A factory produces chocolate and candy. In order to produce 100 kilograms of chocolate, the factory has to use machine A for 1 hour, machine B for 4 hours, and machine C for 2 hours. In order to produce 100 kilograms of candy, the factory has to usc machine A for 2 hours, machine B for 1 hour, and machine C for 1 hour. The factory will carn 600 pounds for each 100 kilograms of chocolate it produces and 400 pounds for cach 100 kilograms of candy it produces. Machincs A and B bclong to the factory and can be run for free 24 hours per day. However, machine C is rented from a different company and, while it can be run up to 24 hours a day, it costs 10 pounds per hour for running this machine. Write down an LP model to maximisc the factory profit per day. Explain what each of the variables in the LP formulation means.

Since a is parallel to b , taking CE as transversal

m< CED = m<3 = 58° (alternate interior angles)

Answer:

Step-by-step explanation:

Since line A is parallel to line B, then angle 1 and angle D are alternate interior and are congruent. That means that angle 1 is 60. Angle 2 can be found by  subtracting 60 + 58 from 180:

180 - 60 - 58 = 62. Now to find angle 3, we just subtract angle 1 and angle 2 from 180:

180 - 60 - 62 = 58 (which works out perfectly because angle 3 and angle E are congruent as we just found out!)

Answer:

15 / 17 = 0.882

round it to the nearest hundreth.

.89

Step-by-step explanation:

In the Clausius-Clapeyron equation, the variables related to the measured values that would typically be graphed on the x and y axes depend on the specific application.

Generally, the natural logarithm of the vapor pressure (ln P) is plotted on the y-axis, while the reciprocal of the absolute temperature (1/T) is plotted on the x-axis. The slope (m) and y-intercept (b) of the resulting linear graph have specific interpretations in the context of the equation.

The Clausius-Clapeyron equation relates the vapor pressure of a substance to its temperature. It is expressed as ln(P) = -ΔHvap/R * (1/T) + C, where P is the vapor pressure, ΔHvap is the enthalpy of vaporization, R is the gas constant, T is the temperature, and C is a constant. When graphing this equation, we often plot ln(P) on the y-axis and 1/T on the x-axis.

The graph obtained from plotting these variables follows a linear relationship. The slope of the resulting line, denoted as m, is equal to -ΔHvap/R. This slope provides valuable information about the enthalpy of vaporization, which is a measure of the energy required to convert a substance from its liquid phase to its gas phase. The y-intercept, denoted as b, represents the constant C in the equation, which accounts for any initial conditions or deviations from the ideal gas behavior.

By plotting ln(P) against 1/T, we can determine the slope and y-intercept of the linear graph. These parameters have specific physical interpretations and can provide insights into the thermodynamic properties of the substance under investigation. Analyzing the slope and y-intercept values can help in quantifying the enthalpy of vaporization and understanding the behavior of the substance as its temperature changes.

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The statement that describes the graph of y-√√-4x-36 compared to the parent square root function is: d. stretched by a factor of 2, reflected over the y-axis, and translated 9 units left

Stretch by a factor of 2: Multiply the input of the function by 2. The new function is f(2x).

Reflect over the y-axis: Negate the output of the function. The new function is -f(2x).

Translate 9 units left: Subtract 9 from the input of the function. The new function is -f(2x - 9). So if you have an original function f(x) the transformed function would be -f(2x - 9).

Therefore the correct option is d.

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Answer:

92°

Step-by-step explanation:

Answer:

f(0) =  3

f(-2) = 19

Step-by-step explanation:

f(x)= 4x^2 +3

1)   f(x) = 4x^2 +3

    f(0) = 4(0)^2 +3

    f(0) =               3

2)   f(x) = 4x^2 +3

      f(-2) = 4(-2)^2 +3

      f(-2) = 4(4) +3

       f(-2) = 19

Linear pairs are two adjacent angles that form a straight line, with their sum equal to 180 degrees.

To determine which of the given angle pairs are linear pairs, we'll check if they meet these criteria.

a. ∠SRT and ∠TRV: These angles are adjacent and form a straight line. They are a linear pair.
b. ∠SRT and ∠TRU: These angles do not form a straight line, so they are not a linear pair.
c. ∠VRW and ∠WRS: These angles are adjacent and form a straight line. They are a linear pair.
d. ∠VRU and ∠URS: These angles do not form a straight line, so they are not a linear pair.
e. ∠URW and ∠WRS: These angles do not form a straight line, so they are not a linear pair.

Thus, the linear pairs are: ∠SRT and ∠TRV, and ∠VRW and ∠WRS.

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Answer:360ml

Step-by-step explanation:

400/10=10%=40

400-40=360ml

It is possible that the probability distribution of arrival times for Friday might be different from the distribution of arrival times for Saturday.

