Joey likes beer and whisky and spends £75 in total on drink. His utility function for whisky (w) and beer (b) is = 5 + .
He can buy beer at £2 a can but the liquor store tries to discourage overconsumption of spirits by charging higher prices for larger quantities: the cost in dollars of bottles of whisky works out at !.
a. How many cans of beer and how many bottles of whisky does Joey consume?
b. Illustrate your answer with a clearly labelled diagram showing Joey's budget constraint and his indifference curve passing through the optimal consumption bundle.
c. Joey's friend Ross shops at the same liquor store and spends the same amount on drink. Jim, however, insists on drinking beer and whisky together. His utility function is = min{5, } How much beer and whisky does Jim buy?​

The number of products of each type that they can assemble each week to maintain maximum production are 3 Type A and 2 Type B.

In order to write a system of linear equations that could be used to model the situation, we would assign variables to the cost of component and the labour man-hours respectively as follows:

Next, we would translate the word problem into system of linear equations as follows. Since the business has $156.00 available to buy components each week, a linear equation that models the situation is given by;

36x + 24y = 156      .....equation 1.

Additionally, the total labour man-hours available each week is 96 man-hours;

16x + 24y = 96      .....equation 2.

Subtracting equation 2 from equation 1, we have:

20x = 60

x = 3.

y = (96 - 16x)/2

y = (96 - 16(3))/24

y = 48/24

y = 2.

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Answer:

y= -x+3

Step-by-step explanation:

The slope is -1

The y-intercept is 3 if you count up with rise over run

Put it all together and you get y= -x+3

a) The exponential function for the situation is V(t) = 60000(0.9)^t.

b) After 6 years the value of the equipment will be $31886.46.

c) The price of the equipment will be half of its original price after 6.6 years.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The price of weaving equipment = $60000.

The depreciation rate per year = 10%

The depreciation value will be -

= (1 - 10%)

= 1 - (10/100)

= 1 - 0.10

= 0.9

Let the time in years be measured in t.

The equation for value after t years will be -

V(t) = 60000(0.9)^t

This is an exponential equation.

To find the value of equipment 6 years after purchase, substitute the value of t = 6.

V(t) = 60000(0.9)^t

V = 60000(0.9)^6

V = 60000 × 0.531441

V = 31886.46

Therefore, the value of equipment will be $31886.46.

To find the time at which the value of the equipment will be half its price, substitute the value of V(t) = 30000.

V(t) = 60000(0.9)^t

30000 = 60000(0.9)^t

(0.9)^t = 60000/30000

(0.9)^t = 2

t ln (0.9) = ln (2)

t =  ln (2)/ln (0.9)

t = 0.301/0.0457

t = 6.58 ≈ 6.6

Therefore, after 6.6 years the value of the equipment will be $30000.

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Answer:

Han gets 15$ every 300 envelopes -> Han gets $1 every 20  envelopes

Claire gets $40 every 400 envelopes -> Claire gets $1 every 10 envelopes

A. Claire would make $150 after stuffing 1500 envelopes and make $75 more than Han (Twice the amount)

B. 2:1 Claire being 2 and Han being 1

C. Claire gets paid more in their job. Han does 20 envelopes and gets 1 dollar and Claire does 20 envelopes but gets 2 dollars.

Answer:

£450

Step-by-step explanation:

Answer:

Samuel will need 614 2/3 feet of material to build eight of his standard fences. To find this answer, we simply need to multiply 76 2/3 feet (the perimeter of one fence) by 8 (the number of fences he wants to build). Thus, 76 2/3 feet x 8 = 614 2/3 feet.

Answer:

45

Step-by-step explanation:

you can see that the time increases by 10.

ex: 5+10=15, 15+10=25.

So, 35 + 10 = 45

The area of a two-dimensional cross-section depends on the shape it represents, such as a square, rectangle, triangle, circle, or any other polygon. Each shape has its own formula for calculating its area.

