The length of each side of a metal cube increases at the rate of 0.025cms' when heated. Find the rate of increase in cm²s¯¹ of the total surface area of the cube, when the length of each side is 6cm.
Plssss I really need this submission due tomorrow by 6 am​

The values of x and y are 7 and 6 respectively

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².

Perimeter is the distance around the edge of a shape. Learn how to find the perimeter by adding up the side lengths of various shapes.

The area of a rectangle = l× w

The perimeter of rectangle = 2(l+b)

length = x

breadth = x+y

57 = x(x+y)

44 = 2( x+(x+y)

therefore ;

57 = x²+y. equation 1

44 = 4x + 2y equation 2

from equation 2, y = 22-2x

substitute 22-2x for y in equation 1

57 = x²+22-2x

57 -22= x²-2x

x²-2x -35 = 0

(x²-7x)(+5x -35 )= 0

x( x-7) 5( x-7) = 0

x+5 = 0

x-7 = 0

therefore x = -5 or 7

but we are going to take the positive answer for x

57 = 7²+y

y = 55-49

y = 6

therefore the value of x and y are 7 and 6 respectively

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The tangent function has asymptotes because it is defined as the ratio of the sine and cosine

The tangent function has asymptotes because it is defined as the ratio of the sine and cosine functions:

tan(x) = sin(x) / cos(x)

When the cosine function approaches zero, the denominator of the tangent function becomes very small, and the tangent function grows to infinity or negative infinity. Therefore, the tangent function has vertical asymptotes where the cosine function is equal to zero.

In contrast, the sine and cosine functions do not have vertical asymptotes because they are periodic functions that oscillate between -1 and 1. They do have horizontal asymptotes at positive and negative infinity, but these are not vertical asymptotes.

Note that the tangent function is not defined at the points where the cosine function is equal to zero because the division by zero is undefined. This also contributes to the existence of the vertical asymptotes in the tangent function.

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Answer: Let's call the first term of the arithmetic progression "a" and the common difference "d". Then we can use the following formulas to find the second, fifth, and seventh terms:

- The second term is a + d.

- The fifth term is a + 4d.

- The seventh term is a + 6d.

We are given that the sum of the second and seventh terms is 25:

(a + d) + (a + 6d) = 25

Simplifying this equation, we get:

2a + 7d = 25 ...(1)

We are also given that the fifth term is 15:

a + 4d = 15 ...(2)

Now we can solve for the common difference "d" by using equations (1) and (2) to form a system of two equations in two variables. One way to do this is to solve equation (2) for "a" in terms of "d", and then substitute that expression for "a" into equation (1):

a = 15 - 4d ...(3)

Substituting equation (3) into equation (1), we get:

2(15 - 4d) + 7d = 25

Simplifying this equation, we get:

30 - 8d + 7d = 25

Solving for "d", we get:

d = -5

Therefore, the common difference is -5.

Step-by-step explanation:

Answer:

5 is the answer

Step-by-step explanation:

As a result, Ana chose 7/8 of a pound of apples , while the Martinez family chose 3 1/2 pounds.

Finding a value of a single unit or the ratio of two values, then using this value to determine the value of a bigger or smaller number, is the unitary method, a problem-solving strategy used in mathematics. The unit method, single unit method, and percentage method are additional names for the unitary approach. The unitary method, which can be used to address issues in a number of disciplines including mathematics, algebra, geometry, and physics, entails using a ratio, proportion, or factor. The approach is founded on the proportionality concept, according to which two ratios or quantities are proportional if they have the same ratio or proportion.

given

Three and a half pounds of apples, which can be expressed as a mixed amount or an incorrect fraction, were harvested by the Martinez family:

3 1/2 = 7/2

Ana selected one-fourth of those apples, so the quantity she selected can be calculated by dividing by the total number of apples selected by the Martinez family:

1/4 × 7/2 = (1 × 7)/(4 × 2) = 7/8

As a result, Ana chose 7/8 of a pound of apples , while the Martinez family chose 3 1/2 pounds.

