A rectangular swimming pool with a length of 18m and width of 8m is surrounded by a concrete patio. The patio is a uniform 3m width around the entire pool. What is the area of the patio

Answer:

B. 1:4

Step-by-step explanation:

Its B

your welcome :)

The following system of equations models this scenario;

A set or group of equations that you solve all at once is referred to as a "system" of equations. The simplest linear system consists of two equations & two variables.

Linear equations (those that graph like straight lines) are easier to understand than non-linear ones.

According to the question,

The art museum had a total of 224 visitors on Tuesday.

Let 'x' be the visitors who are older than 18 years.

Let 'y' be the visitors who are younger than 18 years.

Then, total visitors are;

x + y = 224

Now,

Visitors older than 18 paid $12 for admission.

Total money collected by the older visitors are 12x.

Visitors 18 years or younger paid $8 for admission.

Total money collected by younger visitors are 8y.

Thus, total money collected by all visitors are-

12x + 8y = 2,520.

Therefore, the two set of linear equations are-

x + y = 224 and 12x + 8y = 2,520.

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(b) 5.Let's first express 1 + 2 + ... + n as the sum of an arithmetic series:

1 + 2 + ... + n = n(n+1)/2

Now, we need to find the positive integers n for which 6n is divisible by n(n+1)/2, or equivalently, for which n+1 is divisible by 3.

If n+1 is divisible by 3, then either n+1 = 3, 6, 9, ... or n+1 = 4, 7, 10, .... The first case gives n = 2, 5, 8, ... and the second case gives n = 3, 6, 9, ....

Thus, there are 5 possible values of n: 2, 3, 5, 6, and 9.

An arithmetic series is a sequence of numbers where each term is obtained by adding a constant value to the previous term. This constant value is called the common difference. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic series with a common difference of 3. The formula for the nth term of an arithmetic series is: a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the position of the term in the sequence, and d is the common difference. The sum of the first n terms of an arithmetic series can be calculated using the formula: S_n = n/2(a_1 + a_n).

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The overall heat transfer coefficient (U) represents the combined effect of the individual resistances to heat transfer and depends on the design and operating conditions of the heat exchanger.

The concentric tube heat exchanger with a hot stream having a specific heat capacity of cH = 2.5 kJ/kg.K.

A concentric tube heat exchanger, hot and cold fluids flow in separate tubes, with heat transfer occurring through the tube walls. The parallel flow mode means that the hot and cold fluids flow in the same direction.

To analyze the heat exchange in the heat exchanger, we need additional information such as the mass flow rates, inlet temperatures, outlet temperatures, and the overall heat transfer coefficient (U) of the heat exchanger.

With these parameters, the heat transfer rate using the formula:

Q = mH × cH × (TH-in - TH-out) = mC × cC × (TC-out - TC-in)

where:

Q is the heat transfer rate.

mH and mC are the mass flow rates of the hot and cold fluids, respectively.

cH and cC are the specific heat capacities of the hot and cold fluids, respectively.

TH-in and TH-out are the inlet and outlet temperatures of the hot fluid, respectively.

TC-in and TC-out are the inlet and outlet temperatures of the cold fluid, respectively.

Complete answer:

A concentric tube heat exchanger is built and operated as shown in Figure 1. The hot stream is a heat transfer fluid with specific heat capacity cH= 2.5 kJ/kg.K ...

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Answer:

7

Step-by-step explanation:

since the whole line is 10 and QR Is a part of the line and is 3. we subtract 3 from 10 to get our answer which is 7.

At a significance level of 5%, with a sample size of 800 items produced on a new machine and 48 of them being defective, the null hypothesis is that the proportion of defective items is not significantly more than 5%, while the alternative hypothesis is that it is significantly more than 5%. The level of significance is 0.05. Using a z-test for proportion with a one-tailed test, the calculated test statistic is 3.45. Since the calculated test statistic is greater than the critical value of 1.645, we reject the null hypothesis. Therefore, there is enough evidence to get rid of the machine.

