How do you simplify \(\frac{\sqrt{2} +\sqrt{6} }{\sqrt{8} + \sqrt{6} }\)?

Answer:

let the width be x

perimeter= 2(l+b)

78= 2(7 +x)

78-14= 2x

32= x

this must be the ans

The integral, when rewritten using the indicated order of integration, is ∫₀¹ ∫₀¹-y² ∫₀¹-x² dz dy dx, and the value of the resulting integral is 2/3.

To rewrite the given integral in the indicated order of integration, we integrate with respect to 'z' first, then 'y', and finally 'x'. The given integral is triple nested, and each integral has specific limits.

integrate with respect to 'z':

∫₀¹ ∫₀¹-y² (z ∣₀¹-x²) dy dx

∫₀¹ ∫₀¹-y² (1-x²) dy dx

integrate with respect to 'y':

∫₀¹ (y ∣₀¹) (1-x²) dx

∫₀¹ (1-x²) dx

(x - x³/3) ∣₀¹

evaluate the result:

(1-1/3) - (0-0) = 2/3

Thus, the integral rewritten and evaluated using the indicated order of integration is 2/3. However, this is not the final answer as we still need to perform one more integration with respect to 'y':

∫₀¹ (2/3) dy = (2/3) * (y ∣₀¹) = 2/3 * (1 - 0) = 2/3

Thus, the final result after evaluating all integrals is 2/3 * 1 = 2/3.

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Answer:

(2,4)

Step-by-step explanation:

Answer:

(2,4)

Step-by-step explanation:

The answer is where the two lines cross

x=2

y=4

Answer:

y=0,25x

Step-by-step explanation:

1×0,25=0,25

2×0,25=0,5

3×0,25=0,75

4×0,25=1,0

5×0,25=1,5

hope it'll help you dude

Firstly, we will need to try the following options one after the other in order to ascertain our answer

The first option

To find the distance between two points

Distance = Higher number - Lower number

-3 - 20

= - 23

This is very wrong because it has a negative sign

The second option

7 - (-16)

In mathematics, - x - = +

7 + 16

7 + 16 = 23

The answer is OPTION B

Answer:

37,440

Step-by-step explanation:

To find volume the formula is : Length x Width x Height... So 30 x 24 x 52 = 37, 440

:D

Answer:

Step-by-step explanation:  1133.5.

The correct answer is (d) all of these. when ls1 is actuated and ls2 is not, all the rungs of the program will be evaluated, and as a result, all the output conditions will be true.

In the given ladder logic program, when ls1 is actuated and ls2 is not, all the rungs of the program will be evaluated from left to right and top to bottom to determine the output conditions.

Looking at the program, we see that if ls1 is actuated, it will turn on the output O:2/5 and set the latch L1. Then, in the second rung, if ls2 is not actuated, it will turn on the output O:2/6 and set the latch L2. Finally, in the third rung, if both ls1 and ls2 are not actuated and both latches L1 and L2 are set, it will turn on the output O:2/7.

Therefore, when ls1 is actuated and ls2 is not, all the rungs of the program will be evaluated, and as a result, all the output conditions will be true. Hence, all of the following statements are true:

a) pilot light pl1 (o:2/5) is on.

b) pilot light pl2 (o:2/6) is on.

c) pilot light pl3 (o:2/7) is on.

Therefore, the correct answer is (d) all of these.

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Using pythagoras' theorem in the right-angled triangle

A right-angled triangle is a polygon with 3 sides in which one angle is a right angle

Now, since we have 3 triangles, using Pythagoras' theorem in all three triangles, we have

h² + (12 - x)² = 12² - 6² (1)

Also, h² + x² = 6²  (2)

So, h² + (12 - x)² = 12² - 6²

h² + (12 - x)² = 144 - 36

h² + (12 - x)² = 108  (3)

From equation (2), h² = 36 - x²

Substituting this into equation (3), we have that

h² + (12 - x)² = 108  (3)

36 - x² + (12 - x)² = 108  (3)

Expanding the brackets, we have that

36 - x² + 144 - 24x + x² = 108

36 + 144 - 24x = 108

180 - 24x = 108

-24x = 108 - 180

-24x = -72

x = -72/-24

x = 3

Since  h² = 36 - x²

h = √(36 - x²)

So, substituting the value of x = 3 into the equation, we have that

h = √(36 - x²)

h = √(36 - 3²)

h = √(36 - 9)

h = √27

h = 3√3

So,

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Answer:

27:8

Step-by-step explanation:

189/56 = 27/8

Answer:

3 / 19

Step-by-step explanation:

Given the following :

ratio of college graduates with a graduate degree to non-college graduates = 1:8

ratio of college graduates without a graduate degree to non-college graduates is 2:3

If college graduate with a degree = A

College graduate without a degree = B

Non-college graduate = C

College graduate to non college graduate = A:C

College graduate without degree to non college graduate = B:C

A:C = 1:8 - - - (1) ; B:C = 2:3 - - - (2)

Combining the two ratios :

To do so : the proportion of non college graduate should be the same in both ratios

To do this, multiply (1) by 3 and (2) by 8

A:C = 3 : 24

B:C = 16 : 24

combining both, we have :

A:B:C = 3:16:24

If one random college graduate is picked, what is the probability that they hold a graduate degree?

