A store sells a 33-pound bag of oranges for \$ 3.60$3.60 and a 55-pound bag of oranges for \$ 5.25$5.25. What is the difference between the price per pound for the 33-pound bag of oranges and the price per pound for the 55-pound bag of oranges? ​ ​The difference is \$$ per pound.

True, The objective function in linear programming is formulated to either maximize or minimize a specific value or quantity.

The goal of linear programming is to optimize this objective function by finding the optimal values for the decision variables within the given constraints. Whether it is maximizing profit, minimizing cost, maximizing production, or minimizing waste, the objective function is designed to achieve the desired optimization outcome.

The objective function in linear programming serves as the goal or target to be achieved. It can involve maximizing profits, minimizing costs, maximizing efficiency, minimizing waste, or any other measurable quantity. The objective function guides the optimization process by defining the objective to be pursued in the linear programming problem.

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Both? or just the westbound?

Answer:

$-83.75

Step-by-step explanation:

She won't have any more money to spend

Multiply $36.75 by 5

That would be $183.75

Subtract 183.75 from 100

-83.75

So Helen wouldn't have anything left to spend.

She would actually be in debt because she used more than $100

Answer:

The total price is $312 and the sales tax is 12

Step-by-step explanation:

300 x 0.04= 12

300 + 12 = 312

To determine the consumption when income increases from $9,000 to $9,500, we can use the concept of the marginal propensity to consume (MPC).

The MPC represents the proportion of each additional dollar of income that is consumed. The marginal propensity to save (MPS) is the complement of the MPC, representing the proportion of each additional dollar of income that is saved.

Given that the MPC is 1 - MPS and the MPS is 0.2, we can calculate the MPC as follows:

MPC = 1 - MPS

MPC = 1 - 0.2

MPC = 0.8

Now, let's calculate the increase in consumption due to the increase in income:

Increase in income = $9,500 - $9,000 = $500

Increase in consumption = MPC * Increase in income

Increase in consumption = 0.8 * $500

Increase in consumption = $400

Finally, to find the new consumption level when income increases to $9,500, we add the increase in consumption to the initial consumption level:

New consumption = Initial consumption + Increase in consumption

New consumption = $10,000 + $400

New consumption = $10,400

Therefore, when income increases to $9,500, the consumption will be $10,400.

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Using the mean formular, the sum of the four scores that are not the median would be 360.

Average or mean score = 450 / 5

Mean score = 90

Hence, median score = mean score = 90

The sum of the 4 scores that are not the median can be calculated thus :

Sum of the 4 scores = 450 - 90 = 360

Hence, the sum of the 4 scores that are not the median is 360.

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To solve this problem, we need to find a common denominator for 5/8 and 3/12.

The prime factorization of 8 is 2 x 2 x 2, and the prime factorization of 12 is 2 x 2 x 3.

A common denominator for 5/8 and 3/12 is the least common multiple (LCM) of 8 and 12, which is 24 (2 x 2 x 2 x 3).

We can convert both fractions to have a denominator of 24 as follows:

5/8 = (5/8) x (3/3) x (3/3) = 15/24

3/12 = (3/12) x (2/2) x (4/4) = 6/24

Now we can add the fractions:

15/24 + 6/24 = 21/24

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 3:

21/24 = (21/3) / (24/3) = 7/8

Therefore, 5/8 + 3/12 = 7/8.

The answer is (B) 7/8.

Answer:

B 7/8

Step-by-step explanation:

showed work in the picture

For similar triangle is:

For similar triangle:

and

So

both triangle then :

LE=11 , LD=9 , LM=90, LN=110

For similar triangle ratio of ED and MN is 9/10

The measure of the angles of the cyclic quadrilateral are:

Arc PQ = 130

QR = 50°

Arc RS = 70°

∠PSQ = 65°

∠PSB = 65°

∠SBP = 80°

AQS = 30°

PS = 110°

From the figure, the arc PQ is subtended by the angle PAQ.

This means that:

PQ = ∠PAQ

Given that ∠PAQ = 130, it means that:

Arc PQ = 130

The measure of PSQ is then calculated using:

∠PSQ = 0.5 * Arc PQ ----- inscribed angle is half a subtended angle.

