Need help on this if anyone can

The probability that the equipment will operate for at least 200 hours without failure is \((1-e^{-2} )^2[2e^-2+1]\).

Given:

mean = 1/100

Let X = the number of components that fail before 200 hours . The X has a binomial distribution n = 3 and p = 1 – e^-2.

probability p = 3/2\(p^{2} (1-p)\) + 3/3 \(p^{3}\).

= 3(\(1-e^-2)^2\)\(e^-2\) + (\(1-e^-2)^3\)

= \((1-e^-^2)^2[3e^-^2 - e^-^2+1]\)

= \((1-e^{-2} )^2[2e^-2+1]\)

Therefore the probability that the equipment will operate for at least 200 hours without failure is \((1-e^{-2} )^2[2e^-2+1]\).

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a. d, days since first measurement y, acres burned since fire started

0 0, 1 4800, 2 9600, 3 14400, 4 19200, 5 24000. b. when d = -1, it tells that the area burned in the fire was 4780 acres one day before the area was first measured. When d = -3, y = 4680, this means that the area burned in the fire was 4680 acres three days before the area was first measured. c. The area burned a week before the fire measured 4800 acres was approximately 115.2 acres.

a. To complete the table, we need to plug in the values of d in the given equation and calculate the corresponding values of y.

d, days since first measurement

y, acres burned since fire started

0 0

1 4800

2 9600

3 14400

4 19200

5 24000

b. When d = -1, we have:

y = (4800)(24^(-1))^(1) = 4800 - 20 = 4780

This means that the area burned in the fire was 4780 acres one day before the area was first measured.

When d = -3, we have:

y = (4800)(24^(-3))^(1) = 4800 - 120 = 4680

This means that the area burned in the fire was 4680 acres three days before the area was first measured.

c. A week before the fire measured 4800 acres, the number of days since the fire started would be:

d = 4800 / (4800/24) = 24

Therefore, a week before the fire measured 4800 acres, the fire had been burning for 24 days. Plugging in this value in the given equation, we get:

y = (4800)(24^(-24/24))^(1) = 115.2

So, the area burned a week before the fire measured 4800 acres was approximately 115.2 acres.

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Based on the given information, the net amount your firm will receive on the next transaction date can be calculated by subtracting the variable interest rate from the fixed interest rate.

In the swap agreement, your firm pays a fixed interest rate of 5.50 percent and receives a variable interest rate equal to LIBOR (London Interbank Offered Rate) plus 150 basis points. LIBOR is currently 3.75 percent.

To calculate the net amount your firm will receive on the next transaction date, we need to subtract the variable interest rate from the fixed interest rate.

Fixed interest rate: 5.50%

Variable interest rate: LIBOR (3.75%) + 150 basis points (1.50%) = 5.25%

Therefore, the net amount your firm will receive on the next transaction date is the difference between the fixed interest rate and the variable interest rate, which is 0.25%.

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Answer:

A

Step-by-step explanation:

12x -2y = 4  Subtract 12x from both sides

12x - 12x - 2y = 4

-2y = -12x - 4  Divide all the way through by -2

\(\frac{-2y}{-2}\) = \(\frac{-12x}{-2}\) + \(\frac{4}{-2}\)

y = 6x - 2

Helping in the name of Jesus.

Answer:

(A) y = 6x - 2

Step-by-step explanation:

Answer:

4x + 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

(-4x + 3) + (8x + 2)

Step 2: Simplify

The principal amount in account A was $250.09 and in account B it was $600.

Account B earned you the most interest the first​ month because $1.2 is higher than $0.7711.

What is the simple interest?

Simple interest is a quick and easy way to calculate the interest charge on a loan. Simple interest is calculated by multiplying the daily interest rate by the principal by the number of days between payments.

The formula for simple interest is expressed as

                I = PRT/100

Where, P = the principal or initial amount of money invested.

            R = interest rate

            T = time

On account A,

     I = $6.94

    R = 3.7%

    T = 9 months = 9/12 = 0.75 years.

Using the formula:

         I = PRT/100

         \(6.94 = \frac{P(3.7)(0.75)}{100} \\\\6.94 = 0.02775P\\\\P=250.09\)

On account B,

    I = $39.60

    R = 2.4%

    T = 33 months = 33/12 = 2.75 years

Using the formula:

     I = PRT/100

     \(39.60= \frac{P(2.4)(2.75)}{100} \\\\39.60 = 0.066P\\\\P=600\)

To find the account that earned more interest in the first month we have to divide the interest by the number of months.