Total proportion of college graduate : (college graduates with degree + college graduates without degree)

A + B = (3 + 16) = 19

Proportion who hold a graduate degree = A = 3

Probability = require outcome / Total possible outcomes

Thus :

P = A / (A +B)

= 3/19

Answer: The equation is y = 1.25x

x = number of candy bars

y = total cost

The 1.25 is from the fact that ($2.50)/2 = 1.25

Each bar costs $1.25

The period of the given trigonometric function is: 20.

The distance between the repetition of any function is called the period of the function. For a trigonometric function, the length of one complete cycle is called a period.

Sine and cosine functions start repeating the same pattern of y-axis values after every 2(pi). The period is defined as just the distance on the x-axis before the pattern repeats.

Now, looking at the trigonometric graph, we see that the x-interval for which the graph repeats itself is 20

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Answer:

-3(x - 3) (x + 1)

Step-by-step explanation:

Let's check

-3(x - 3) (x + 1)

(-3x + 9) (x + 1)

-3\(x^{2}\) -3x + 9x + 9

-3\(x^{2}\) + 6x + 9

Answer:

-3(x-3)(x+1)

Step-by-step explanation:

A common factor that all three numbers share is that they are divisible by 3, so we can factor 3 out. Typically, I take out the negative first:

-3(\(x^2-2x-3\)) (always remember to change signs!)

Now, we are left with \(x^2-2x-3\), and to factor that out, we need to find two numbers that add up to -2 and multiply to -3. These two numbers will be 1 and -3, so we can write our factor like this:

(x-3)(x+1)

Let's add back in the -3 from earlier to complete our factoring:

-3(x-3)(x+1)

The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

One general method for determining all the factors of a counting number is by using the prime factorization method.

Here are the steps:

1. Start with the smallest prime number, 2, and divide the number by 2.

2. If the number is divisible by 2, write down 2 as a factor and divide the number by 2 to get a new number.

3. If the new number is still divisible by 2, repeat the process. If not, move on to the next smallest prime number, 3.

4. Continue this process with each prime number until you have fully factored in the original number.

Let's illustrate this method with the number 150:

1. 150 ÷ 2 = 75. So, 2 is a factor and our new number is 75.

2. 75 is not divisible by 2, so we move on to the next smallest prime number, 3.

3. 75 ÷ 3 = 25. So, 3 is a factor and our new number is 25.

4. 25 is not divisible by 3, so we move on to the next smallest prime number, 5.

5. 25 ÷ 5 = 5. So, 5 is a factor and our new number is 5.

6. 5 ÷ 5 = 1. So, 5 is a factor and our new number is 1.

We have now fully factored 150 into its prime factors: 2, 3, 5, and 5. To find all the factors of 150, we can multiply these prime factors in different combinations:

1 × 150 = 150
2 × 75 = 150
3 × 50 = 150
5 × 30 = 150
6 × 25 = 150
10 × 15 = 150

So, the factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

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Answer:

12.5 minutes.

Step-by-step explanation:

The number -8 indicates that the paper uses 8 pages per minute. You can solve the equation by simply dividing 100/8.

You can also find the answer by solving the equation for the value t. Subtract 100 from both sides, and you will get -8t = -100. Then, divide both sides by -8 and you will get 12.5.

Answer:

0.71428571428 square yards

Step-by-step explanation:

Divide: 25 divided by 35=0.71428571428

Hope I helped!! :)

Sorry if it's wrong! :(

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P

OQ = 4S - 10

OP = 23

PQ = 1

Equation

OQ = OP + PQ

Substitution

4S - 10 = 23 - 1

Simplification

4S = 22 + 10

4S = 32

S = 32/4

S = 8

Determine OP

OQ = 4(8) - 10

OQ = 32 - 10

OQ = 22

Derivative of six inverse trigonometric functions are as follow:

d/dx(sin⁻¹x) = 1 / √1 - x²

d/dx(cos⁻¹x) = -1 / √1 - x²

d/dx(tan⁻¹x) = 1 / √1 + x²

d/dx(cosec⁻¹x) = -1 / |x|√ x² - 1

d/dx(sec⁻¹x) = 1 / |x|√ x² -1

d/dx(cot⁻¹x) = -1 / √1 + x²

As given in the question,

Explanation of the derivative of six inverse trigonometric functions are as follow:

