An ounce of gold costs $1310 and an ounce of silver costs $20. Find all possible weights of
silver and gold that make an alloy (combination of metals) that costs less than $900.
s = number of ounces of silver
g = number of ounces of gold

Find the inequality for this question

2/ ( 1 + x) ( 1 - x) is express  into partial fractions.

With an example, what is a partial fraction?

The division of an algebraic fraction into smaller, "partial fractions," components is possible. Think about the algebraic fraction (3x+5) (2x2-5x-3). This formula can be broken down into its simplest form, [2/(x - 3)] - [1/(2x + 1)]. Partial fractions are the more straightforward pieces [2/(x - 3)] and [1/(2x + 1)].

                        The four categories of partial fractions are linear factors, degree 2 irreducible factors, repeated linear factors, and repeated irreducible degree 2 factors.

= 2/(1-(x^2))

= 2 / (1)² - (X)²

=  2/ ( 1 + x) ( 1 - x)

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The length of AC in the given triangle is 126.6.

The length of AC in the given triangle can be calculated using the Pythagorean Theorem. The length of AC is the hypotenuse of the right triangle, and can be calculated by taking the square root of the sum of the squares of the other two sides of the triangle. In this case, the length of AC is equal to the square root of (b² + 99.6²). Using the Pythagorean Theorem, the length of AC is equal to 126.6.

To calculate this, we take the square root of (b² + 99.6²). First, we square b, which is 85. This gives us 7225. Then, we square 99.6, which gives us 9920.41. We then add these two values together to get 17145.41. Finally, we take the square root of this value, which gives us 126.6. This is the length of AC in the given triangle.

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Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

Answer:

The mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively.

Step-by-step explanation:

Let the random variable X be defined as the number of correct answers marked by a student.

It is provided that each question has 5 possible choices, 1 of the which is correct.

Then the probability of marking thee correct option is:

\(P(X)=\frac{1}{5}=0.20\)

There are a total of n = 20 questions to be answered.

As the students does not the answer to any question, they would be guessing for each question. This implies that for a random question, all the five options has the equal probability of being correct and each of the five options can be correct independently from the other.

All these information above indicates that the random variable X follows a Binomial distribution with parameters n = 20 and p = 0.20.

The mean and standard deviation of a Binomial distribution are:

\(\mu=np\\\\\sigma=\sqrt{np(1-p)}\)

Compute the mean and standard deviation of the random variable X as follows:

\(\mu=np=20\times 0.20=4\\\\\sigma=\sqrt{np(1-p)}=\sqrt{20\times 0.20\times(1-0.20)}=1.789\)

Thus, the mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively.

According to the question,

The probability of making 3 correct options will be:

→ \(P(X) = \frac{1}{5}\)

            \(= 0.20\)

Total number of questions,

As we know,

The mean will be:

→ \(\mu = np\)

By substituting the values, we get

     \(= 20\times 0.20\)

     \(= 4\)

and,

The standard deviation will be:

→ \(\sigma = \sqrt{np(1-p)}\)

      \(= \sqrt{20\times 0.20\times (1-0.20)}\)

      \(= 1.789\)

Thus the responses above are correct.

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Missing part of the question

Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 25% of all homeowners.....................

Answer:

\(P(X = x) = ^4C_x * 0.25^x * 0.75^{4-x}\)

\(Mean = 1\)

\(Pr = 0.2617\)

Step-by-step explanation:

Given

\(n = 4\)

\(p = 25\%\)

Solving (a): The probability distribution of x

We have:

\(n = 4\)

\(p = 25\%\) \(= 0.25\)

The probability of not having earthquake insurance (q) is:

\(q = 1 - p\)

\(q = 1 - 0.25\) \(= 0.75\)

If x has insurance, then n - x do not.

The distribution follows a binomial pattern. So, the probability distribution is:

\(P(X = x) = ^nC_x * 0.25^x * 0.75^{n-x}\)

Substitute 4 for n

\(P(X = x) = ^4C_x * 0.25^x * 0.75^{4-x}\)

Solving (b): The most likely value of x i.e. The mean

We have:

\(n = 4\) and

\(p = 25\%\) \(= 0.25\)

\(Mean = np\)

\(Mean = 4 * 0.25\)

\(Mean = 1\)

Solving (c): At least 2 of 4 selected have earthquake insurance.