This gives: ∠PSQ = 0.5 * 130

∠PSQ = 65°

Hence, the measure of ∠PSQ is 65°

The measure of arc QR

A semicircle measures 180°

Thus:

QR + PQ = 180°

Thus, we get:

QR = 180° - PQ

Substitute 130° for PQ

QR = 180° - 130°

QR = 50°

Hence, the measure of QR is 50°

The measure of arc RS

The measure of arc RS is then calculated using:

∠RPS = 0.5 * Arc RS ----- inscribed angle is half a subtended angle.

Where ∠RPS = 35

So, we have:

35 = 0.5 * Arc RS

Multiply both sides by 2

Arc RS = 70°

The measure of angle AQS

In (a), we have:

∠PSQ = 65°

This means that:

∠PSQ = ∠PSB = 65°

So, we have:

∠PSB = 65°

Next, calculate SBP using:

∠SBP + ∠BPS + ∠PSB = 180° ---- sum of angles in a triangle.

So, we have:

∠SBP + 35 + 65 = 180°

∠SBP + 100 = 180

∠SBP = 80°

The measure of AQS is then calculated using:

AQS = AQB = 180 - (180 - SBP) - (180 - PAQ)

AQS = 180 - (180 - 80) - (180 - 130)

AQS = 30°

The measure of arc PS

A semicircle measures 180°

This means that:

PS + RS = 180°

This gives

PS = 180 - RS

RS = 70

Thus:

PS = 180 - 70

PS = 110°

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Answer:

Step-by-step explanation:

The given function is an increasing function that intercepts the x- axis at -6, -2 and 4 and touches at 0.

It has minimum at negative infinity, maximum at positive infinity, local minimums between -2 and 0 and between 0 and 4, local maximum between -6 and -2.

Approximate shape is given in the attached.

Correct choice is the first one, the rest choices are all incorrect.

Answer:

12:8

Step-by-step explanation:

Bill receives £12, and Sue receives £8.

In order to divide £20 between Bill and Sue in the ratio 3:2, we first need to find the total number of parts in the ratio. The sum of the parts in a 3:2 ratio is 3 + 2 = 5.

Next, we determine the value of one part by dividing the total amount (£20) by the total number of parts (5): £20 ÷ 5 = £4.

Now, we can allocate the money to Bill and Sue according to their shares in the ratio. For Bill, who gets 3 parts, we multiply his share of one part (£4) by 3: £4 × 3 = £12. For Sue, who gets 2 parts, we multiply her share of one part (£4) by 2: £4 × 2 = £8.

Thus, Bill receives £12, and Sue receives £8.

In mathematical terms, we can represent the division of £20 between Bill (B) and Sue (S) as follows:

Let the ratio be represented as B:S = 3:2.

Total parts in the ratio = 3 + 2 = 5.

Value of one part (Vp) = Total amount / Total parts = £20 ÷ 5 = £4.

Amount received by Bill (Ab) = 3 parts × Vp = 3 × £4 = £12.

Amount received by Sue (As) = 2 parts × Vp = 2 × £4 = £8.

Thus, Bill receives £12, and Sue receives £8.

In summary, when dividing £20 between Bill and Sue in the ratio 3:2, we follow the steps of finding the total parts in the ratio, calculating the value of one part, and then distributing the amount based on each individual's share in the ratio.

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Answer: Identify the input and output values

Step-by-step explanation: As little information to find the slope we must first find these two values then convert them into two coordinate pairs.

The value of x in the triangle is 777.9

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

The triangle

The value of x in the triangle can be calculated using the following sine rule

sin(40) = 500/x

Make x the subject of the formula

So, we have

x = 500/sn(40)

Evaluate

x = 777.9

Hence, the value of x is  777.9

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Answer:

25x²-60x+36

Step-by-step explanation:

(5x-6)²

Expand the brackets.

(5x-6)(5x-6)

5x(5x-6)-6(5x-6)

Multiply.

25x²-30x-30x+36

Add or subtract the like terms.

25x²-60x+36

Perfect squares trinomials are those expressions which are found by squaring binomial expressions. The expansion of the given binomial expression, (5x - 6)² is (25x² + 36 - 60x).