1. y = sin⁻¹x

⇒ x = siny

⇒d/dx(x) = d/dx(siny)

⇒ 1 = cosy dy/dx

⇒dy/dx = 1/cosy

⇒dy/dx = 1/√1-sin²y

⇒dy/dx = 1/√1-x²

⇒d/dx( sin⁻¹x) = 1/√1-x²

2. y = cos⁻¹x

⇒ x = cosy

⇒d/dx(x) = d/dx(cosy)

⇒ 1 =-siny dy/dx

⇒dy/dx = -1/siny

⇒dy/dx = -1/√1-cos²y

⇒dy/dx = -1/√1-x²

⇒d/dx( cos⁻¹x) = -1/√1-x²

3. y = tan⁻¹x

⇒ x = tany

⇒d/dx(x) = d/dx(tany)

⇒ 1 =sec²y dy/dx

⇒dy/dx = 1/sec²y

⇒dy/dx = 1/√1+ tan²y

⇒dy/dx = 1/√1 + x²

⇒d/dx( tan⁻¹x) = 1/√1+x²

4. y = cosec⁻¹x

⇒ x = cosecy

⇒d/dx(x) = d/dx(cosecy)

⇒ 1 =-cosecy coty dy/dx

⇒dy/dx = -1/cosecy coty

⇒dy/dx = -1/cosecy√cosec²y-1

⇒dy/dx = -1/|x|√x²-1

⇒d/dx( cosec⁻¹x) = -1/|x|√x²-1

5.   y = sec⁻¹x

⇒ x = secy

⇒d/dx(x) = d/dx(secy)

⇒ 1 =secy tany dy/dx

⇒dy/dx = 1/secy tany

⇒dy/dx = 1/secy√sec²y-1

⇒dy/dx = 1/|x|√x²-1

⇒d/dx( sec⁻¹x) = 1/|x|√x²-1

6. y = cot⁻¹x

⇒ x =coty

⇒d/dx(x) = d/dx(coty)

⇒ 1 =-cosec²y dy/dx

⇒dy/dx = -1/cosec²y

⇒dy/dx = -1/√1+ cot²y

⇒dy/dx = -1/√1 + x²

⇒d/dx( cot⁻¹x) = -1/√1+x²

Therefore, the derivative of the six inverse trigonometric functions are given below:

d/dx(sin⁻¹x) = 1 / √1 - x²

d/dx(cos⁻¹x) = -1 / √1 - x²

d/dx(tan⁻¹x) = 1 / √1 + x²

d/dx(cosec⁻¹x) = -1 / |x|√ x² - 1

d/dx(sec⁻¹x) = 1 / |x|√ x² -1

d/dx(cot⁻¹x) = -1 / √1 + x²

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Answer:

The quotient of a number to the fifth power and six.

Step-by-step explanation:

Step 1: Convert k⁵ into words

k⁵ = a number to the fifth power

Step 2: Convert / into words

/ = quotient

Step 3: Convert 6 into words

6 = six

Step 4: Combine

The quotient of a number to the fifth power and six.

Answer:

3

Explanation:

Apply Multiplicative Distribution Law:

{x + y =9

{8x + 24y = 120

Reduce the greatest common factor on both sides of the equation.

{x + y = 9

{x + 3y = 15

Subtract the two equations: x + y - (x +3y) = 9 - 15

Remove paranthesis: x + y - x - 3y = 9 - 15

Cancel the unknown variables: y - 3y = 9 - 15

Combine like terms: -2y=9 - 15

Calculate the sum or difference: -2y = -6

Reduce the greatest common factor on both sides of the equation: y =3

Substitute one unknown quantity into the elimination: x + 3 = 9

Rearrange unknown terms to the left side of the equation: x = 9 - 3

Calculate the sum or difference: x = 6

Write the solution set of equations: {x = 6

                                                           {y = 3

Substitute: 6 - 3

Calculate the sum or difference: 3

Answer: 3

12. Arithmetic

xn = a + (n-1) d

n = 5 (three aritmetic, 4 and 12)

Input the value:

12 = 4 + 4d

8 = 4d

d = 2

the value: 4, 6 , 8 , 10 , 12

13. Arithmetic

xn = a + (n-1) d

n = 4 (two aritmetic, 4 and 19)

Input the value:

19 = 4 + 3d

15 = 3d

d = 5

the value: 4, 9 , 14 , 19

14. geometric

\(\tt a_n=ar^{n-1}\)

n = 4 (two geometric, 2 and 54)

input the value:

52 = 2r³

r = 3

the value: 2, 6, 18, 54

15. geometric

\(\tt a_n=ar^{n-1}\)

n = 4 (two geometric, 5 and 40)

input the value:

40 = 5r³

r = 2

the value: 5, 10, 20, 40

The rewritten expression using the summation notation is ∑ k = 1 1! + 2! + 3! + ... + (n+1)!

