x, and y  are the   variables,  b is the multiplier and a is the initial value.Considering y be the mass of sample remaining after x hours. It is given that  the   initial  value  a is  2952g sample, there  is a decay of 13% per hour, so : b = 100% - 13% = 87% = 0.87

substituting the values in  The equation is:

y = 2952(0.87)ˣ,  so After 5 hours:

y = 2952(0.87)⁵ = 1471g

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A biologist has a 2952 -gram sample of a radioactive substance. Find the mass of the sample after five hours if it decreases according to a continuous exponential decay model, at a relative rate of 13% per hour. Do not round any intermediate computations, and round your answer to the nearest tenth.

Using the Central Limit Theorem, the given statements are true or false in following

a) True

b) True

c) True

d)True

e) True

a) From the definition of central limit theorem, by law of large number to sample average converge almost slowly to the population average.

So, based on CLT the sample mean be used a3 gond estimator of the population mean assuing that the sample size. sufficiently large i.e ., True.

b) Same reason as (a) , based on CLT the usually considers that sample 51Z6 30 is sufficiently large is true

c) If we generate 1000 samples of Binomial (10;0.3)distribution are plot a histogram then it looks like normal distribution.

So, the Central Limit Theorem be applied to both discrete and continols Fandom variables is true.

d) Whatever be the parent distribution , if sample size ,n is large then sample mean means

converges in probability to the population mean.

So, the given option (d) is true .

e) If population size is normally distributed then sample mean is also normally distributed for all sample size.

So, option(e) is also true.

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Complete question:

Problem Central Limit Theorem) _ Are the following statements true or false?

a)Easy. Based the Central Limit Theorem_ the sample mean be used a3 gond estimator of the population mean assuing that the sample size. sufficiently large.

b)Easy. Then applying the Central Limit Theorem. l usually conziders that sample 51Z6 30 is sufficiently large.

c)Easy. the Central Limit Theorem be applied to both discrete and continols Fandom variables .

d): Assuming that the sample size is sufficiently large the Central Limit Theorem permits draw conclusions about the population based strictly sample data. and without having aIV knowledge about the distribution of the underlying population:

(e) Moderate_ Assuming that the population is normally distributed_ the sampling distribution of the sample mean is normally distributed for samples of all sizes_

The revolution of the gear having 200 teeth was 500 rpm.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Given that the rotational speed of a driven gear is inversely proportional to the number of teeth on a gear.

T1/T2 = R2/R1

As per the question, the required values as

T1 = 200

T2 = 50

R2 = 2,000 rpm

200/50 = 2,000 /R1

R1 = (2,000 × 50)/200

R1 = 500

Therefore, the revolution of the gear having 200 teeth was 500 rpm.

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The alleles, or genes for a attribute, square measure referred to as the genotype. A phenotypical quantitative relation represents a relationship between the various physical characteristics and the way usually they occur. Ratios square measure usually worn out relationship to one attribute among the people.

Phenotypic quantitative relation pertains to the relative range of offspring manifesting a selected attribute or combination of traits. It will be determined by doing a check cross and characteristic the frequency of a attribute or attribute mixtures that may be expressed supported the genotypes of the offspring.

For example: once a tall plant is crossed to a brief plant, a number of their offspring are tall whereas others are short. to work out the phenotypical quantitative relation, the quantity of times the phenotypes (either tall or short) square measure expressed is counted. during this case, the phenotypical quantitative relation shall indicate several|what percentage|what number} of the offspring are tall and the way many are short supported the genotype.

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115, 540, and 876 are legitimate random samples.

An irregular example is an example that is picked haphazardly. It might be more appropriate to refer to it as a sample chosen at random. In order to avoid bias and other undesirable effects, random samples are used.

Three distinct values between 1 and 1410 will constitute a legitimate random sample. As a result, the first sample cannot be random because 772 are being repeated.

Because 1470 is greater than 1410, the third sample cannot be random.

Because there are four values, the fourth sample cannot be random.

Thus, 115, 540, and 876 are accurate plots.

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The personnel team should not believe that the mean number is ten

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

x = the number of sick days they took for the past year

Also, we have the following representation of the values of x

x = 12; 4; 15; 3; 11; 8; 6; 8

The mean of a set of observations can be calculated using the following equation

Mean = Sum of observations/Count of observations

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

Mean = (12 + 4 + 15 + 3 + 11 + 8 + 6 + 8)/8

Evaluate the sum in the above equation

So, we have the following representation

Mean = 67/8

Evaluate the quotient in the above equation

So, we have the following representation

Mean = 8.375

8.375 does not approximate to 10

So, the mean number is not ten

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The value of c2 is 10

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

1) erode the slope.

2) Decide on the point.

3) In the point-slope form, y y 1 = m (x x 1), substitute the values. y − y 1 = m (x − x 1) .

4) Slope-intercept form should be used to write the equation.

In the above equation, the equation is written in point-slope form

Hence from the above method

m is 4

c2 is 10

Hence the answer is 10

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The time period after which they will cross the start line together is  after 32 minutes as per the given data.

After either has completed a certain number of full laps in the exact same amount of time as the other has finished an integer number of full laps, they will both cross the starting line together.

That time will be the least common multiple (LCM) of their lap times, 128 seconds and 120 seconds.

LCM

LCM(120, 128) = 120×128/GCD(120, 128)

LCM = 120×128/8 = 1920

Converting this to minutes, we get

(1920 s)/(60 s/min) = 32 min

They will next cross the start line together after 32 minutes.

LCM of any two is the value that is evenly divisible by the two given numbers. The full form of LCM is Least Common Multiple. It is also called the Least Common Divisor (LCD). For example, LCM (4, 5) = 20. Here, the LCM 20 is divisible by both 4 and 5 such that 4 and 5 are called the divisors of 20.

It is also used to add or subtract any two fractions when the denominators of the fractions are different. While performing any arithmetic operations such as addition, subtraction with fractions, LCM is used to make the denominators common. This process makes the simplification process easier.

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Answer:


the answer is 3,5 and 7

Step-by-step explanation:

if congruent means identical or technically parallel if you think about it what is on the opposite side of one and that is how you would get the answer of 3,5 and 7 because they are congruent to The Answer 1

Answer:

Step-by-step explanation:

We can expand a binomial to the 6th power by simplifying each of the expansion's terms.

An algebraic expression with two non-zero terms is called a binomial. Binomial expression examples: The binomial with two variables, a and b, is a2 + 2b. A binomial in two variables, x and y, is 5x3 - 9y2. A binomial is a polynomial in algebra that is created by adding two terms, each of which is a monomial. After monomials, it is the most basic type of sparse polynomial.

Given,

We can expand a binomial to the 6th power in following steps:

From the nth row of Pascal's triangle, count the number of terms and their coefficients.

Start with the first phrase that has no b terms and only an an.

With each term of the expansion, a loses power.

With each term of the expansion, b's power grows.

Simplify each of the expansion's terms.

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A number is decreased by 8%, the result is 79. So the original number to the nearest tenth is 85.8.

These are the specified parameters:

a number is decreased by 8%, the result is 79.

Suppose, a number = x

a number - 8% a number = 79

x - 8/100 x = 79

100/100 x - 8/100 x = 79

92/100 x = 79

            x = 79 × 100/92

            x = 7900/92

            x = 85.8

So these numbers are 85.8.

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The probability of getting at least one run of 3 heads in a row be

1021/1024.

Given, a simulation is performed to estimate the probability of getting at least one run of 3 heads in a row in 10 flips of a fair coin.

We have to find the probability of getting at least one run of 3 heads in a row.

Required Probability = 1 - P(X = 0) - P(X = 1) - P(X = 2)

P(X = 0) = P(X = 1) = P(X = 2) = (1/2)^10

Required Probability = 1 - (1/2)^10 - (1/2)^10 - (1/2)^10

Required Probability = 1 - 3/1024

So, the probability of the given event be,

1021/1024

Hence, the probability of getting at least one run of 3 heads in a row be

1021/1024.

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The absolute deviation of the data set 7 10 14 and 20 is 4.25.

What is the mean deviation method?

When calculating the average departure from the mean value of a particular data set, statisticians employ a measure known as the mean deviation. Following the steps below will make it simple to determine the mean deviation of the data values.

In statistics, the term "deviation" refers to the discrepancy between the observed value of a data point and its expected value. As a result, mean deviation, also known as mean absolute deviation, is the typical departure of a data point from the mean, median, or mode of the data collection.

data set is 7, 10, 14, 20,

Mean = m = 51/4 = 12.75

So the MAD is 1/4 |7-12.75| |10-12.75| |14-12.75| 20-12.75|

MAD = 17/4 = 4.25

Hence the mean absolute deviation of the data set 7 10 14 and 20 is 4.25.

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Examples of Linear function are 6x + y = -1; and y = x + 5;

A linear function is the function that consists of one independent variable and one dependent variable without any exponents or powers.

The order of a linear function is always 1.

An example of such an equation can be:

6x + y = -1

Another definition of a linear function is the function that represents a straight line on the graph.

Except y=0; x=0; As y=0 represents the y-axis on the graph while x=0 represents the x-axis on the graph. Any other straight line other that these are known as Linear function.

Example of such a linear function can be:

y = x + 5

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The equation of a line in point slope form is y - y₁ = m(x - x₁) and the equation of a line in slope intercept form is y = mx + b.

The equation of a line can be represented in different form such as point slope form, slope intercept form, general form and standard form.

The equation of a line in point slope form is as follows:

y - y₁ = m(x - x₁)

where

The equation of a line in slope intercept form is as follows:

y = mx + b

where

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Answer:352 square inches

Step-by-step explanation:edge

The rate of change of f(x) = 2(4)^x is equal to the rate of change of the function in the graph. Therefore, the correct answer option is: A. equal to.

Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the value of y with respect to the value of x for the function in the graph, which represents a line that passes through the points (0, 2) and (1, 6):

Rate of change, m = (6 - 2)/(1 - 0)

Rate of change, m = 4/1

Rate of change, m = 4.

From function 1 [f(x) = 2(4)^x], we can logically deduce that the rate of change is equal to 4.

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When the coffee in the cone is 5 inches high, we need to determine how quickly the level in the pot is rising. deep and how quickly is the cone's level falling? Use the equation for the volume of a cone and a cylinder pot. Make use of it to achieve your goals.

We know that a conical filter with "r" as the radius and "h" as the height will have a volume of V conical 1/3 πr²h (2)

The coffee is draining from a conical filter at a rate of dVdt=10in3/min, and the volume of the cylindrical coffeepot will be Vcylindrical=r2h.

The term "rate of change" (ROC) describes the rate at which something changes over time. Therefore, it is not the magnitude of individual changes but rather the acceleration or deceleration of changes (the rate). Rate of change is used in finance to understand price returns and determine trend momentum.

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When we are writing the steps for solution of this. Then , the first step of solution is simplfy the expression using multiplication of outside bracket terms with inside terms .

We have given that

equation , 3(2x + 6) – 4x = 2(5x – 2) + 6

from expression we eaisly seen it ia an linear equation with one variable "x" .

we will solve it step by step using linear operations like substraction, addition , multiple etc .

first step : simplfy the algebaric expression (multiplication)

=> 3 ×2x + 3× 6 - 4x = 2×5x - 2×2 + 6

=> 6x - 18 - 4x = 10x - 4 + 6

Step 2 : subtraction and addition of similar terms (i.e constant with constant and variable x cofficient with varible cofficient) both sides we get ,

=> 2x - 18 = 10x +2

=> 10x - 2x = 18+ 2

=> 8x = 20

finally , divided by 8 both side to get the value of x .

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The graphs only show the sampling distributions of X and Y, and do not provide any information on whether the estimators are biased or unbiased.

Creating, storing, manipulating, and analyzing graphs and graph data is referred to as "graph management." Graphs are a visual representation of data that are frequently used to highlight correlations between various data points or parameters to depict trends and patterns. Graph handling is the use of specialized software and algorithms to generate and edit graphs, as well as to derive insights from the data they represent. This might involve activities like converting raw data into a graph, utilizing filters to emphasize particular trends, or employing mathematical algorithms to look for patterns in the data. Graph manipulation is an important part of data analysis and visualization, and it is used in a variety of fields such as business, science, and engineering.

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6.5 = n This step uses the division property of equality to divide the total number of pounds of raisins and peanuts (8) by the difference in the amounts of raisins and peanuts (1.5)

The link between two or more variables can be shown mathematically in a straight line using linear equations. A linear equation has the following fundamental form: y = mx + b, where m is the slope of the line, x is the independent variable, and b is the y-intercept (the point where the line intersects the y-axis). Since the slope of a linear equation is constant, the values of the variables have no effect on it. This allows for a predictable and consistent relationship between the variables. In many disciplines, including algebra, geometry, physics, and economics, linear equations are employed.

How to solve?

Given: Ms. Jones needs 8 pounds of raisins and peanuts

Step 1: 8 - n = 1.5

This step uses the subtraction property of equality to subtract the unknown number of pounds of peanuts (n) from the total number of pounds of raisins and peanuts (8) in order to determine how much more peanuts there are compared to raisins.

Step 2: 8 - 1.5 = n

This step uses the subtraction property of equality to subtract the difference in the amounts of raisins and peanuts (1.5) from the total number of pounds of raisins and peanuts (8) in order to determine the number of pounds of peanuts.

Step 3: 6.5 = n

This step uses the division property of equality to divide the total number of pounds of raisins and peanuts (8) by the difference in the amounts of raisins and peanuts (1.5) in order to determine the number of pounds of peanuts.

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