In order to determine the area of the cross-section, we need additional information such as the shape of the cross-section, its dimensions, or any other relevant details. Without this information, it is not possible to calculate the area. Please provide more details or a specific shape or scenario so that an accurate answer can be generated. Once the shape is specified, the appropriate formula can be applied to calculate the area.

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Answer:

6,75sugar

Step-by-step explanation:

2,25

2,25

2 25

=6,75

(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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The given problem involves finding the values of SST, SSR, and SSE, as well as the coefficient of determination and the sample correlation coefficient.  In this case, SST = 1936, SSR = 1504, SSE = 432, The coefficient of determination= 0.776, sample correlation coefficient= 0.88

The sum of squares total (SST) represents the total variability in the response variable, y. This is calculated as the sum of the squared differences between each y value and the mean of all y values. In this case, SST = 1936.

The sum of squares regression (SSR) represents the variability in y that is explained by the regression equation. This is calculated as the sum of the squared differences between the predicted y values from the regression equation and the mean of all y values. In this case, SSR = 1504.

The sum of squares error (SSE) represents the unexplained variability in y. This is calculated as the sum of the squared differences between each observed y value and the predicted y value from the regression equation. In this case, SSE = 432.

The coefficient of determination, denoted as R-squared, measures the proportion of the total variability in y that is explained by the regression equation. In this case, R-squared = SSR/SST = 1504/1936 = 0.776. This means that the regression equation explains 77.6% of the variability in y.

The sample correlation coefficient (r) measures the strength and direction of the linear relationship between x and y. It is calculated as the square root of R-squared. In this case, r = sqrt(R-squared) = sqrt(0.776) = 0.88 (to 2 decimal places).

In conclusion, the regression equation has a relatively good fit with the data as indicated by the high R-squared value of 0.776.

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Answer:

346m^2

Step-by-step explanation:

this is a rectangular prism, find the area of each face and add it up you'll get 346m^2

Answer:

its either A, or B

Step-by-step explanation:

hehehhe

Answer:

B

Step-by-step explanation:

The numbers in each of the circle halves are all in the blue side therefore all numbers on the red side would be eliminated. Leaving you with the options of B or C.

Now the Blue side for every pair is facing each other. So C would be eliminated because the red side is facing the start of the second pair ( A.K.A the third circle)

Leaving us with B.

I apologies if this is wrong! But I hope I helped a little bit

The equation of the tangent plane to the surface at the point (2, -1, -3) is z = -7x - 6y + 5.

To find the equation of the tangent plane to the surface, we need to evaluate the gradient vector ∇f at the given point (2, -1, -3) and use it to write the equation of the tangent plane in the form:

z - z0 = ∇f(x0, y0, z0) · (x - x0, y - y0)

where (x0, y0, z0) is the given point and ∇f(x0, y0, z0) is the gradient vector evaluated at that point.

First, let's compute the partial derivatives of f(x, y) = 3y^2 - 2x^2 + x:

∂f/∂x = -4x + 1

∂f/∂y = 6y

Then, we can evaluate the gradient vector at the point (2, -1, -3):

∇f(2, -1, -3) = (-7, -6, 12)

Now, we can substitute the given point and the gradient vector into the equation of the tangent plane:

z - (-3) = (-7, -6, 12) · (x - 2, y + 1, z + 3)

Expanding the dot product, we get:

z + 3 = -7(x - 2) - 6(y + 1) + 12(z + 3)

Simplifying, we get:

z = -7x - 6y + 5

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Answer:

Step-by-step explanation:

Hi there... I understood your "2" as a typo and considering it as x.

       -(x - 3y = 5)

       -x + 3y = -5

Hence, the resulting equation is '4y = 2'

Hoped this helped.