For account A,

                6.94/9 = $0.7711

For account B,  

                39.60/33 = $1.2

Hence, the principal amount in account A was $250.09 and in account B it was $600.

Account B earned you the most interest the first​ month because $1.2 is higher than $0.7711.

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because we use simple rule of three

2 inches ---------------- 5 miles

20inch -------------- xmiles

x = 100/2

x = 50

Answer: 185.7 miles

Step-by-step explanation:

To find the total distance, add the smaller distances together.

47.8 + 72 + 65.9 = 185.7

They are similar because they have the same slope the equation is

y = -2/3x + 531

What is in slope-intercept form?

changing 2x+3y=1470 to slope intercept form is solving for y

minus 2x both sides and divide by 3

y = -2/3x + 490

the slope is -2/3

the y intercept is y=490 or the point (0,490)

to graph it, I would start at the origin and go up 490 units on the y axis and put a point there

then go -2 units up (2 down) and 3 to the right and put a point there

then connect the 2 points with a line

in function notation, replace y with f(x) to get

y = -2/3x + 490

graph below

intercepts labeled

2x+3y=1593

they are similar because they have the same slope

the equation is  y = -2/3x + 531

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The proportion that solves for the distance between D and E is  x/15 = 6/9

An equation is an expression that shows the relationship between two or more numbers and variables.

Triangle ABC and CDE are similar triangles, hence the ratio of their corresponding sides are in the same proportion.

Hence:

x/15 = 6/9

The proportion that solves for the distance between D and E is  x/15 = 6/9

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Numerical integration is a numerical analysis technique for calculating the approximate numerical value of a definite integral.

In general, integrals can be either indefinite integrals or definite integrals. A definite integral is an integral with limits of integration, while an indefinite integral is an integral without limits of integration.A numerical integration formula is an algorithm that calculates the approximate numerical value of a definite integral. Numerical integration is based on the approximation of the integrand using a numerical quadrature formula.

The numerical quadrature formula is used to approximate the value of the integral by breaking it up into small parts and summing the parts together.Equations for the calculation of integration by trapezoidal rule (1/2)h[f(x0)+2(f(x1)+...+f(xn-1))+f(xn)] where h= Δx [the space between the values], and x0, x1, x2...xn are the coordinates of the abscissas of the nodes. The basic principle is to replace the integral by a simple sum that can be calculated numerically. This is done by partitioning the interval of integration into subintervals, approximating the integrand on each subinterval by an interpolating polynomial, and then evaluating the integral of each polynomial.

Based on the given table of unequally spaced data, we are to calculate the approximate numerical value of the definite integral. To do this, we will use the integration formula as given by the trapezoidal rule which is 1/2 h[f(x0)+2(f(x1)+...+f(xn-1))+f(xn)] where h = Δx [the space between the values], and x0, x1, x2...xn are the coordinates of the abscissas of the nodes.  The table can be represented as follows:x            0.1 0.3 0.5 0.7 0.95 1.2f(x)      1 0.9048 0.7408 0.6065 0.4966 0.3867 0.3012Let Δx = 0.1 + 0.2 + 0.2 + 0.25 + 0.25 = 1, and n = 5Substituting into the integration formula, we have; 1/2[1(1)+2(0.9048+0.7408+0.6065+0.4966)+0.3867]1/2[1 + 2.3037+ 1.5136+ 1.1932 + 0.3867]1/2[6.3972]= 3.1986 (to 4 decimal places)

Therefore, the approximate numerical value of the definite integral is 3.1986.

The approximate numerical value of a definite integral can be calculated using numerical integration formulas such as the trapezoidal rule. The trapezoidal rule can be used to calculate the approximate numerical value of a definite integral of an unequally spaced table of data.

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Answer:

function b

Step-by-step explanation:

When its asking for which function has a greater rate of change its asking for which slope has a greater value

the slope is calculated by change in y over change in x

for function a, as y goes up 2 x goes up 1

so the slope ( rate of change) is 2/1

for function b is y goes up 3 x goes up 1

so the slope (rate of change) is 3/1

3/1 is greater than 2/1 so function b has a greater rate of change

Answer:

can I get a hiaaa

How was the government able to make children go to residential school?

By solving for the density of the two metal cubes, we can determine that the two metal cubes are not made from the same material.

Density, denoted by ρ, is a property of any substance that is defined as the ratio between the mass and volume of the substance.

ρ = m/v

where ρ = density

m = mass

v =  volume

Solving the density of each cube.