This is calculated as

\(Pr = P(x = 2) + P(x = 3) + P(x = 4)\)

\(P(X = x) = ^4C_x * 0.25^x * 0.75^{4-x}\)

\(P(X=2) = ^4C_2 * 0.25^2 * 0.75^{4-2}\)

\(P(X=2) = 6 * 0.25^2 * 0.75^2 = 0.2109375\)

\(P(X=3) = ^4C_3 * 0.25^3 * 0.75^{4-3}\)

\(P(X=3) = 4 * 0.25^3 * 0.75 = 0.046875\)

\(P(X=4) = ^4C_4 * 0.25^4 * 0.75^{4-4}\)

\(P(X=4) = 1 * 0.25^4 * 1= 0.00390625\)

So:

\(Pr = P(x = 2) + P(x = 3) + P(x = 4)\)

\(Pr = 0.2109375 + 0.046875 + 0.00390625\)

\(Pr = 0.26171875\)

\(Pr = 0.2617\) --- approximated

Answer:

The expression l*w means length times Width, which you will learn in Geometry

Answer:

(a) 3178

(b) 14231

(c) 33152

Step-by-step explanation:

Given

\(y = \frac{269573}{1+985e^{-0.308t}}\)

Solving (a): Year = 1998

1998 means t = 8 i.e. 1998 - 1990

So:

\(y = \frac{269573}{1+985e^{-0.308*8}}\)

\(y = \frac{269573}{1+985e^{-2.464}}\)

\(y = \frac{269573}{1+985*0.08509}\)

\(y = \frac{269573}{84.81365}\)

\(y = 3178\) --- approximated

Solving (b): Year = 2003

2003 means t = 13 i.e. 2003 - 1990

So:

\(y = \frac{269573}{1+985e^{-0.308*13}}\)

\(y = \frac{269573}{1+985e^{-4.004}}\)

\(y = \frac{269573}{1+985*0.01824}\)

\(y = \frac{269573}{18.9664}\)

\(y = 14213\) --- approximated

Solving (c): Year = 2006

2006 means t = 16 i.e. 2006 - 1990

So:

\(y = \frac{269573}{1+985e^{-0.308*16}}\)

\(y = \frac{269573}{1+985e^{-4.928}}\)

\(y = \frac{269573}{1+985*0.00724}\)

\(y = \frac{269573}{8.1314}\)

\(y = 33152\) --- approximated

Answer:

Below

Step-by-step explanation:

The equation to use for CONTINUOUS compounding is :

FV = PV e^(it)

18532.08 = 8327 * e^( i*10)        where i is the interest in decimal form

18532.08/8327  = e^(10i)

2.225541 = e^(10i)             now take natural log  (ln) of both sides to get

.8000 = 10i

i = .08     or 8% interest

Answer:0.70

Step-by-step explanation:

The system of equations plotted on graph 3 has two solutions.

In the given figure, three different parabola and lines are drawn.

The intersection of the parabola and the line represent the solution of that system of equations.

Graph 1:

The parabola and the line do not intersect at each other.

Therefore, the equation has no solution.

Graph 2:

The parabola and the line intersect each other at one point, that is (1, 1).

Therefore, the equation has one solution.

Graph 3:

The parabola and the line intersect each other at two points that is (4, 1) and (0.5, -1).

Therefore, the equation has two solutions.

Therefore, the system of equations plotted on graph 3 has two solutions.

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Answer:

c

Step-by-step explanation:

third graph

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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Step-by-step explanation:

This is a geometric series where our common ratio is -1/2, and a is -4

Since r is less than -1, this series converges so

The sun is

\( \frac{ - 4}{1 + 0.5} \)

\( \frac{ - 4}{1.5} = - \frac{8}{3} \)

The sum is -8)3

Let's take the ratio of the sides

Using proportion,

5/10 = 4/x

cross-multiply

5x = 40

Divide both-side of the equation by 5

x = 8

By definition, Scientific Notation has the following form:

Where "a" is a number greater than or equal to 1, but less than 10 and "b" is an Integer.

In this case, you have this number:

To express it in Scientific notation, follow these steps:

-The decimal point must be after the first digit (which must not be zero), so you must move de the decimal point 7 spaces to the left, so "b" will be positive.

-Then, the exponent "b" will be 7.

So, you get 38,050,000 expressed in scientific notation is :

1. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

2. Probability of no breakdowns = (reliability of a single machine)^3. Probability of at least one breakdown = 1 - Probability of no breakdowns

1. To determine how often the computer should be scheduled for maintenance, we need to consider the reliability and the desired level of operational condition. Since the duration for trouble-free operation follows a gamma distribution with a mean of 40 days, this means that, on average, the computer can operate for 40 days before a breakdown occurs.

To ensure operational condition with a 95% probability, we can calculate the maintenance interval using the concept of reliability. The reliability represents the probability that the machine will not break down within a certain time period. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

Using the gamma distribution parameters, we can find the corresponding reliability for a specific time duration. By setting the reliability equation equal to 0.95 and solving for time, we can find the maintenance interval:

reliability = 0.95

time = maintenance interval

Using reliability and the gamma distribution parameters, we can calculate the maintenance interval.