Null Hypothesis: p = 0.05

Alternative Hypothesis: p > 0.05

Level of Significance: α = 0.05

Sample Size: n = 800

Number of Defective Items: x = 48

Sample Proportion:P= x/n = 48/800 = 0.06

Since the sample size is large, we can use the normal distribution to approximate the binomial distribution.

Test Statistic: z = (P - p) / sqrt(p * (1 - p) / n)

Under the null hypothesis, the test statistic follows a standard normal distribution.

Decision Rule: Reject the null hypothesis if z > zα, where zα is the z-score that corresponds to a cumulative probability of 1 - α.

From the standard normal distribution table, we have:

zα = 1.645

Computation:

z = (0.06 - 0.05) / sqrt(0.05 * 0.95 / 800) = 1.33

Since z (1.33) is less than zα (1.645), we fail to reject the null hypothesis.

Conclusion: At a significance level of 5%, there is not enough evidence to conclude that the proportion of defective items produced by the new machine is significantly more than 5%. Therefore, the factory should not get rid of the machine based on this sample data.

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The probability that the red die shows a three and the blue die shows a number greater than three is 1/12

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

Red die

Blue die

The sample space of a die is

{1, 2, 3, 4, 5, 6}

using the above as a guide, we have the following:

P(3) = 1/6

P(Greater than 3) = 1/2

So, we have

P = 1/2 * 1/6

Evaluate

P = 1/12

Hence, the probability of a three and and a number greater than three is 1/12

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Answer:

Correct answer is option D) drawing the 6 of clubs or the 6 of spades

Step-by-step explanation:

Given that:

A standard deck of 52 playing cards with 4 suits.

A be the event of drawing a card with 6 from the deck.

B be the event of drawing a black card from the deck.

So, event A will have 4 possibilities i.e. {6 of club, 6 of spade, 6 of diamond, 6 of heart}

And event B will have 26 possibilities {Any card (including 6) from club or spade}

Intersection of two sets is defined as the common elements in the two sets.

As per the explanation of the sets and elements in the sets given above:

If we take intersection it will be:

{6 of club or 6 of spade}

Hence, Correct answer is option D) drawing the 6 of clubs or the 6 of spades

Answer:

drawing the 6 of clubs or the 6 of spades is the right answer

Step-by-step explanation:

9514 1404 393

Answer:

  30 m²

Step-by-step explanation:

The figure can be thought of as a 6 m × 6 m square with a triangle cut off of the corner. That triangle has a base of 6-3 = 3 m, and a height of 6-2 = 4 m. Then the area of the figure is ...

  pen area = square area - triangle area

  pen area = (6 m)² - (1/2)(3 m)(4 m)

  pen area = 36 m² -6 m²

  pen area = 30 m²

__

The formula for the area of a square of side s is ...

  A = s²

The formula for the area of a triangle with base b and height h is ...

  A = (1/2)bh

It is useful to remember these formulas.

Answer:

all of them

Step-by-step explanation:

There are different types of triangles, these would all be scalene triangles.

The total number of candies in the store is 312. It is obtained by using the concept of exponent and power on the given problem.

What is an Exponent?

The number of times a quantity is multiplied by itself is referred to as an exponent or power of the given quantity. For eg: 25, where 5 is an exponent or power of 2 and 2 is called the base of exponent 5. Any quantity raised to the power 0 always returns 1 as result.

Calculation of the total number of candies in the store

(36)2 * 30

Using the properties of an exponent, we have

A number with an exponent of 0 always gives 1

(36)2 * 1

(3)6×2 * 1

312 * 1

312

Thus, the total number of candies in the store is 312.