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Answer:

E

Step-by-step explanation:

NO

Answer:

Given as steps.

Step-by-step explanation:

Step 2: Opposite angles of a parallelogram are Equal
Step 4 ( After " Definition of a parallelogram"): Given
Step 5: ASA congruency Property / Therom
Step 6: CPCTC


P.S: It is ASA congruency Therom as both angles are adjacent to the side they are trying to prove.


Hope It Helps!

Therefore , the solution of the given problem of probability comes out to be  the likelihood that they have four girls is 1/15.

The assessment of the probability that a claim is true or that a particular event will happen is the main objective of the constructions inside style known as criteria. Chance can be symbolised by any number between zero and 1, for which 1 typically denotes certainty range and 0 typically denotes possibility. A probability diagram illustrates the likelihood that a particular occurrence will take place. Decimal digits 0, 1, rationals with just 0% and roughly 100%.

Here,

Given that the family has at least one girl, we can use Bayes' theorem to determine the likelihood that they have four girls:

=> P(4 girls | at least one girl) = P(4 girls)

=> Times P(at least one girl | 4 girls) / P. (at least one girl)

Additionally, we are aware that the probability of having at least one female is

=> P(at least one girl = 1 - P(no girls) = 1 - (1/2)4 = 15/16.

The likelihood of not having any females is equal to the likelihood of having four boys,

which is

=>  (1/2)4 = 1/16.

Given that all four of the children are female, the likelihood of producing girls is one.

Combining everything, we have:

=> P(4 females | a girl)

=> 1 * (1/16) / (15/16) = 1/15

Given that the household has at least one girl, the likelihood that they have four girls is 1/15.

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Answer:

-4721613632.87 or -4721613632.9 or -4721613633

Step-by-step explanation:

10x9.2^-13 = 10x-472161363.287 = -4721613632.87 or you can round -4721613632.9 or -4721613633

The strengths and weaknesses of the data will help to identify the areas that need to be improved.

The steps that are to be taken to apply hypothesis tests to the case of Bayview University are given below:Open the dataset of Bayview University and read the case in its entirety at the end of Chapter 9. After opening the dataset of Bayview University, read the case in its entirety at the end of Chapter 9. It is important to read the case carefully in order to understand it properly. This is the first step that is to be taken in order to apply hypothesis tests to the case of Bayview University.

Use descriptive statistics to summarize the data and comment on your findings. Once the case has been read carefully, descriptive statistics are to be used to summarize the data. Descriptive statistics are statistical techniques that are used to describe and summarize the data. They are used to summarize the data in a way that is meaningful and easy to understand. The descriptive statistics will help to identify the central tendency and the variability of the data. After summarizing the data, comments are to be made on the findings. These comments will help to identify the strengths and weaknesses of the data. The strengths and weaknesses of the data will help to identify the areas that need to be improved.

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Answer:

6.25

Step-by-step explanation:

If the company orders 27 boxed lunches from a deli for $245.70 and each boxed lunch costs the same amount then the unit cost of each boxed lunch is $9.1.

This example belongs to a word problem.

What is the unit cost of each boxed lunch?

Given that;

27 boxed lunches from a deli cost $245.70

Cost of 1 box =?

To determine the unit cost of each boxed lunch, we say;

Cost of each box = $245.70 ÷ 27

Cost of each box = $9.1

Hence, if the company orders 27 boxed lunches from a deli for $245.70 and each boxed lunch costs the same amount then the unit cost of each boxed lunch is $9.1

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Answer:

Step-by-step explanation:

variable means we can put any value to it.

the variable is 2x

the constant is +1

The ratios for the similar triangles are given as follows:

Similar triangles are triangles that share these two features listed as follows:

The length of one side of one triangle is 4 times that of the corresponding side of the other, hence the constant of the proportional relationship for the side lengths is given as follows:

k = 4.

The perimeter is measured in units, just like the side lengths, while the area is measured in units squared, hence the ratios are given as follows:

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The difference between the total and the initial contribution, which is: Interest [tex]= $5,409.09 - $5,000, I[/tex] nterest $409.09, is the amount of interest earned. Lupita will have accrued interest of $409.09, rounded to the closest penny, after 48 months.

We can use the compound interest calculation to determine how much money Lupita will receive after 48 months:

Where: [tex]A = P(1 + r/n)(nt)[/tex] A represents the whole sum after t years.

P represents the primary sum.

The yearly interest rate is r.

Given that interest is compounded yearly, [tex]P = $5,000, r = 0.02, n = 1,[/tex]and[tex]t = 48/12 = 4[/tex] (since the time is given in months, we need to convert to years by dividing by 12).

Hence, the equation is: [tex]A = $5,000(1 + 0.02/1)^(1*4)[/tex]

[tex]A = $5,000(1.02)^4\sA ≈ $5,409.09[/tex]

The amount that differs between the total and the original deposit that represents interest earned is: Interest equals [tex]$5,000 - $5,409.09$409.09[/tex] in interest

Lupita will have accrued interest of $409.09, rounded to the closest penny, after 48 months.

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Answer:b

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 mile = 1609 meters

24 miles = 38624 meters

So, Adam drives 38624 meters.

Answer:

Let x be the number of watermelons the farmer needs to sell to earn at least $200.

The amount of money earned from selling x watermelons is 8x dollars.

After paying $50 to rent the booth, the farmer's profit is 8x - 50 dollars.

The problem states that the farmer wants to earn at least $200, so we can set up the following inequality:

8x - 50 ≥ 200

Adding 50 to both sides, we get:

8x ≥ 250

Dividing both sides by 8, we get:

x ≥ 31.25

Since the number of watermelons must be a whole number, the farmer needs to sell at least 32 watermelons to earn at least $200 after paying for the booth.

When selecting the appropriate number of treatment conditions, it is essential to consider factors such as resources, research complexity, and confounding variables.

Having conditions that are proportional to each other means that the level or intensity of each condition varies in direct proportion to the others, such that if one condition is increased or decreased, the others are also adjusted in a corresponding manner.

When choosing the appropriate number of treatment conditions for an experiment, there are several issues to consider. One of these is the ability to distinguish differences between treatment conditions.

Having conditions that are proportional to each other means that the differences between treatment conditions are consistent across all levels of the independent variable. In other words, if the independent variable increases by a certain amount, the difference between the treatment conditions remains constant. This can be important for ensuring that the treatment effects are interpretable and generalizable to other populations.

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Answer:

So the number of girls is 7 times the number of boys. If we want a specific number, we would need to know the total number of students in the class.

Step-by-step explanation:

Let's use algebra to solve the problem:

Let's say the number of boys in the classroom is "b", and the number of girls is "g".

From the problem statement, we know that:

g > b (the number of girls is greater than the number of boys)

g/b = 7/5 (the ratio of girls to boys is 7:5)

We can use the second equation to write g in terms of b:

g/b = 7/5

g = (7/5) * b

Now we can substitute this expression for g into the first equation:

g > b

(7/5) * b > b

Simplifying this inequality:

7b/5 > b

7b > 5b

2b > 0

b > 0

So we know that b is positive.

To find the exact value of b, we can use the fact that the ratio of g to b is 7:5:

g/b = 7/5

(7/5) * b/b = 7/5

7b/5b = 7/5

7/5 = 7/5

This equation is true for any value of b (as long as b is positive), so we don't actually get a unique solution for b. However, we can still make a statement about the relationship between b and g:

g/b = 7/5

g = (7/5) * b

g = (7/5) * 5x

g = 7x

So the number of girls is 7 times the number of boys. If we want a specific number, we would need to know the total number of students in the class.

Answer:

B = (5/7)G where B and G are the numbers of Boys and Girls,

Step-by-step explanation:

The ration of girls to boys is 7/5. If we let G and B represent the numbers of Girls and Boys, we can write:

   G/B = 7/5

The problem dioes not tell us the number of either boys or girls, so we cannot calculate the number of boys, as the question seems to ask.  If the actual number of girls is provided, then we can calculate the number of boys:

  G/B = 7/5

   5G = 7B  [Multiply both sides by 5B]

    7B = 5G and so

              B = (5/7)G

If, for example, there were 14 girls, there would be B = (5/7)*(14) or 5 Boys.

The rate of increase is 1% and the variable x represents when the population will double

The rate of increase is determined by the value of the exponent x. In this case, x represents the number of years that have passed since the population was at its initial value.

The exponent x increases by 1 for each year that passes, indicating that the population is increasing by a factor of 1.01 each year.

Therefore, the rate of increase is 1%, or 0.01 as a decimal.

The variable x represents when the population will double

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Random sampling is the correct answer. Which is option (A).

Sampling refers to a method to select a subset of individuals for the sample from the population so that each has an equal chance of being assigned to the various study conditions is referred to as Random sampling.

What is sampling?

In statistics, sampling is the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population. Sampling is frequently employed in social science research. The method employed to select a subset of individuals for the sample from the population so that each has an equal chance of being assigned to the various study conditions is known as random sampling.

Content-loaded sampling refers to a form of sampling that is more sophisticated than simple random sampling.

In order to form a sample, it involves first determining which variables (or characteristics) are essential to the study, and then choosing people based on those variables, hence the name "content-loaded."On the other hand, in Stratified sampling, the population is divided into subgroups (strata) based on one or more characteristics that are expected to impact the study's outcomes. The proportion of people chosen from each group should reflect the group's percentage of the overall population.

Snowball sampling is a method for selecting a sample of individuals by locating others who share the characteristics being studied and asking them to suggest additional individuals who might participate in the study. Among the given options, (A) random sampling is the correct answer.

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If the volume of the frustum is 2855 cm³ and the value of r  = 28.4

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point called the apex or vertex.

Volume of the = (1/3*п*R²*H) + 1/3*п*r²*h

2855 = 1/3*22/7*10*30 + 1/3*22/7*r²*3

2855 = 314.3 + 66r²/21

2540.7 *21= 66r²

53354.7 = 66r²

r² = 808.4

r √808.4

Therefore the value of r = 28.4

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Answer:

12%

Step-by-step explanation:

147/ 1225 x 100/ 1

0.12 x 100 = 12%

Answer:

Therefore, 147 is 12% of 1225.

The relatiοnship in the given diagram is nοt a functiοn, because fοr each input there is nοt exactly οne οutput. Sο Optiοn A is cοrrect

Functiοn is a relatiοn between a set οf inputs and a set οf οutputs which are permissible. In a functiοn, fοr particular values οf x we will get οnly a single image in y. It is denοted by f(x).

Vertical line test:-

Whenever we want tο check whether a given expressiοn is a functiοn οr nοt we can apply a vertical line test, in this test we check fοr a single image οf x , we are getting a single image οr mοre.

If we get mοre images then it will nοt be a functiοn.

Fοr example, let us take, y² = 4ax

y = ±√4ax

Fοr single value οf x we get twο values οf y

Hence, it will nοt be a functiοn.

Given that,

Values οf x and values οf y

In given diagram,

fοr x = 0,

there are twο values οf y, -4 and -2

but accοrding tο definitiοn οf y, it shοuld give οnly οne value

Hence, it is nοt a functiοn

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In triangle ABC, if AB is parallel to QR and if AP:PB=BR:RC, then PQ is parallel to BC.

Since AB is parallel to QR, we can use the alternate interior angles theorem to conclude that ∠PAB = ∠QBR and ∠PBA = ∠QRB.