Cube 1 :

ρ = m/v

ρ = m/e^3

ρ = 43. 63 g/(3. 2 cm)^3

ρ = 1.3315 g/cm^3

Cube 2 :

ρ = m/v

ρ = m/e^3

ρ = 683. 5 g/(8. 34 cm)^3

ρ = 1.1783 g/cm^3

If two objects have the same density, then they are made from the same material. Since the density of the two cubes are not equal, then they are not made form the same material.

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Answer:

st=pq su=rp and for the other ones angle q is 75 degrees so just add 59 and 75 then subtract it from 180 because that's how many degrees is in a triangle and angle s is 59

\(\huge\underline{\overline{\mid{\bold{\red{ANSWER}}\mid}}}\)

Both triangles are congruent, Hence Angles of both triangle will be equal,

We have got two angles,

LP = 59°, LT = 75°

let the third angle be x

The sum of all angles of a triangle is 180°

So,

59° + 75° + x = 180

x = 46°

a) ST = 8m

b) SU = 7m

c) mLR = 75°

d) mLQ = 46°

e) mLS = 59°

Answer:

x = 7

Step-by-step explanation:

To get rid of the x^2, do the opposite of x^2: radicals, or square roots.

x^2 = 121

x = √121

Think about what number can multiply by itself to get 121...

7 • 7 or 7^2 = 121

So, in x^2 = 121, x = 7.

x^2 = 121

x = √121

7 = √121

7 = 7 ✔

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The function f(x) = 2x³ - 6x² + 90x is increasing on the intervals (-∞, -5) and (3, ∞), and decreasing on the interval (-5, 3). The local minimum value of f is -162, and the local maximum value of f is 350.

To find the intervals on which f is increasing or decreasing, we can use the derivative of f. The derivative of f is f'(x) = 6(x + 5)(x - 3). f'(x) = 0 for x = -5, 3. Since f'(x) is a polynomial, it is defined for all real numbers. Therefore, our critical points are x = -5 and x = 3.

f'(x) is positive to the left of x = -5 and to the right of x = 3, and it is negative between x = -5 and x = 3. This means that f is increasing on the intervals (-∞, -5) and (3, ∞), and decreasing on the interval (-5, 3).

To find the local minimum and maximum values of f, we can look for the critical points and the endpoints of the function's domain. The critical points are x = -5 and x = 3. The endpoints of the function's domain are x = -∞ and x = ∞.

f(-5) = -162 and f(3) = 350. Therefore, the local minimum value of f is -162, and the local maximum value of f is 350.

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Answer:

Find x,If x + 15 = 30.

Step-by-step explanation:

Answer:

40 ounces

Step-by-step explanation:

2.5x 16= 40

Based on mathematical operations, when designing a prefabricated home, you must ensure that the width of the door opening is greater than A. 33.75 inches, given the sample mean of 36 inches with a tolerance (margin of error) of ±0.0625 inches.

The margin of error is the tolerance level that creates the confidence interval for the sample mean.

With a sample mean of 36 inches for the door opening and a tolerance level of ±0.0625 inches, the width can be designed to measure between 35.9375 inches and 36.0625 inches.

This measurement implies that the upper limit for the width (confidence interval) is 36.0625 inches while the lower limit is 35.9375 inches.

Thus, the width of the door opening must be greater than Option A.

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Answer:

Step-by-step explanation:

The answer is the difference between Total water and Ocean Water.

Fresh water = Total Water - Ocean Water

Total Water  =   361

Ocean Water = 335        Subtract

Fresh water   =    26       millions of Km^2

The observation is located to the left of the mean by a distance of 1.2 standard deviations.

The z-score of an observation represents the number of standard deviations the observation is away from the mean.

If the z-score for a particular observation is z = -1.2, this means that the observation is 1.2 standard deviations below the mean.

If the mean is represented by μ and the standard deviation by σ, then we can express this observation as:

observation = μ + (z * σ)

observation = μ + (-1.2 * σ)

This means that the observation is located to the left of the mean by a distance of 1.2 standard deviations.

For example, The z-score represents the number of standard deviations an observation is above or below the mean of the distribution.

In this case, a z-score of -1.2 indicates that the observation is 1.2 standard deviations below the mean height of the group.

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Answer:

Decrease by 3

Step-by-step explanation:

The range of a set of data is the difference between the largest and smallest values.

Set of numbers: 9, 5, 1, 7, 4, 4, 7, 9

Order: 1, 4, 4, 5, 7, 7, 9, 9

Range: 9 - 1 = 8

If the number 7 replaced the number 1 in the set?