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Step-by-step explanation:

for x=8,y=4

4=8x-4

8x=4+4

8x=8

x=1

y=8 (8)-4

y=64-4

y=60

for x=0.5, y= -4

-4=8x-4

8x= -4+4

8x=0

x=0

y=8 (0.5)-4

y=4-4

y=0

for x=2,y=-4

-4=8x-4

8x=4-4

8x=0

x=0

y=8 (2)-4

y=16-4

y=12

for x= -4,y=8

8=8x-4

8x=8+4

8x=12

x=1.5

y=8 (-4)-4

y= -32-4

y= -36

\(\large \mathfrak{Solution : }\)

let's find the value of added tax :

The value of added tax (VAT) = ₹ 3277.5

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\(9(x +3) = 3(3x + 6) + 9\)

\(9x + 27 = 9x + 18 + 9\)

\(9x + 27 = 9x + 27\)

The two sides of this equation are exactly the same, so the above equation holds for any value of x , thus we have infinite solution for it.

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Answer:

x ≈ 10.4

Step-by-step explanation:

BD is an angle bisector and divides the opposite side into segments that are proportional to the other two sides , that is

\(\frac{AD}{CD}\) = \(\frac{AB}{BC}\) ( substitute values )

\(\frac{x}{11}\) = \(\frac{18}{19}\) ( cross- multiply )

19x = 11 × 18 = 198 ( divide both sides by 19 )

x ≈ 10.4 ( to the nearest tenth )

In the given list, 3 elements would be checked to find the element 20 using binary search.

Binary search is a search algorithm that divides the search space in half at each step. It is efficient for sorted lists, allowing us to quickly find the desired element.

In the given list [2, 3, 6, 10, 20, 25, 100], the binary search algorithm would start by comparing the middle element, which in this case is 10, with the target element, which is 20. Since the target is greater than 10, we know that the target element must be in the second half of the list.

In the next step, the algorithm would consider the sub-list [20, 25, 100]. Again, it would compare the middle element, which is 25, with the target element. Since the target is less than 25, we know that the target element must be in the first half of this sub-list.

The algorithm would then continue dividing the search space in half until it finds the target element. In this case, it would take a total of 3 steps to find the element 20 using binary search.

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Answer:

it is c

Step-by-step explanation:

because I said it is

Answer:

around 15.3

Step-by-step explanation:

3^2 + 15^2=c^2

Answer:

Step-by-step explanation:

Formula:

a^2 + b^2 + c^2

3^2 + 15^2 + c^2 = To find hypotenuse

3 • 3 + 15 • 15 = -c^2

9 + 225 = -c^2

234 = c^2

square root of 234 = 15.2970585408

c = 15.2970585408

The roof is 15.2970585408

To prove two triangles are similar in the given circles need to prove that intercepted arc formed by the pair of angles should be equal or same.

As given in the question,

Two triangles formed in the circle are similar required following steps to prove it correct:

Therefore, to prove the two triangles are similar in the circle need to prove they have same intercepted arc formed by the pair of angles.

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The interest earned during the year will be $104.95 on the investment.

The given interest rate is $6\ 3/4$%. So, the rate in decimal form will be: $$6\ 3/4 \% = \frac{6\ 3}{4} \% = \frac{27}{4}\% = \frac{27}{400}$$. Now, we will use the formula for compound interest, which is: $$ A=P\left(1+\frac{r}{n}\right)^{nt}$$ Where, $A$ = Final Amount P = Principal amount r = annual interest rate n = number of times interest compounded per year t = time in years Now, we will substitute the given values in the formula: $$ A=P\left(1+\frac{r}{n}\right)^{nt}$$ $$  A=1400\left(1+\frac{\frac{27}{400}}{365}\right)^{(365)(1)}$$ $$A=1400\left(1+\frac{27}{400(365)}}\right)^{(365)(1)}$$. Simplify this expression. $$ A=1400\left(\frac{400(365)+27}{400(365)}\right)$$ $$ A=1400\left(\frac{146527}{146000}\right)$$Find the difference between the final amount $A$ and the principal amount $P$ which will give us the interest earned during the year. $$I = A - P $$ $$I = 1400\left(\frac{146527}{146000}\right)-1400$$ $$I = 104.95$$ Therefore, the interest earned during the year will be $104.95$. Hence, option (A) is correct.

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Answer:

y  = -2/3x + 2

Step-by-step explanation:

slope = -2/3

y-intercept is at 2

It has proved that the equation \(e^{(x)} * (dy/dx) = y * e^{(x)} * (dy/dx)\) is linear and the equation \((dy/dx) + x^2 * e^{(x)} * y = e^{(x)}\) is not linear.

The equation \(e^{(x)} * (dy/dx) = y * e^{(x)} * (dy/dx)\) is linear because it can be written in the standard form of a linear first-order ordinary differential equation, which is:
dy/dx + P(x) * y = Q(x)

In this case, we can divide both sides of the equation by \(e^{(x)}\) to obtain:
dy/dx = y * (dy/dx)

Now, we can compare this to the standard form and observe that P(x) = 0 and Q(x) = y * (dy/dx).

Since the equation is in the standard form, it is linear.

On the other hand, the equation \((dy/dx) + x^2 * e^{(x)} * y = e^{(x)}\) is not linear.

While it may seem similar to the standard linear form, the presence of the \(x^2 * e^{(x)} * y\) term is what makes it non-linear.

In a linear equation, the term involving y should be of the form P(x) * y, where P(x) is a function of x only.

However, in this case, the term \(x^2 * e^{(x)} * y\) involves both x and y, making the equation non-linear.

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Answer:

(0,12)

Step-by-step explanation:

substitute!

7x + 2y

6,3

7(6) + 2(3) = 48

4,0

7(4) + 2(0) = 28

3,9

7(3) + 2(9) = 39

0,12

7(0) + 2(12) = 24

this is the smallest, or minimum of these points!

I will use the law of exponent below

⇒if you re multiplying powers of them same base, keep  one base and add the exponents mathematically we say:

\(x^{n} *x^{n} \\=x^{n+n}\)

\(=m^{9+(-3)} \\=m^{9-3} \\=m^{6}\)

OPTION D is the solution

On adding the provided equations, 4x +7y= 17 and 9x + 13y = 46 the resultant equation we will be getting is 13x + 20y = 63.

In order to perform addition of two equations together, we are needed to add the left-hand side of each equation and the right-hand side of each equation separately. This gives us:

(4x + 7y) + (9x + 13y) = 17 + 46

Combining like terms on both the sides, we will be getting ,

13x + 20y = 63

Therefore, from the above calculations this inference can be drawn that the overall equation is calculated to be  13x + 20y = 63.

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The complete question is :

4x +7y= 17

9x + 13y = 46

when these equations are added together, what will the overall equation be? assume that no equations need to be reversed.

Answer:

30241530

Step-by-step explanation:

The length of JK is 42 and the length of KL is 69

From the question, we are to determine the length of JK and KL

From the given information,

JK = 4x + 6

KL = 7x + 15

In the diagram,

JL = JK + KL

120 = 4x + 6 + 7x + 15

120 = 11x + 21

120 - 21 = 11x

99 = 11x

x = 99/11

x = 9

∴ JK = 4x + 6  = 4(9) + 6

JK = 36 + 6

JK = 42

and

KL = 7x + 15 = 7(9) + 6

KL = 63 + 6

KL = 69

Hence, the length of JK is 42 and the length of KL is 69

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Yes, the table contains the solution of the system of equations, and the solution is (7, 6).

Here we have a table that defines a system of equations of the form:

ya = f(x)

yb = f(x)

And a solution of that system is a point of the form:

yb = f(x) = ya

So we wan to find a pair such that for the same value of x, the values of ya and yb are the same ones.

We can see that when x = 6 that happens, then yes, the table has the solution to the system of equations, and the solutions is (6, 7)

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