Perfect squares trinomials are those expressions which are found by squaring binomial expressions. A few examples of perfect squares trinomials are,

a² + b² + 2ab = (a + b)²

a² + b² - 2ab = (a - b)²

The expansion of the given binomial expression, (5x - 6)² can be done as,

(5x - 6)²

= (5x)² + 6² - 2(5x)(6)

= 25x² + 36 - 60x

Hence, The expansion of the given binomial expression, (5x - 6)² is (25x² + 36 - 60x).

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A differential equation is a mathematical equation that relates an unknown function to its derivatives. It describes how the function changes in relation to its independent variable and provides a framework for solving various scientific and mathematical problems.

To solve this problem, let's use the given information to set up a differential equation.

Let's assume that the fraction of the population that has heard the rumor at time t is represented by the variable p(t).

According to the given information, the rate at which the rumor spreads is proportional to the product of p(t) and (1 - p(t)), where (1 - p(t)) represents the fraction of the population that has not yet heard the rumor.

So, we can set up the following differential equation:

dp/dt = k * p(t) * (1 - p(t))

Here, k represents the constant of proportionality.

To solve this differential equation, we can separate the variables and integrate both sides:

1/[p(t) * (1 - p(t))] * dp = k * dt

Integrating both sides:

∫[1/[p(t) * (1 - p(t))]] * dp = ∫k * dt

This integration can be solved using partial fraction decomposition, which is beyond the scope of this platform.

Once you solve the integral, you will obtain an equation in terms of p(t) and t. You can use this equation to find the fraction of the population that has heard the rumor at any given time t.

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If we fix x = 0 and z = 0 only y coordinate can change. So triple (0, y, 0) can only represent a point in y axis.

What do you mean by a plane?

In geometry, a plane is a surface made up of all the lines that are parallel to one another and connect any two locations on it. It is, in other words, a level or flat surface.

                          A plane is defined uniquely through any of the following in a Euclidean space of any number of dimensions: with the aid of three non-collinear points.

For the triple  (x,y,z ) to represent the point on the y - axis .

    x must be 0    y must be a real number

  and z must b 0

For the triple  (x,y,z ) to represent the point on the y - axis .

    x must be 0    y must be 0

  and z must be  a real number

For the triple  (x,y,z ) to represent the point on the y - axis .

    x must be real number     y must be 0

  and z must be  a real number

For the triple  (x,y,z ) to represent the point on the y - axis .

    x must be 0     y must be real number

  and z must be  a real number

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The natural numbers are "closed" under addition and multiplication. ... The subtraction of two natural numbers does NOT necessarily create another natural number (3 - 10 = -7). The division of two natural numbers does NOT necessarily create another natural number (1 ÷ 2 = ½). not closed under subtraction and division.

Answer:

56

Step-by-step explanation:

f(x)= 3x² -2x

f(-4)= 3*(-4)² -2(-4)

= 3*16 +8

=48+8

=56

Answer:

7.

Step-by-step explanation:

7^8 x 7^3 x 7^4 / 7^9 7^5

= 7^(8+3+4) / 7^(9+5)

= 7^15 / 7^14

= 7^(15-14)

= 7.

Answer:

7

Step-by-step explanation:

When the bases of the numbers are the same when multiplying numbers with exponents, you can just add the exponents like so:

\(7^8 * 7^3 * 7^4 = 7^{15}\)

Now, look at the rest of the simplified equation and do the same to the denominator:

\(\frac{7^{15}}{7^9*7^5}\) ⇒ \(\frac{7^{15} }{7^{14} }\)

When the bases are the same in the fraction, you are allowed to subtract the exponents. This will lead you to the simplified answer \(7^{15-14}\) = \(7^1\) = \(7\)

Answer:

-1/2

Step-by-step explanation:

The formula for slope is [ y2-y1/x2-x1 ].

We are given the points (1, 4) and (3, 3).

3-4/3-1

-1/2

Best of Luck!

Answer:

the slope equation is y2-y1/x2-x1

the points given are (1,4) and (3,3)

plug it into the equation and you get:

3-4/3-1

-1/2 is your answer. I hope this helps :)

Answer:

y = 4/3x - 6

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (0, -6) and (6, 2)

We see the y increase by 8, and the x increase by 6, so the slope is

m = 8/6 = 4/3

Y-intercept is located at (0, -6)

So, the equation is y = 4/3x - 6

The work required to pump the oil out of the spout is 4 × 10⁶ Joules.

We have the information from the question:

A tank is is half full of oil that has a density of 900 kg/m3.

We have to find the work w required to pump the oil out of the spout.

By using Pythagoras theorem :

\(r^2+y^2=3^2\\\\r^2+y^2=9\\\\r =\sqrt{9-y^2}\)

Now, We have to find the volume of a tank :

V = \(\pi r^2\)Δy

V = \(\pi (\sqrt{9-y^2})^2\)Δy

V = \(\pi ({9-y^2})\)Δy

Mass = Density × Volume

m = \(\pi ({9-y^2})\)Δy × 900

m = 900 \(\pi ({9-y^2})\)Δy

Now, Find the force

Force = Mass × acceleration due to gravity

Force = 900 \(\pi ({9-y^2})\)Δy × 9.8

Force = 8820  \(\pi ({9-y^2})\)Δy

A distance of 4 - y is moved :

Work  = force × distance

Work =  8820  \(\pi ({9-y^2})\)Δy × 4 -y

Work = \(\int\limits^3_-_3 {8820\pi ({9-y^2})} (4-y)\)

Work =  4 × 10⁶ J

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Answer:

14

Step-by-step explanation:

Note that 14 is a factor of 28 and also a factor of 56.  Thus, 14 is the greatest common factor of 14, 28 and 56.

Answer:

The common factors for 56,28,14 56 , 28 , 14 are −14,−7,−2,−1,1,2,7,14 - 14 , - 7 , - 2 , - 1 , 1 , 2 , 7 , 14 .

Hope that helps

we have the expression

Create the table

For x=0.9

f(x)=0.2041

For x=0.99

f(x)=0.2004

For x=0.999

f(x)=0.2000

For x=1.001

f(x)=0.19996

For x=1.01

f(x)=0.1996

For x=1.1

f(x)=0.1961

using a graphing tool

the exact value of the limit is 0.20

the approximate value of the limit is about 0.1996

Using the percentage method, we know that the original price of the TV set was $400.

Percentages are just fractions with a denominator of 100.

To show that a number is a percentage, we place the percent sign (%) next to it.

For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).

So, we know that the percentage is always out of 100.

Then we automatically know that:

100% - 15% = 85%

We know:
85% = $340

15% = ?

Now, calculate the reduced price as follows:
85/340 = 15/x

85x = 15(340)

85x = 5,100

x = 5100/85

x = $60

Original price of the TV set:

Sold cost + Reduced cost

$340 + $60

$400

Therefore, using the percentage method, we know that the original price of the TV set was $400.

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Answer:

Toby Vail wis taxed for $456

Step-by-step explanation:

First, we make the deductions:

gross pay 18,200 - 1,500 deductions = 16,700 taxable income

Now, we make the tax-calculations:

first $3,000 x 0.015 =       $ 45

above:

(16,700 - 3,000) x 0.03 =  $411

Total tax levied from the State:  $45 + $411 = $456

Notice how the tax is calcualte in brackets to solve for the different taxation rate at different income levels.

The expected number of tails is E(X) = = 1128p^3  and  Var(X)= 1884p^3 1272384p^6

To solve this problem, let's denote the probability of getting a tail as p and the probability of getting a head as 5p, where p is the probability of getting a tail.

a) Expected number of tails (E(X)):

The expected value of a random variable X is calculated by multiplying each possible value of X by its corresponding probability and summing them up.

In this case, X represents the number of tails when the coin is tossed three times. The possible values of X are 0, 1, 2, and 3.

The probability of getting 0 tails is (5p)^3 = 125p^3.

The probability of getting 1 tail is 3*(5p)^2 * p = 375p^3.

The probability of getting 2 tails is 3*(5p)*p^2 = 375p^3.

The probability of getting 3 tails is p^3.

The expected number of tails is:

E(X) = 0*(125p^3) + 1*(375p^3) + 2*(375p^3) + 3*(p^3)

     = 0 + 375p^3 + 750p^3 + 3p^3

     = 1128p^3

b) Expected value of X² (E(X²)):

Similarly, we calculate the expected value of X² by multiplying each possible value of X² by its corresponding probability and summing them up.

