If h(x) = 3 – x, find:
c. h(x + 1)
d. h(5 - x)

Step-by-step explanation:

step 1. let cows = c and chickens = h

step 2. c + h = 40

step 3. 4c + 2h = 100 (cows have 4 legs and chickens have 2)

step 4. solve the system. multiply step 2 by 2 and subtract from step 3

step 5. 2c = 20 or c = 10 (10 cows)

step 6. h = 30 (30 chickens)

Answer:

35

Step-by-step explanation:

The 14 sweets Peter gets is 2 parts of the ratio, then

14 ÷ 2 = 7 ← number of sweets in 1 part of the ratio , then

5 parts = 5 × 7 = 35 ← number of sweets Bridget gets

The posterior density f(θ|x) is given by ß₀²θ exp(-θx), and the MMSE estimate for θ is E[θ|x] = x/(1+x).

To find the posterior density f(θ|x), we use Bayes' theorem. The prior density f(θ) is given as ß₀² exp(-θ₀). The likelihood function f(x|θ) is the uniform density over the interval 0≤x≤θ. Multiplying the prior and likelihood, we get the unnormalized posterior density f(θ|x) = ß₀²θ exp(-θx). To obtain the normalized posterior density, we divide by the marginal likelihood or evidence, which is the integral of the unnormalized posterior over the entire parameter space. In this case, the integral can be solved, resulting in the posterior density f(θ|x) = ß₀²θ exp(-θx)/x².

To compute the MMSE (Minimum Mean Squared Error) estimate for θ, we find the expected value of the posterior density f(θ|x). Integrating θ times the posterior density from 0 to infinity and dividing by the integral of the posterior density gives us the MMSE estimate. In this case, the MMSE estimate for θ is E[θ|x] = x/(1+x).

In summary, the posterior density f(θ|x) is ß₀²θ exp(-θx)/x², and the MMSE estimate for θ is E[θ|x] = x/(1+x).

Bayesian inference, posterior density, and MMSE estimation to delve deeper into these concepts and their applications.

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Answer:

9.4

Step-by-step explanation:

a2+b2=c2

8^2 + 5^2 = c2

64 + 25 = 89

square root of 89 = 9.4

Answer:

y² = 7

Step-by-step explanation:

The cost of a 13-foot tube with a 5-inch diameter is $13000.

To find the cost, we can set up a proportion using the given information. Since the cost varies jointly with the length and diameter, we can write:

C ∝ L × D

where C is the cost, L is the length, and D is the diameter.

Using the given values for the 14-foot tube with a 5-inch diameter (C = $280, L = 14, D = 5), we can set up a proportion:

280 ∝ 14 × 5

To find the cost of the 13-foot tube, we can rearrange the proportion:

C ∝ L × D

C = (280/14) × (13 × 5)

C = 20 × 65

C = $1300

Therefore, the cost of a 13-foot tube with a 5-inch diameter is $1300.

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Y in represents the following in this linear regression Y = α₀+α₁X+α₂X₂+ε: C. dependent variable.

In Mathematics and Geometry, a regression line is a statistical line that best describes the behavior of a data set. This ultimately implies that, a regression line simply refers to a line which best fits a set of data.

In Mathematics and Geometry, the general functional form of a linear regression can be modeled by this mathematical equation;

Y = α₀+α₁X+α₂X₂+ε

Where:

In conclusion, Y represent the dependent variable or response variable in a linear regression.

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Answer:

true

Step-by-step explanation:

they're not dilated in anyway.

Answer:

How do you want us to answer this?

Answer:

is there a graph because I don't see it

Answer:

3/250

Step-by-step explanation:

21/35 divided by 50 = 21/1750

Simplify this into 3/250

The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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Answer:

D. 11 feet 11 inches

1 foot= 12 inches

143/ 12 = 11 11/12

Answer:

D) 11 feet and 11 inches

Step-by-step explanation:

First we know that there is 12 inches in a foot. So let's start with a.

14 inches x 12 inches (one foot) is 168 inches (so it's not this one:)

13 inches x 12 inches is 156 inches (It's not this one either)

12 inches x 12 inches is 144 inches (not this one)

11 inches x 12 inches is 132 inches (so it could be this one, let's add the remaining inches).

132 + 11 inches = 143 inches.

(Notice I didn't add the remaining inches on A, B, or C because the number of inches was already too much. I did on D because the number of inches was below the given number of 143.

Hope this helps!!

Have a wonderful day!!

Answer:

2/15

Step-by-step explanation:

4/10 * 3/9 = 12/90 = 2/15

======================================================

Work Shown:

x = total bill amount ignoring the tip

18% of x = 0.18x = tip amount

x+0.18x = 1.18x = amount Martin paid = 27

1.18x = 27

x = 27/1.18

x = 22.8813559322033 approximately

x = 22.88 dollars was the total bill.