Also, since AP:PB=BR:RC, we can let AP=x and PB=y, so that BR=z and RC=w. Then we have:

Cross-multiplying, we get:

Now consider triangles ABP and QBR. By the angle-angle similarity theorem, we have that these triangles are similar. So:

Substituting our values for PB and BR, we get:

Cross-multiplying, we get:

Similarly, considering triangles APC and RCB, we can use the angle-angle similarity theorem to conclude that these triangles are also similar. So:

Substituting our values for RC and RB, we get:

Cross-multiplying, we get:

Now, let's consider the ratio of the lengths of PQ and BC. We have:

Substituting in the values we found earlier for ABz, QBy, ACz, and RBw, we get:

Using the fact that ABz = QBy and ACz = RBw (which we found earlier), we can simplify this expression to:

This means that PQ and BC are parallel, which is what we wanted to prove.

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After dilating the triangle abc about point a by a scale factor of 1/3, the length of new side length of ac' is equals to the 3 units.

Dilation is a transformation used to change the size of an object. Dilation is used to make objects larger or smaller. This transformation produces an image of the same shape as the original. For a scale factor k, the algebraic representation of inflation is (x, y) → (kx, ky). Here we have a triangle abc with side length, ac = 9 units

side length, cb = 9 units

side length, ab = 7 units

remove triangle abc around point a, and

factor dilation scale = 1/3

We need to determine the length of the new side ac'. Dimensions of original shape, ac × scale factor = Dimensions of new shape, ac'

=> length of ac' = 9 units × 1/3

=> length of ac' = 3 units

Hence, required length is 3 units.

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The mean of the given probability distribution is 0.2007.

The probability distribution table for the given scenario can be completed as follows:

| x | P(x) |
|---|------|
| 0 | 0.8036 |
| 1 | 0.1929 |
| 2 | 0.0036 |
| 3 | 0.0000 |

The probabilities are calculated using the hypergeometric distribution formula:

P(x) = (C(N-K, n-x) * C(K, x)) / C(N, n)

Where N is the total number of items (14), K is the number of items that are not correctly calibrated (2), n is the number of items selected (3), and x is the number of items that are not correctly calibrated in the selection.

For x = 0:

P(x) = (C(14-2, 3-0) * C(2, 0)) / C(14, 3) = (C(12, 3) * C(2, 0)) / C(14, 3) = (220 * 1) / 364 = 0.8036

For x = 1:

P(x) = (C(14-2, 3-1) * C(2, 1)) / C(14, 3) = (C(12, 2) * C(2, 1)) / C(14, 3) = (66 * 2) / 364 = 0.1929

For x = 2:

P(x) = (C(14-2, 3-2) * C(2, 2)) / C(14, 3) = (C(12, 1) * C(2, 2)) / C(14, 3) = (12 * 1) / 364 = 0.0036

For x = 3:

P(x) = (C(14-2, 3-3) * C(2, 3)) / C(14, 3) = (C(12, 0) * C(2, 3)) / C(14, 3) = (1 * 0) / 364 = 0.0000

The mean of this probability distribution can be calculated by multiplying each value of x by its corresponding probability and summing the results:

mean = (0 * 0.8036) + (1 * 0.1929) + (2 * 0.0036) + (3 * 0.0000) = 0.2007

Therefore, the mean of this probability distribution is 0.2007.

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Answer:

Part A 4 Part B 20 Part C C

there are total 28 balls. 1 / 7 = 4 balls.

Here some examples of math by using Mr. Maxs life outside the classroom.

One example of math in Mr. Max's life outside the classroom could be calculating the amount of gas needed to fill up his car's tank before a road trip. This involves using basic arithmetic operations such as addition, subtraction, multiplication, and division to calculate the total distance he intends to travel, the fuel efficiency of his car, and the capacity of the fuel tank. By doing so, he can estimate the amount of gas needed for the trip and plan accordingly. Additionally, he may also use math to calculate the cost of the gas based on the current price per gallon or liter, and decide on the most cost-effective way to fill up his tank.

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complete question is:

What is one example of math in Mr. Max's life outside the classroom? 10. Is math everywhere, as Bobby believes? Support your answer with evidence.