The possible values of X² are 0² = 0, 1² = 1, 2² = 4, and 3² = 9.

The expected value of X² is:

E(X²) = 0*(125p^3) + 1*(375p^3) + 4*(375p^3) + 9*(p^3)

     = 0 + 375p^3 + 1500p^3 + 9p^3

     = 1884p^3

c) Variance and standard deviation of X:

The variance of X is calculated as Var(X) = E(X²) - [E(X)]².

Var(X) = E(X²) - [E(X)]²

       = 1884p^3 - (1128p^3)²

       = 1884p^3 - 1272384p^6

The standard deviation of X is the square root of the variance, so the standard deviation of X is:

σ(X) = √[Var(X)]

     = √[1884p^3 - 1272384p^6]

These are the calculations for the expected number of tails, expected value of X², Variance, and standard deviation of X for the given biased coin.

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The expected number of tails is E(X) = = 1128p^3  and  Var(X)= 1884p^3 1272384p^6
To solve this problem, let's denote the probability of getting a tail as p and the probability of getting a head as 5p, where p is the probability of getting a tail.

a) Expected number of tails (E(X)):

The expected value of a random variable X is calculated by multiplying each possible value of X by its corresponding probability and summing them up.

In this case, X represents the number of tails when the coin is tossed three times. The possible values of X are 0, 1, 2, and 3.

The probability of getting 0 tails is (5p)^3 = 125p^3.

The probability of getting 1 tail is 3*(5p)^2 * p = 375p^3.

The probability of getting 2 tails is 3*(5p)*p^2 = 375p^3.

The probability of getting 3 tails is p^3.

The expected number of tails is:

E(X) = 0*(125p^3) + 1*(375p^3) + 2*(375p^3) + 3*(p^3)

    = 0 + 375p^3 + 750p^3 + 3p^3

    = 1128p^3

b) Expected value of X² (E(X²)):

Similarly, we calculate the expected value of X² by multiplying each possible value of X² by its corresponding probability and summing them up.

The possible values of X² are 0² = 0, 1² = 1, 2² = 4, and 3² = 9.

The expected value of X² is:

E(X²) = 0*(125p^3) + 1*(375p^3) + 4*(375p^3) + 9*(p^3)

    = 0 + 375p^3 + 1500p^3 + 9p^3

    = 1884p^3

c) Variance and standard deviation of X:

The variance of X is calculated as Var(X) = E(X²) - [E(X)]².

Var(X) = E(X²) - [E(X)]²

      = 1884p^3 - (1128p^3)²

      = 1884p^3 - 1272384p^6

The standard deviation of X is the square root of the variance, so the standard deviation of X is:

σ(X) = √[Var(X)]

    = √[1884p^3 - 1272384p^6]

These are the calculations for the expected number of tails, expected value of X², Variance, and standard deviation of X for the given biased coin.

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Answer:

93

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

-(-1) - (-2(-1) +3)

1 - (2+3)

1-5=-4

Based on the information provided, we can estimate that a 2100 square expression foot house will cost around $102,770.

In mathematics, an expression is a group of representations, digits, and conglomerates that resemble a statistical correlation or regimen. An expression can be a real number, a mutable, or a combination of the two. Addition, subtraction, rapid spread, division, and exponentiation are examples of mathematical operators. Arithmetic, mathematics, and shape all make extensive use of expressions. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.

We can use linear interpolation based on the given data points to estimate the cost of a 2100 square foot house.

To begin, we can compute the price per square foot for the 1900 and 2200 square foot houses as follows:

Price per square foot for a 1900 square foot house = 196,000 / 1900 = $103.16

Price per square foot for a 2200 square foot house = 225,000 / 2200 = $102.27

Then, using linear interpolation, we can estimate the cost of a 2100 sqft house:

$103.16 + (2100 - 1900) / (2200 - 1900) * ($102.27 - $103.16) = $103.16 + 0.4 * ($102.27 - $103.16) = $103.16 + 0.4 * (-$0.89) = $102.77 thousand

Based on the information provided, we can estimate that a 2100 square foot house will cost around $102,770.

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