----------

Checking the answer:

18% of 22.88 = 0.18*22.88 = 4.1184 = 4.12

Martin left a tip of $4.12

Add this on top of the bill to get 22.88+4.12 = 27

This matches with the fact he paid $27.

The answer is confirmed.

Step-by-step explanation:

To find the direction of the resultant vector, we can use the formula:

θ = tan⁻¹(y/x)

where θ is the angle between the vector and the x-axis, y is the vertical component of the vector, and x is the horizontal component of the vector.

First, we need to find the sum of the two vectors:

(11, 11) + (9, -4) = (20, 7)

Now we can plug in the values for x and y:

θ = tan⁻¹(7/20)

Using a calculator, we get:

θ ≈ 19.44° W of V

Therefore, the direction of the resultant vector is approximately 19.44° W of V.

The value of a for which v is a linear combination is given as follows:

a = -8.

v will be a linear combination of the set H if it can be obtained as the solution of a system of equations from the set H.

From the vectors, the system is defined as follows:

From the first equation, the value of x is obtained as follows:

-x = -1

x = 1.

From the second equation, the value of y is obtained as follows:

2x - y = 4

2 - y = 4

y = 2 - 4

y = -2.

From the third equation, the value of z is obtained as follows:

5x + 4y - 3z = -6.

5 - 8 - 3z = -6

3z = 3

z = 1.

Then the value of a needed for the linear combination is of:

a = -x + 3y - z

a = -1 - 6 - 1

a = -8.

The problem is given by the image shown at the end of the answer.

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Answer:

10

I did the calculations

Answer:

Below.

Step-by-step explanation:

This area = circumference of the base x height

= 2 * pi * 8 * 15

= 754.29 cm^2.

Answer:

The answer is 754.29cm^2

Step-by-step explanation:

radius= 8 cm

height= 15 cm

This is an area question

The formula to calculate the curved surface area will be,:

2 pile r  times h which will be = to: 2 pile r h

2 x 22/7/3.14 x the radius which is 8 x height which is 15.

2 x 22/7 x 8 x 15 =

754.29 cm^2.

Okay.

Answer:

x = 23

Step-by-step explanation:

if line j is parallel to line k then

5x + 9 + 33 + x = 180 add like terms

6x + 42 = 180 subtract 42 from both sides

6x = 138 divide both sides by 6

x = 23

The expression that equals 2B+C in standard form is 4x² + 6

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

B = x² + 2

C = 2 + 2x²

The expression to calculate is given as

2B + C

Substitute the known values in the above equation, so, we have the following representation

2B + C = 2x² + 4 + 2 + 2x²

Evaluate the like terms

2B + C = 4x² + 6

Hence, the expression is 4x² + 6

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The function rule for g(x) is f(x) = (x - 5)² + 0.

In Mathematics and Geometry, the translation of a graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

Since the parent function is represented by f(x) = x², a function rule for g(x) is given by;

f(x) = a(x − h)² + k

f(x) = 1(x - 5)² + 0.

f(x) = (x - 5)² + 0.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answers are :

   4.1 :   y = [(3-2k)/(k+1)]x - 12/(k+1)

4.2(a):  k = -1/2

    (b):  k = 17/10

    (c): (3-2k)x = 12

    (d): (k+1)y =12

The given equation is

(3-2k)x + (k+1)y =12   ....(i)

4.1 Rearrange this equation to obtain the form of  y =mx + c

⇒ (k+1)y = (3-2k)x - 12

⇒        y = [(3-2k)/(k+1)]x - 12/(k+1)  is the required form

4.2(a) if (i) is parallel to y = 4x + 7

slope of this line = 4

And slope of line (i)  = (3-2k)/(k+1)

Since these are parallel lines therefore slopes must be equal,

⇒ (3-2k)/(k+1) = 4

⇒ 3-2k = 4k + 4

⇒       k = -1/2

(b) The value of k line passing through (-3, 4)

Put (x, y) = (-3, 4) in (i)

⇒(3-2k)(-3) + (k+1)4 = 12

⇒  -9 + 6k + 4k + 4 = 12

⇒                       10k = 17

⇒                           k = 17/10

(c) line parallel to x axis the put y = 0 in (i)

⇒ (3-2k)x = 12

(d) line parallel to y axis the put x = 0 in (i)

⇒ (k+1)y =12

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Value if p is $16 which maximizes the total revenue.

We need to first find the total revenue equation and then maximize it. Here are the steps:

Step 1: Write the demand equation.
x = 960 - 30p

Step 2: Write the total revenue equation.
Total Revenue (R) = price (p) × quantity (x)
R = px

Step 3: Substitute the demand equation into the total revenue equation.
R = p(960 - 30p)

Step 4: Simplify the total revenue equation.
R = 960p - 30p²

Step 5: Differentiate the total revenue equation with respect to p.
dR/dp = 960 - 60p

Step 6: Set the derivative equal to zero to find the critical points.
0 = 960 - 60p

Step 7: Solve for p.
60p = 960
p = 960/60
p = 16

So, the value of p that maximizes the total revenue is $16.