(a) We need to find the time after the doors open by which 90% of the people who are coming to the Saturday show will have arrived. We can use the inverse normal distribution to find this value. Let X be the time after the doors open. Then, we have:

P(X ≤ x) = 0.90

We know that the mean arrival time is 3 hours and 48 minutes, which is equivalent to 3.8 hours or 228 minutes. We also know that the standard deviation is 52 minutes. Therefore, we can standardize X as follows:

Z = (X - 228) / 52

Using a standard normal distribution table or calculator, we can find the Z-score that corresponds to a cumulative probability of 0.90, which is approximately 1.28. Therefore, we have:

1.28 = (X - 228) / 52

Solving for X, we get:

X = 288.56 minutes or 4 hours and 49 minutes

Therefore, 90% of the people who are coming to the Saturday show will have arrived by 4 hours and 49 minutes after the doors open.

(b) We need to find the time after the doors open by which only 15% of the people who are coming to the Saturday show will have arrived. Using the same approach as in part (a), we have:

P(X ≤ x) = 0.15

Using a standard normal distribution table or calculator, we can find the Z-score that corresponds to a cumulative probability of 0.15, which is approximately -1.04. Therefore, we have:

-1.04 = (X - 228) / 52

Solving for X, we get:

X = 174.32 minutes or 2 hours and 54 minutes

Therefore, only 15% of the people who are coming to the Saturday show will have arrived by 2 hours and 54 minutes after the doors open.

(c) It is possible that the probability distribution of arrival times for Friday is different from the distribution of arrival times for Saturday. There could be several factors that affect the arrival times, such as the day of the week, the type of exhibition, the location, the weather, and so on.

For example, people may have different work schedules or leisure activities on Fridays and Saturdays, which could influence their arrival times. Additionally, people may have different preferences or expectations for Friday and Saturday exhibitions, which could affect their motivation and urgency to arrive.

Therefore, we cannot assume that the probability distribution of arrival times for Friday is the same as the distribution of arrival times for Saturday without further evidence or analysis.

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Answer:

0.41

Step-by-step explanation:

To find h'(3) given h(x) = f(x) xg(x), we use the product rule of differentiation:

h'(x) = f'(x) xg(x) + f(x) g(x) + f(x) xg'(x)

We are not given the functions f(x) and g(x), but we can use the given graphs to estimate their values near x = 3. Let's say that f(3) = 2 and g(3) = 5. We also need to estimate f'(3) and g'(3) in order to calculate h'(3). We can estimate these values using the slopes of the tangent lines to the graphs at x = 3.

Let's say that the slope of the tangent line to the graph of f(x) at x = 3 is 1, and the slope of the tangent line to the graph of g(x) at x = 3 is 3. Then we have:

f'(3) ≈ 1

g'(3) ≈ 3

Substituting these values into the product rule for h'(x), we get:

h'(x) = f'(x) xg(x) + f(x) g(x) + f(x) xg'(x)

h'(3) = f'(3) 3 g(3) + f(3) g(3) + f(3) 3

h'(3) = (1)(3)(5) + (2)(5) + (2)(3)

h'(3) = 19

Therefore, h'(3) is approximately equal to 19, based on the given graphs and our estimates of f'(3) and g'(3).

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The population is estimated to increase by approximately 38,880 people in 1 day.

To calculate the population increase in 1 day, we first need to convert the birth and death rates to a per-day basis. Since there are 60 seconds in a minute and 60 minutes in an hour, there are 60 x 60 = 3600 seconds in an hour, and 24 x 3600 = 86,400 seconds in a day. Therefore, in a day, the population will increase by: [(9 people/2 seconds) x (86,400 seconds/day) / 2] - [(3 people/2 seconds) x (86,400 seconds/day) / 2] = 38,880 people/day.

We multiply the per-second rates by the number of seconds in a day (divided by 2 since we are counting births and deaths separately) to get the per-day rates. We subtract the death rate from the birth rate to get the net population increase per day.

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Answer:

x^2 + {a/(a + b) + (a + b)/a}x + 1 = 0

Delta =  {a/(a + b) + (a + b)/a}^2 - 4

         =  {a/(a + b)}^2 + {(a + b)/a}^2 + 2 - 4

         =  {a/(a + b)}^2 + {(a + b)/a}^2  - 2

         =  {a/(a + b) - (a + b)/a}^2

If a is not equal to zero and a is not equal to -b => delta is always larger than 0

=>  Solution 1 =  - [ {a/(a + b) + (a + b)/a} + |{a/(a + b) - (a + b)/a}| ]/2

=>  Solution 2 = - [ {a/(a + b) + (a + b)/a} - |{a/(a + b) - (a + b)/a}| ]/2

Hope this helps!

:)

Answer:

114

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

1 - 5 = -4

Answer:

x = 1

Step-by-step explanation:

x - 5 = -4 *add 5 to both sides*

x = 1

hope this helps!

The cost price that was used to get the book is: R.S 172

The parameters given are:

Marked Price: M.P = RS. 250

Discount allowed = 10%

The formula to find the selling price here will be:

S.P = M.P * (100 - Discount)/100

Thus:

S.P = 250 * (100 - 14)/100

S.P = 250 * 0.86

S.P = R.S 215

Since the profit is 25%, then we have:

Cost Price = (S.P * 100)/(100 + Gain%)

Cost price = (215 * 100)/(100 + 25)

Cost Price = 21500/125

Cost price = R.S 172

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The possible change in volume (in mm3) resulting from the error in measuring the radius is 32. 06 mm³

Given,

A spherical golf ball is measured to have a radius of $$5 mm, with a possible measurement error of $$0.1 mm

How to determine the volume

The formula for volume of a sphere is expressed by;

Volume = 4/3 πr³

Where;

r is the radius of the sphere

pi takes the value 3.14

From the information given, we have that the measured radius is 5 mm, with a possible measurement error of 0.1 mm

Then, radius  a = 5mm

Radius b = 5 + 0. 1 = 5. 01mm

Now, substitute the values into the formula

Volume, v = 4/ 3 (3.14)(5)³

v = 4/ 3 (392.5)

v = 523. 3 mm³

For radius of 5.01mm

Volume =  4/ 3 (3.14)(5.1)³

expand the bracket

Volume = 4/3 (416.52)

Volume = 555. 4 mm³

The change in volume = 555. 4 - 523. 3 = 32. 06 mm³

Hence, the change in volume is 32. 06 mm³

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Answer:

mei invests $1,924 in a retirement account with a fixed annual interest rate of 3% compounded continuously. what will the account balance be after 19 years?

Answer:

20

Step-by-step explanation:

The interest earned increases with higher principal amounts, higher interest rates, and longer time periods.

Principal (P) | Interest Rate (r) | Time Period (t) | Interest Earned (I)

$1,000 | 2% | 1 year | $20

$5,000 | 4% | 2 years | $400

$10,000 | 3.5% | 3 years | $1,050

$2,500 | 1.5% | 6 months | $18.75

$7,000 | 2.25% | 1.5 years | $236.25

To calculate the interest earned (I), we can use the simple interest formula: I = P * r * t.

For the first row, with a principal of $1,000, an interest rate of 2%, and a time period of 1 year, the interest earned is calculated as follows: I = $1,000 * 0.02 * 1 = $20.

For the second row, with a principal of $5,000, an interest rate of 4%, and a time period of 2 years, the interest earned is calculated as follows: I = $5,000 * 0.04 * 2 = $400.

For the third row, with a principal of $10,000, an interest rate of 3.5%, and a time period of 3 years, the interest earned is calculated as follows: I = $10,000 * 0.035 * 3 = $1,050.

For the fourth row, with a principal of $2,500, an interest rate of 1.5%, and a time period of 6 months (0.5 years), the interest earned is calculated as follows: I = $2,500 * 0.015 * 0.5 = $18.75.

For the fifth row, with a principal of $7,000, an interest rate of 2.25%, and a time period of 1.5 years, the interest earned is calculated as follows: I = $7,000 * 0.0225 * 1.5 = $236.25.

These calculations show the interest earned for different savings principals, interest rates, and time periods.

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Answer:

16

Step-by-step explanation:

To find her hourly rate we need to divide her total salary by the number of hours she worked. In this case we have:

the slope is 1 cos its goin ovr one, up one

y-int is (0,3) or jus strait up 3 cos thts where it crosses the y

iiiif you write it using y=mx+b,, m is the slope n b is the y int so itd jus be: y=x+3

True.

The determinant  of a matrix A is defined as the scaling factor of the linear transformation determined by A.

The determinant  of a matrix A is defined as the scaling factor of the linear transformation determined by A. Geometrically, the absolute value of the determinant of a matrix A can be interpreted as the factor by which the linear transformation determined by A changes the volume of a unit cube.

Consider the columns of A as vectors in n-dimensional space. The parallelepiped determined by the columns of A is the n-dimensional generalization of a parallelogram in two dimensions or a parallelepiped in three dimensions. The volume of this parallelepiped can be computed as the absolute value of the determinant of A.

To see why this is true, consider the special case of a 2x2 matrix A:

```
A = [[a, c],
[b, d]]
```

The columns of A are the vectors `[a, b]` and `[c, d]`. The parallelogram determined by these vectors has area equal to the absolute value of the determinant of t of

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Answer:

To find the constant of proportionality between the cost of the game tickets and the number of tickets purchased, we can write an equation that represents the relationship between the two values. Let's call the constant of proportionality "k".

Step 1: Write an equation for Rocko's purchase:

12.50 = k * 25

Step 2: Solve for k:

k = 12.50 / 25 = 0.50

Step 3: Write an equation for Louisa's purchase:

17.50 = k * 36

Step 4: Substitute the value of k from step 2 into the equation:

17.50 = 0.50 * 36

Step 5: Check if the value of k is the same for both equations:

17.50 / 36 = 0.50

The constant of proportionality is 0.50, which means that for each additional game ticket purchased, the cost increases by $0.50.

Answer:

6

Step-by-step explanation:

This is GCF or greatest common factor. The gcf of 30 and 24 is 6

Becca made a total of 24 rolls and 12 biscuits.

Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.

Becca made 2 trays of rolls and biscuits, with 12 rolls and 6 biscuits in each tray. To find the total number of rolls and biscuits, we need to multiply the number of rolls and biscuits per tray by the number of trays, and then add them together:

Total rolls = 2 trays × 12 rolls per tray = 24 rolls

Total biscuits = 2 trays × 6 biscuits per tray = 12 biscuits

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The amount of interest is $1,782 and the monthly payment is $187.

To find the amount of interest and monthly payment for the loan, we need to use the add-on interest formula. The add-on interest formula is:

\(Total interest = Principal x Interest Rate x Time\)

Total amount due = Principal + Total interest

Monthly payment = Total amount due ÷ Number of payments

Given:

Principal (P) = $4,950

Interest rate (r) = 12%

Time (t) = 3 years

Number of payments (n) = 36 (12 months × 3 years)

Using the formula:

Total interest = P x r x t = $4,950 x 0.12 x 3 = $1,782

Total amount due = P + Total interest = $4,950 + $1,782 = $6,732

Monthly payment = Total amount due ÷ Number of payments = $6,732 ÷ 36 = $187

Therefore, the amount of interest is $1,782 and the monthly payment is $187.

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Answer:

The correct answers for the possible locations for the are;

(-9, 1)

(0, 0)

Step-by-step explanation:

The coordinates of two of the three posts are given in feet as (-5, 4) and (2, 6)

The length of the available fencing = 25 feet

The length, l, of the segment between the coordinates of the two old posts vertices of the fence is given by the following equation;

\(l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}\)

Where;

(x₁, y₁) = (-5, 4)

(x₂, y₂) = (2, 6)

\(l = \sqrt{\left (6-4 \right )^{2}+\left (2-(-5) \right )^{2}} = \sqrt{53} \approx 7.25 \ feet\)

Given the coordinates of the third point as (x₃, y₃), we have;

Therefore, we have;

\(\sqrt{\left (y_{3}-4 \right )^{2}+\left (x_{3}-(-5) \right )^{2}} + \sqrt{\left (y_{3}-6 \right )^{2}+\left (x_{3}-(2) \right )^{2}} = 25 - \sqrt{53}\)

For the point (2, 6), we have;

\(\sqrt{\left ((-6)-4 \right )^{2}+\left (2-(-5) \right )^{2}} + \sqrt{\left ((-6)-6 \right )^{2}+\left (2-(2) \right )^{2}} = 24.2 > 25-\sqrt{53}\)

For the point (-9, 1), we have;

\(\sqrt{\left ((-6)-4 \right )^{2}+\left (2-(-5) \right )^{2}} + \sqrt{\left ((-6)-6 \right )^{2}+\left (2-(2) \right )^{2}} = 17.08 < 25-\sqrt{53}\)

For the point (0, 0), we have;

\(\sqrt{\left ((0)-4 \right )^{2}+\left (0-(-5) \right )^{2}} + \sqrt{\left ((0)-6 \right )^{2}+\left (0-(2) \right )^{2}} = 12.73 < 25-\sqrt{53}\)

For the point (8, 8), we have;

\(\sqrt{\left ((8)-4 \right )^{2}+\left (8-(-5) \right )^{2}} + \sqrt{\left ((8)-6 \right )^{2}+\left (8-(2) \right )^{2}} = 19.92 > 25-\sqrt{53}\)

For the point (-4, -5), we have;

\(\sqrt{\left ((-5)-4 \right )^{2}+\left ((-4)-(-5) \right )^{2}} + \sqrt{\left ((-5)-6 \right )^{2}+\left ((-4)-(2) \right )^{2}} = 22.04 > 25-\sqrt{53}\)

Therefore, the correct answers for the possible locations for the are (-9, 1) and (0, 0).