The summation notation is a way to represent the sum of a series of terms. In the summation notation, the series of terms is represented by an expression that is followed by a summation symbol (∑). The summation symbol is usually followed by an index of the summation (k in this case), an equal sign (=), the starting value of the index, and a colon (:). The series of terms is then written below the summation symbol, with the index replacing the variable in each term.

To rewrite the given expression using the summation notation, we can use the following steps:

Identify the series of terms: 1 + 2 + 3 + ... + n.

Write the series of terms below the summation symbol: ∑ k = 1

Replace the variable in each term with the index: 1! + 2! + 3! + ... + (n+1)!

The rewritten expression using the summation notation is ∑ k = 1 1! + 2! + 3! + ... + (n+1)!

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Answer: x = 5

Step-by-step explanation: it is 392079∞¢•¶¶§∞¶∞§¶6

You would need to add up the probabilities for the combinations 1-5 out of the total 8 possible combinations.

To find P(a ∨ (b ∧ c)), we need to consider all possible combinations of values for the boolean variables a, b, and c.

Since each boolean variable can take two values (true or false), there are 2 possibilities for each variable. Therefore, for 3 variables (a, b, and c), there are \(2^3\) = 8 possible combinations.

To calculate P(a ∨ (b ∧ c)), we need to add up the probabilities for each of these combinations. However, since the expression involves an OR operation, we only need to consider the combinations where either a is true or (b ∧ c) is true.

Let's enumerate the possible combinations for a, b, and c:

1. a = true, b = true, c = true

2. a = true, b = true, c = false

3. a = true, b = false, c = true

4. a = true, b = false, c = false

5. a = false, b = true, c = true

6. a = false, b = true, c = false

7. a = false, b = false, c = true

8. a = false, b = false, c = false

Out of these combinations, we need to find the ones that satisfy the expression a ∨ (b ∧ c).

Let's evaluate the expression for each combination:

1. True ∨ (True ∧ True) = True

2. True ∨ (True ∧ False) = True

3. True ∨ (False ∧ True) = True

4. True ∨ (False ∧ False) = True

5. False ∨ (True ∧ True) = True

6. False ∨ (True ∧ False) = False

7. False ∨ (False ∧ True) = False

8. False ∨ (False ∧ False) = False

From the evaluations, we can see that the expression a ∨ (b ∧ c) is true for combinations 1-5. Therefore, we need to add up the probabilities for these combinations.

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Answer:

83°

Step-by-step explanation:

Set (4x+3)=(5x-17)

x=20

Substitute x in (5x-17)

=83

Answer:

B =83

Step-by-step explanation:

5x-4x=4x+3

5x-4x=17+3

x=20

Again

for angle CGF

5x-17

5×20-17

100-17

83

answer

x=180-87-33

= 60

Answer:

1/14 ; 1/35

Step-by-step explanation:

A

6/10 x 5/9 x 4/8 x 3/7

3/5 x 5/9 x 1/2 x 3/7

1 x 1/3 x 3/14

1/14

B

4/10 x 3/9 x 2/8 x 6/7

2/5 x 1/3 x 1/4 x 6/7

2/15 x 3/14

1/5 x 1/7

1/35

The probability that  4 creature cards is pulled is 1/14 and the probability that 3 land cards and 1 creature card is pulled is 4/35

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here there are 4 land cards and 6 creature cards

thus selecting four cards at random from 10 cards is  ¹⁰C₄=210

and the event of selecting 4 creature cards from a total of 6 cards is ⁶C₄ =15

Therefore probability of pulling 4 creature cards is = 15/210

                                                                                     = 1/14

The probability of pulling 3 land cards and 1 creature cards is    

= ⁴C₃ × ⁶C₁   /  ¹⁰C₄

= 4/35

Hence 1/14 and 4/35 are the respective probabilities.

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Based on the information provided regarding same as cash loans, Chelsea won't be charged interest for the first 6 months of the loan, nor will she have to make payments for the first 6 months. (Option D)

A Same-As-Cash Loan refers to a short-term lending solution in which no interest or monthly payment are required to be paid during a set “Same-As-Cash” period. At the end of a predetermined period, the loan is paid off. Hence, the customer owes no interest or monthly payments during a set promotional period and pays the same amount on the loan as they would have paid up front with cash. These are interest deferred loans in which the loans interest still accrues during that promotional period, however if the customer pays off the entire principal balance before the period ends, they are not required to pay that interest. The advantage of these loans is that customers may spend the same amount they would have if they had paid with cash up front. Hence, if Chelsea opts for loan that offered 6 months, same as cash, there would be no requirement of payment or interest charged for the 6 months.

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