Order: 4, 4, 5, 7, 7, 7, 9, 9

Range: 9 - 4 = 5

How much would the range decrease if the number 7 replaced the number 1 in the set?

8 - 5 = 3

So, the range decrease by 3 if the number 7 replaces the number 1 in the set.

The solution 96th term of the given sequence is -1126.

Monthly payment for the given mortgage is $2802.03.

Find the sum of the first 8 terms of the following series, to the nearest integer.

The given series is 18, 3, 2^(1/2), …, 20, 21, 22

Here, a = 18 and d = 3 - 18 = -15

For sum of first n terms,

we use the formula:

Sum of first n terms

= n/2[2a + (n-1)d]

Plugging in the values we get,

Sum of first 8 terms = 8/2[2(18) + (8-1)(-15)]

= 4[36 - 105]

= -276 ≈ -276

Which row of Pascal's Triangle would we use to expand this binomial?

The given binomial is (4x^2 - 1)^5

For finding the row of pascal triangle to expand this binomial we look at the power which is 5.

The row of pascal's triangle for 5th power is 1 5 10 10 5 1

Therefore, we will use the 5th row to expand this binomial.

Find the 10th term of the geometric sequence 10, −20, 40,…

The given sequence is 10, -20, 40, …

Since the given sequence is a geometric sequence,

we can find the 10th term using the formula given below:

T_n = a * r^(n-1)Here, a = 10, r = -2 and n = 10

Plugging in the values we get,

T_10 = 10 * (-2)^(10-1) = 10 * (-2)^9 = 10 * (-512)

= -5120

Therefore, the 10th term of the given sequence is -5120.

Find the 96th term of the arithmetic sequence -16, -28, -40, …

The given sequence is -16, -28, -40, …

Since the given sequence is an arithmetic sequence,

we can find the nth term using the formula given below:

T_n = a + (n-1) * dHere, a = -16, d = -28 - (-16) = -12 and n = 96

Plugging in the values we get,

T_96 = -16 + (96-1)*(-12) = -16 - 1110 = -1126

Therefore, the 96th term of the given sequence is -1126.

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Answer:

cos (theta) = √21/5

Step-by-step explanation:

sin (theta) = 2/5

(sin (theta))^2 = 4/25

4/25 + (cos (theta))^2 = 1

(cos (theta))^2 = 1 - 4/25 = 21/25

cos (theta) = √21/5

Answer:

Step-by-step explanation:

divide through by the coefficient of \(x^{2}\)

\(\frac{5x^{2} }{5}\) + \(\frac{16x}{5} + \frac{-40}{5} = \frac{8}{5}\)

\(x^{2} +\frac{16}{5}x -8 =\frac{8}{5}\)

\(x^{2} +\frac{16}{5} x = \frac{8}{5} +8\)

\(x^{2} + \frac{16}{5} x =\frac{48}{5}\)

Add half of the square of the coefficient of x  to both sides \((\frac{1}{2} X \frac{16}{5} ) ^{2}\)

\(x^{2} + \frac{16}{5}x + (\frac{1}{2} X \frac{16}{5} )^{2} =\) \(\frac{48}{5} +(\frac{1}{2} X \frac{16}{5} )^{2}\)

\(x^{2} +\frac{16}{5} x +(\frac{16}{10}) ^{2} =\frac{48}{5} +\frac{64}{25}\)

\((x +\frac{16}{10})^{2} =\frac{304}{25}\)

\(x +\frac{16}{10} =\)±\(\sqrt{\frac{304}{25} }\)

\(x = -\frac{16}{10}\) ± \(\sqrt{\frac{304}{25} }\)

\(x=-\frac{16}{10} + \sqrt{\frac{304}{25} }\) or\(-\frac{16}{10} - \sqrt{\frac{304}{25} }\)

\(x = 1.89\) or -5.09

The number of subs in the order is 8 or 9

Let's call the number of subs in the order "x".

Since the cost of 3 subs is $20, the cost per sub is $20 / 3 = $6.67.

And since the cost of 4 subs is $26, the cost per sub is $26 / 4 = $6.50.

So the cost per sub is between $6.50 and $6.67.

If the total cost is $56, then the cost per sub must be $56 / x.

So:

x = 56/6.5 or x = 56/6.67

Evalutate

x = 8.6 or x = 8.4

Approximate

x = 9 or 8

Hence, the subs is 8 to 9

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