\(BrainiacUser1357\)

Answer:

Step-by-step explanation:

It seems a typo:

Subtract to eliminate x and solve for y:

Now you can find the value of x:

Answer:

The median is 47

Answer:

$7.5/hour

Step-by-step explanation:

Sonya is paid time and half for hours worked in excess of 40 hours

She has a gross weekly wages of $345 for 44 hours

Let y represent sonya's hourly rate

Since she is paid one and half then it can be represented as 1.5y

Sonya is suppose to work for a period of 40 hours, this means that she has 4 overtime hours

Therefore Sonya regular hourly rate can be calculated as follows

40y + 4(1.5y) = 345

40y + 6y = 345

46y= 345

y = 345/46

y= 7.5

Hence Sonya's regular hourly rate is $7.5/hour

Answer:

2.67 feet long

Step-by-step explanation:

Create a proportion where x is the length of the parking meter's shadow:

\(\frac{23.9}{17.7}\) = \(\frac{3.6}{x}\)

Cross multiply and solve for x:

23.9x = 63.72

x = 2.67

So, the parking meter's shadow is approximately 2.67 feet long

Answer:

\(22\sqrt{2}\)

Step-by-step explanation:

This is a 45-45-90 triangle and the side lengths are in the ratio \(p : p : p\sqrt{2}\). Given that the hypotenuse is \(44\), \(p\sqrt{2} = 44\) and \(p = 22\sqrt{2}\).

Answer:

4h> 14\ cm^{2}

Step-by-step explanation:

Let

b -----> the base of parallelogram

h ----> the height of parallelogram

we know that

The area of parallelogram is equal to

so

substitute the value of b

---->inequality that represents all possible values of h

Answer:

D: 4h> 14

Step-by-step explanation:

Answer:

x=20.5

Step-by-step explanation:

Perimeter of rectangle = 2(L+B)

L- Length and B - Breadth

150 = 2( 2x+4 +30)

150÷2 = 2x + 34

75 = 2x + 34

2x = 75 -34

2x = 41

x = 20.5

The required inequality expression is 8x + 6.50y ≤ 200

Maximum amount he can spend = $200

Cost of doll, = $6.50

Cost of car = $ 8.00

Mathematically, the maximum amount he can spend on restocking is cars and doll is :

(Cost of cars × number of cars) + (cost of doll × number of dolls) ≤ maximum amount

8x + 6.50y ≤ 200

Hence, the required inequality expression is : 8x + 6.50y ≤ 200

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1. The length of the safety rail = Arc length is: 15.7 yd

2. The area of the deck = area of sector is: 78.5 yd²

Area of sector = ∅/360 × πr²

Arc length = ∅/360 × 2πr

1. Length of the safety rail = Arc length = ∅/360 × 2πr

= 90/360 × 2π(10)

= 15.7 yd

2. Area of the deck = area of sector = ∅/360 × πr²

= 90/360 × π(10²)

= 78.5 yd²

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Answer:

median:30 mode:42 range:36

Step-by-step explanation:

i did the math on my netpad and i dont want to type it but there you go goodluck.

Answer:

C

Step-by-step explanation:

The graphs are reflected across the y-axis.

Step-by-step explanation:

.7071 is the value to convert peak to RMS

The missing step in the given solution to the inequality −x − 3 < 13 + 3x is: −4x < 16.

To solve the inequality, we'll perform the necessary steps to isolate the variable x. Let's go through each step:

−x − 3 < 13 + 3x (original inequality)

−4x − 3 < 13 (combine like terms by subtracting 3x from both sides)

−4x < 16 (add 3 to both sides)

At this point, we have −4x < 16 as the inequality, which represents the missing step in the given solution. This step is crucial because it simplifies the inequality further, allowing us to continue solving for x.

To complete the solution, we would divide both sides of the inequality by −4, remembering to reverse the inequality sign because we're dividing by a negative number. However, the missing step provided doesn't show this final division step.

Therefore, the correct missing step is: −4x < 16.

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Answer:

three thousand three hundred and fifty.3,350

Step-by-step explanation:

the question given was:1/4 take a speech, so how many?: one fourth, if you divide 13,400 by 4 its 3,350. that is one fourth  of 13,400. So, if you add 3,350 four times, it would be 13,400.

Hope this helped!<3

Answer:

No

Step-by-step explanation:

(100-5) divided by 7 is about 12 and 100 - (5 divided by 7) is 99 and 2/7