2. To calculate the probability that at least one of the three machines will break down within the first scheduled maintenance time, we can use the complementary probability approach.

The probability that none of the machines will break down within the first scheduled maintenance time is given by the reliability of a single machine raised to the power of the number of machines:

Probability of no breakdowns = (reliability of a single machine)^3

Since the breakdown times between the machines are statistically independent, we can assume that the reliability of each machine is the same. Therefore, we can use the reliability calculated in the first part and substitute it into the formula:

Probability of at least one breakdown = 1 - Probability of no breakdowns

By calculating this expression, we can determine the probability that at least one of the three machines will break down within the first scheduled maintenance time.

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Hi 

let call "a number" X.

then we have: 4-13X = X + 8 ..

Answer: 2500

Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500

To know if this is a function, simply perform a vertical line test on it.

If it passed the vertical line test then it is a function but if it fails it then it is not a function

In the graph given, if you draw a vertical point at any point, we woulld not have two points on the vertical line, hence it is a function

Answer:

376

Step-by-step explanation:

47 times 8 would be the number of miles that the family took in 8 trips.

Answer:

The slope is 3 and equation of the line is y=3x. I think the answer is the 1st option

Step-by-step explanation:

Given:

y=3x

Direct variation equations have the form:

y=kx,

where

k is the constant of proportionality

so k=3

Answer:

D 9%

Explanation

Answer:

156 cm³

Step-by-step explanation:

The solid is a prism with a trapezoid base.

volume = (area of base) × height

V = (8 cm + 5 cm)(1/2)(4 cm) × 6 cm

V = 156 cm³

Answer:

  1/60 gallon

Step-by-step explanation:

You want to know what is left of 4/5 gallon of paint if 3/4 gallon was used to paint a doghouse, and 2/3 of the remaining amount was used to paint a door.

To find the amount remaining we subtract the amount used for the doghouse from the original amount:

  4/5 -3/4 = (16 -15)/20 = 1/20 . . . . . gallon

2/3 of that was used, so 1/3 of it remains:

  (1/3)(1/20 gallon) = 1/60 gallon

There is 1/60 of a gallon of paint left in the can.

__

Additional comment

In a standard size gallon paint can, that's about 0.11 inches of paint in the bottom.

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Answer:

100 miles

Step-by-step explanation:

Let m be the number of miles.

\(100 + .30m = 50 + .80m\)

\(100 = 50 + .50m\)

\(.50m = 50\)

\(m = 100\)

Answer:

100

Step-by-step explanation:

You can put into a graph such as desmos and see where the lines intersect. the x value of the intersection is the answer you want.

Answer : 5 Step-by-step explanation:

To find the 2 significant figures:

A. 45

Since, there are two non zeros 4 and 5.

Therefore, this has 2 significant figures.

B. 90

Since, it has only one non zero digit 9.

Therefore, it has not 2 significant figures.

C. 180

Since, there are two non zeros 1 and 8.

Therefore, this has 2 significant figures.

D. 22.5

Since, there are three non zeros 2, 2 and 8.

Therefore, this has not 2 significant figures.

Hence, the correct options are A and C.

The interest earned during the third month of the 7th year is $3,613.55.

What is interest rate?

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate.

Let PMT be the monthly payment, r be the monthly interest rate, and n be the total number of payments. Then:

FV = PMT × [(1 + r)n - 1]/r

In this case, we want to find PMT, given that FV = $900,000, r = 0.038/12, and n = 10 × 12 = 120:

\($900,000 = PMT * {[(1 + 0.038/12)}^{120} - 1]/(0.038/12)\)

Solving for PMT, we get:

PMT = $682.48

\(FV = $682.48 * [(1 + 0.038/12)^87 - 1]/(0.038/12)\\\\ = $89,324.47\\\\PV = $682.48 * [(1 + 0.038/12)^83 - 1]/(0.038/12) \\\\= $85,710.92\)

The interest earned during the third month of the 7th year is:

$89,324.47 - $85,710.92 = $3,613.55

Therefore, the interest earned during the third month of the 7th year is $3,613.55.

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Answer:

The power is 32 because that is what 2 to th 5 is , 2 is the base as its the number being multiplied 5 times which leaves 2 as the exponent.

Answer:

P = 1 / 40320       or   P  = 2.48*10⁻⁵

Step-by-step explanation:

The total number of outcomes To is:

To  =  8!       To  =  8*7*6*5*4*3*2

To  =  40320

Of all these outcomes there is only one proper outcome, therefore the probability of having all men and women in alphabetical order is:

P = 1 / 40320       or   P  = 2.48*10⁻⁵