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Answer:

m∠DAB is 114°

Step-by-step explanation:

The given parameters are;

The dimensions of the given parallelogram ABCD are AD = 19, EC = 15, m∠ABC = 66°, m∠DAC = 78°, m∠BDC = 19°

Given that in parallelogram ABCD, the same side interior angles are supplementary, we have;

m∠ABC and m∠DAB are supplementary

Therefore;

m∠ABC + m∠DAB = 180° by definition of supplementary angles

66° + m∠DAB = 180°

m∠DAB = 180° - 66° = 114°

m∠DAB = 114°.

Answer:

Step-by-step explanation:

To determine the value of k such that (x-4) is a factor of the polynomial f(x) = x³ + 2x² - 11x + k, we need to find the remainder when f(x) is divided by (x-4). If the remainder is zero, then (x-4) is a factor of the polynomial.

Using polynomial long division, we divide f(x) by (x-4):

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Copy code

         x² + 6x + 5

    ____________________

x - 4 | x³ + 2x² - 11x + k

         - (x³ - 4x²)

         ___________

                 6x² - 11x

                 - (6x² - 24x)

                 ___________

                          13x + k

                          - (13x - 52)

                          ___________

                                  k + 52

The remainder is k + 52. For (x-4) to be a factor of the polynomial, the remainder should be zero. Therefore, we have the equation k + 52 = 0.

Solving for k, we get:

k = -52

So, the value of k that makes (x-4) a factor of the polynomial is k = -52.

The project's profitability index (PI) is 1.085 and Yes, the project should be accepted.

To determine the profitability index (PI) of the project, we need to calculate the present value of the cash inflows and compare it to the initial investment.

Given:

Initial investment (Cost of grooming equipment) = $445,000

Expected cash inflows per year = $96,000

Project duration = 6 years

Required return = 11%

a. To calculate the profitability index (PI), we first need to find the present value of the cash inflows using the required return rate. Then we divide the present value of cash inflows by the initial investment.

Using the formula for present value of cash inflows:

PV = CF1 / (1 + r) + CF2 / (1 + r)^2 + ... + CFn / (1 + r)^n

where PV is the present value, CF is the cash inflow, r is the required return rate, and n is the year.

Calculating the present value of cash inflows:

PV = $96,000 / (1 + 0.11)^1 + $96,000 / (1 + 0.11)^2 + ... + $96,000 / (1 + 0.11)^6

PV = $455,090.91

Now we can calculate the profitability index:

PI = PV / Initial investment

PI = $455,090.91 / $445,000

PI = 1.085 (rounded to 3 decimal places)

b. The profitability index (PI) is greater than 1, which indicates that the present value of cash inflows is higher than the initial investment. Therefore, the project should be accepted.

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To evaluate the series Σ(n^2 - 4n + 5)/(n-1) from n=8 to ∞ using the Integral Test, we compare it with the integral of the corresponding function.

Step 1: Determine the corresponding function f(n):

f(n) = (n^2 - 4n + 5)/(n-1) Step 2: Check the conditions of the Integral Test:

(a) The function f(n) is positive and decreasing for n ≥ 8: To check positivity, observe that the numerator (n^2 - 4n + 5) is always positive (quadratic with positive leading coefficient). To check decreasing, take the derivative of f(n) with respect to n and show that it is negative:

f'(n) = (2n - 4)(n-1)/(n-1)^2

The factor (n-1)/(n-1)^2 is always positive, and (2n - 4) is negative for n ≥ 8, so f'(n) is negative for n ≥ 8.

(b) The integral ∫(8 to ∞) f(n) dn is finite or infinite: Let's evaluate the integral: ∫(8 to ∞) f(n) dn = ∫(8 to ∞) [(n^2 - 4n + 5)/(n-1)] dn

= ∫(8 to ∞) [n + 3 + 2/(n-1)] dn

= [(1/2)n^2 + 3n + 2ln|n-1|] evaluated from 8 to ∞

As n approaches infinity, the terms involving n^2 and n dominate, while the term involving ln|n-1| approaches infinity slowly. Therefore, the integral is infinite.

Step 3: Apply the Integral Test:

Since the integral ∫(8 to ∞) f(n) dn is infinite, by the Integral Test, the series Σ(n^2 - 4n + 5)/(n-1) from n=8 to ∞ is also divergent.

Therefore, the series does not converge.

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Answer:

It depends

Step-by-step explanation:

Based on the given info it depends on how much the recipe calls for.  32 fluid ounces is equal to 4 cups, 1 quart, .25 gallons, 64 tablespoons, 192 teaspoons, and 2 pints.  I really hope this answer helped you, and it honestly depends on how much the recipe calls for. :)

Answer:7

Step-by-step explanation: