simplify the following expression
(3/4x-5/8) + (1/8x + 3/5)

Answer:

x = 8°

y = 21°

Step-by-step explanation:

27 + 3y = 90

3y = 63

y = 21°

x + 8x + 18 = 90

9x = 72

x = 8°

AMSAA growth model

The MTTF at the conclusion of the test cycle is 232.59 hours. 22423.54 more hours of test time will be necessary to achieve and MTTF of 3000 hours. 52.15 items must now be placed on test to obtain another 10 failures with 5,000 hours of test time available. If the testing continues for only 600 more hours, 1.75 is the expected number of failures.

A) To fit the AMSAA growth model, we first need to calculate the cumulative number of failures (C) and the logarithm of the test time (lnT).

| Test Time (T) | C | lnT |
|---------------|---|-----|
| 28            | 1 | 3.33|
| 146           | 2 | 4.98|
| 258           | 3 | 5.55|
| 426           | 4 | 6.05|
| 521           | 5 | 6.26|
| 1027          | 6 | 6.93|
| 1273          | 7 | 7.15|

Next, we can use linear regression to estimate the parameters of the AMSAA model, β and η:

C = βlnT - η

Using linear regression, we get β = 1.11 and η = 3.82.

To estimate the MTTF at the conclusion of the test cycle, we can use the formula:

MTTF = (T/C)^(1/β)

Plugging in the values for T (1273), C (7), and β (1.11), we get:

MTTF = (1273/7)^(1/1.11) = 232.59 hours

B) To achieve an MTTF of 3000 hours, we need to solve for T in the equation: 3000 = (T/C)^(1/β)

Plugging in the values for C (7), β (1.11), and rearranging the equation, we get:

T = 3000^(β) * C = 3000^(1.11) * 7 = 23696.54 hours

Since we have already tested for 1273 hours, we need an additional 23696.54 - 1273 = 22423.54 hours of test time to achieve an MTTF of 3000 hours.

C) To obtain another 10 failures with 5000 hours of test time available, we can use the formula:

C = βlnT - η

Plugging in the values for C (10), β (1.11), η (3.82), and T (5000), and rearranging the equation, we get:

10 = 1.11ln(5000) - 3.82

ln(5000) = (10 + 3.82)/1.11 = 12.47

5000 = e^(12.47) = 260753.13

Therefore, we need to place 260753.13/5000 = 52.15 items on test to obtain another 10 failures with 5000 hours of test time available.

D) If the testing in (c) continues for only 600 more hours, we can use the formula:

C = βlnT - η

Plugging in the values for β (1.11), η (3.82), and T (600), and rearranging the equation, we get:

C = 1.11ln(600) - 3.82 = 1.75

Therefore, the expected number of failures in 600 more hours of testing is 1.75.

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Log x+y = logbx − logbyGiven log630 ≈ 1.898 and log62 ≈ 0.387, log615 ≈ 2.086.

Given log 630 ≈ 1.898 and log 62 ≈ 0.387,

We have log 630 = log (6 * 62 * 10) = log 6 + log 62 + log 10 = 1 + 0.387 + 1 = 2.387

And log 615 = log (6 * 62 * 5) = log 6 + log 62 + log 5 = 1 + 0.387 + 0.699 = 2.086

So, log 615 ≈ 2.086

In the example given, log 630 ≈ 1.898 and log 62 ≈ 0.387. These logarithmic values are used to simplify other logarithmic expressions and, the logarithm of 615 was found to be approximately 2.086.

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Answer:

at what?

Step-by-step explanation:

Answer:

All you have to do is ask a question and someone will find and answer.

Answer: m∠2 =60

60=4x+12

subtract 12 from both sides

60-12=4x+12-12

60-12=4x

48=4x

divide both sides by 4

48÷4=4x÷4

48÷4=x

x=12

Plug it into the equation

4(12)+12=

48+12=

m∠2 =60

another proof is that they are congruent

I hope this is good enough:

Anthony and Cleopatra were lying dead on the floor in a villa because they were fishes in the water bowl that might have fallen and broke down.

Since, there was a broken bowl nearby the dead bodies,

it seems like Anthony and Cleopatra were fishes who were in the water in the bowl that broke down.

Since the bowl in which the fishes were, broke down, the water of the bowl spilled and the fishes were no more in water due to which they died. This is the because there was no mark on their body and were neither poisoned.

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Answer:

Because Howard converted the lengths into feet

12 inches = 1 foot

24 inches = 2 feet

1 x 2 = 2 feet(area)

Answer:

The number of sweatshirts for which cost and income are equal

Step-by-step explanation:

Let y₁ represent the revenue from selling "x" sweatshirts and y₂ represent the cost of producing "x" sweatshirts, solving the system:

\(y_1=35x\\y_2=-0.05(x-400)^2+9,492\\y_1=y_2\\35x=-0.05(x-400)^2+9,492\\-0.05(x-400)^2-35x+9,492=0\)

The solution of the equation above yields the number of sweatshirts for which the cost of production (y₂ ) is equal to the revenue from sales (y₁).

Therefore, the solution represents the number of sweatshirts for which cost and income are equal .

The number of sweatshirts for which cost and income are equal and this can be determined by using the substitution method.

Given :

The following steps can be used in order to determine the solution of the system of the equation:

Step 1 - Write the given system of equations.

\(y = 35x\)              ---- (1)

\(y = -0.05(x - 400)^2+9492\)              ---- (2)

Step 2 - Now, substitute the value of 'y' in equation (2).

\(35x = -0.05(x - 400)^2+9492\)

Step 3 - Simplify the above equation.

\(35x = -0.05x^2-8000+40x+9492\)

Step 4 - Now, write the above equation in generalized quadratic form.

\(0.05x^2-5x-1492=0\)

From the above steps, it can be concluded that the correct statement is given by option D).

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The derivative dz/dt can be found using the chain rule. By differentiating each term with respect to t and applying the chain rule, we can calculate dz/dt as follows:

\(dz/dt = 2sin(t)cos(t) + 4e^tcos(t) + 4e^tsin(t) + 4e^t + 4sin(t)e^t.\)

By applying the chain rule, we can find dz/dt as follows: differentiate z with respect to x, then multiply it by dx/dt, and finally differentiate z with respect to y and multiply it by dy/dt.

The function z = x² + y² + xy can be rewritten as z = (sin(t))² + (4e^t)² + (sin(t))\((4e^t)\).

To find dz/dt, we need to find the partial derivatives of z with respect to x and y and multiply them by dx/dt and dy/dt, respectively.

The partial derivative of z with respect to x is (2x + y), and the partial derivative of z with respect to y is (2y + x).

Next, we differentiate x = sin(t) with respect to t, giving us dx/dt = cos(t).

Similarly, differentiating\(y = 4e^t\) with respect to t yields \(dy/dt = 4e^t.\)

Now we can apply the chain rule:

dz/dt = (2x + y) * dx/dt + (2y + x) * dy/dt

Substituting the expressions for x, y, dx/dt, and dy/dt:

\(dz/dt = (2sin(t) + 4e^t) * cos(t) + (2(4e^t) + sin(t)) * (4e^t)\)

Simplifying this expression will yield the final result.

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Answer:

1.53.6

2.6.11

3.-21.11

4.37.77

5.-9.4

Step-by-step explanation:

Answer:

1. 53.6 2. 6.11111 3. -21.1111 4. 37.7778 5. -9.4

Step-by-step explanation:

I just look it up.

Answer:

A: 6

B: 16

C: 2

D: -12

Step-by-step explanation:

They are asking you to multiply the equations:

(3x^2 + 2x - 3)(2x + 4)

Distribute and you should get:

6x^3 + 16x^2 + 2x - 12

The Coefficients A,B,C, and D are 6, 16, 2, and -12.

The solution to the system of equations is x = -3 and y = -2. To solve the system of equations using the addition method, we can eliminate one variable by adding or subtracting the equations in a way that results in a new equation with only one variable.

Then, we can solve for that variable and substitute it back into one of the original equations to find the value of the remaining variable. For the given system of equations: 7x - 4y = 15 and 5x + 28y = -51, the solution is x = -3 and y = -2.

To eliminate the y variable, we can multiply the first equation by 7 and the second equation by 4, resulting in the equations: 49x - 28y = 105 and 20x + 112y = -204. Now, we can subtract the first equation from the second equation, which gives us 20x + 112y - (49x - 28y) = -204 - 105.

Simplifying the equation, we have -29x + 140y = -309. Rearranging the terms, we get 29x - 140y = 309.

Now, we have a new equation with only one variable. To solve for x, we divide both sides of the equation by 29, resulting in x - 140y/29 = 309/29. Simplifying further, we get x = -3.

Substituting the value of x = -3 into the first equation, we have 7(-3) - 4y = 15. Simplifying, we get -21 - 4y = 15. Rearranging the terms, we have -4y = 36. Dividing both sides by -4, we find y = -2.

Therefore, the solution to the system of equations is x = -3 and y = -2.

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Answer:

the last one

Step-by-step explanation:

when something asks for product it means multiplication

to get 2 times -5, you move first to -5 then to -10

Answer:

The place of 9 = 10,000 (ten thousand)

The place value of 9 = 9 x 10,000 =  90,000

I hope its right  ;)

Answer:

y = 3

Step-by-step explanation:

2y - 3 = \(\sqrt{3y^2-10y+12}\)

square both sides to remove sqrt bracket

(2y - 3)^2 = ( \(\sqrt{3y^2-10y+12}\) )^2

simplify both sides

(2y - 3)(2y - 3) = \(3y^2\) - 10y + 12

\(4y^2\) - 12y + 9 = \(3y^2\) - 10y + 12

bring all value to left side

\(y^2\) - 2y - 3 = 0

factor

(y - 3)(y + 1)

solve for y

y = 3, y = -1

When plugged back into the equation, only y = 3 is true

Answer:

y = 3

Step-by-step explanation :

\(2y - 3 = \sqrt{ 3y² - 10y + 12} \)

Swap the sides both of the equation.

\(\sqrt{ 3y² - 10y + 12} = 2y - 3 \)

To remove the brackets of equations square both side and simplify .

3y² - 10y + 12 = 4y² - 12y + 9

Move the expression to left-hand side and change its sign.

3y² - 10y + 12 - 4y² + 12y - 9 = 0

collect like terms

3y² - 4y² - 10y + 12y + 12 - 9 = 0

-y² + 2y + 3 = 0

Change the sign of expression. because it helps to solve.

y² - 2y - 3 = 0

Splits the term -2y

y² + y -3y - 3 = 0

Factor out y from the first pair and -3 from second pair of expression.

y ( y + 1 ) - 3 ( y + 1) = 0

Factor out y + 1 from the expression.

( y + 1 ) ( y - 3 ). = 0

When product and factors equals 0. at least one factor is 0.

y + 1 =0

y - 3 = 0

Solve for y

y = -1 and y = 3

If we plug the 3 as y in the expression we find that y = 3 is the true solution of this expression.

This equation has one solution which is y = 3.

Answer: d: -2,2

Step-by-step explanation:

The coordinates of W' after the rotation and the translation is (-2, 2).

Option D is the correct answer.

We have,

The rule for a rotation by 270° about the origin.

(x, y) → (y, −x)

Now,

W = (-4, -3)

Applying the rule.

W = (-3, 4)

Now,

A translation of 2 units down and 1 unit to the right.​

So,

W = (-3, 4)

W = (-3 + 1, 4 - 2)

W = (-2, 2)

Thus,

The coordinates of W' after the rotation and the translation is (-2, 2).

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Answer:

7/4a + 1/3

1 3/4a + 1/3

Step-by-step explanation:

Answer:

1 3/4AN + 1/3

Step-by-step explanation:

The equation 3x₁ + 5x₂ = 30 intersects the x₁-axis at point D (10, 0) and the x₂-axis at point C (0, 6). Option B (0, 8) is not an intercept on the x₂-axis. Option C (6, 10) is not an intercept on the x₁-axis. The correct answer is option D (10, 0) as the x₁-axis intercept.

The equation given is 3x₁ + 5x₂ = 30. To find the axis intercept, we need to determine the points at which the line intersects the x₁ and x₂ axes. To find the x₁-axis intercept, we set x₂ = 0 and solve for x₁ 3x₁ + 5(0) = 30 3x₁ = 30
x₁ = 10

So, the x₁-axis intercept is (10, 0) which corresponds to point D in the given options. To find the x₂-axis intercept, we set x₁ = 0 and solve for x₂: 3(0) + 5x₂ = 30 5x₂ = 30 x₂ = 6 Therefore, the x₂-axis intercept is (0, 6) which corresponds to point C in the given options. To summarize, the equation 3x₁ + 5x₂ = 30 intersects the x₁-axis at point D (10, 0) and the x₂-axis at point C (0, 6).

In the given options, option A (10, 6) is not an intercept on either axis. Option B (0, 8) is not an intercept on the x₂-axis. Option C (6, 10) is not an intercept on the x₁-axis. The correct answer is option D (10, 0) as the x₁-axis intercept.

Remember, the x₁-axis intercept is found by setting x₂ = 0, and the x₂-axis intercept is found by setting x₁ = 0 in the equation.The correct answer is option D

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Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

Answer:

a= 18 girls in the class, b= 20 boys and 15 girls, 12 oranges better price.

Step-by-step explanation:

for question a, there are 18 girls in the class, this is how i worked it out:

the ratio of boys to girls is 4:3.

there are 24 boys.

24 is 6 times more than 4.

if boys are 6 times more than the original ratio, we also have to times the amount of girls by 6.

6x3= 18.

for question b i got 20 boys and 15 girls, this is how i did it.

there are 35 students in total.

4:3= boys to girls.

4+3=7

7 goes into 35 five times.

ratio of boys to girls is 4:3 so 5x4 for boys = 20 and 3x5 for girls = 15.

answer= 20 boys and 15 girls.

12 oranges is a better deal, this is how i worked it out.

it is 60 for 12 oranges.

it is 48 for 8 oranges.

12x5= 60 , 8x6=48.

you only have to times 12 by 5 to get it to the price but you have to times 8 by 6 to get it to the price, proving that 12 oranges for 60 is a better deal.

Answer: True, with a dice probability calculator, you can easily find the various probabilities related to rolling a set of dice. A dice probability calculator can be used to determine the probability of rolling a certain number or set of numbers on one or more dice, as well as the probability of achieving specific combinations or sums of numbers. By entering the number of dice and the number of sides on each die, a dice probability calculator can calculate the probability of rolling any given combination of numbers. This can be useful in a variety of applications, such as games of chance, statistical analysis, and simulations.

Step-by-step explanation:

Volume:-

= 12 × 11 × 11

= 12 × 121

= 1452 cm³

Answer:

it is 1452 I believe (๑ↀᆺↀ๑)

The remainder when 101⁴⁸⁰⁰⁰⁰⁰⁰²³ is divided by 35 is 12.

Now, let's look at how we can use the Chinese Remainder Theorem to compute 101⁴⁸⁰⁰⁰⁰⁰⁰²³ mod 35. First, we need to express 35 as a product of prime powers:

=> 35 = 5 x 7.

Then, we can consider the congruences 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ a (mod 5) and 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ b (mod 7), where a and b are the remainders we want to find.

Since 101 is not divisible by 5, we have 101⁴ ≡ 1 (mod 5). Therefore,

=> 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ (101⁴)¹²⁰⁰⁰⁰⁰⁰⁰⁵ ≡ 1 (mod 5).

This means that a = 1.

Since 7 is a prime number, φ(7) = 6, so we have 101⁶ ≡ 1 (mod 7). Therefore,

=> 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ (101⁶)⁸⁰⁰⁰⁰⁰⁰⁰³ ≡ 1 (mod 7).

This means that b = 1.

Now, we need to find a number that is equivalent to 1 modulo 5 and 1 modulo 7. This number is

=> 1 x 7 x 1 + 5 x 1 x 1 = 12.

Therefore,

=> 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ 12 (mod 35).

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Sylvia and Patrick gathered information on the weight of cars and the mileage they get, and then proceeded to plot the data on a graph.

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Answer:

El número más pequeño es 3665844.

Step-by-step explanation:

Deje que los números sean X e Y

Por algoritmo euclidiano, tenemos

Por lo tanto tenemos X / Y = 11 + R

Y / R = 9 + S

R / S = 1 + T

S / T = 1 + U

T / U = 2

Dónde:

R, S, T y U son el resto en cada paso

Por lo tanto, 2U = T

Lo que da;

MCD (X, Y) = MCD (Y, R) = MCD (R, S) = MCD (S, T) = MCD (T, U) = 13

T / U = 2

y MCD (T, U) = 13

Por lo tanto, 2 y 13 son factores de T y U si T = 26 y U = 13, tenemos;

S = T (1 + U) = 364

R = S (1 + T) = 9828

Y = R (9 + S) = 3665844

X = Y (11 + R) = 36068239116

Los números son 36068239116 y 3665844

Por lo tanto, el más pequeño de los números = 3665844.

Answer:

2;3, that is the ratio =)

Step-by-step explanation:

Answer:The answer would be 4 to 6 or 4:6

These steps are often referred to as the principle of mathematical induction or PMI.

The steps for mathematical induction are:

Base Case: Show that the statement holds for some particular value of n, usually n = 1 or n = 0.

Inductive Hypothesis: Assume that the statement holds for some arbitrary value of n = k, where k is a positive integer.

Inductive Step: Using the inductive hypothesis, show that the statement also holds for n = k + 1.

Conclusion: By the principle of mathematical induction, the statement is true for all positive integers n.

These steps are often referred to as the principle of mathematical induction or PMI. They are used to prove statements that involve an infinite set of integers by showing that the statement holds for a base case, assuming that it holds for an arbitrary value, and then showing that it holds for the next integer in the set.

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B. 9/19

Step-by-step explanation:

there was 20 dogs in total he took 1 black dog now 19 in total, now 9 black dogs and 10 brown dogs so one less probability of black dogs so 9 black dogs and 10 brown dogs so 9/19