Imagine that 30% of all U.S. Households own a dog, P(A)=.3 and that 10% of U.S. households own a Honda vehicle, P(B)=.1. In addition, you know that 60% of dog owners own a Honda, P(A|B)=.6. What is the probability of a household owning a Honda given that they are a dog owner?

Answer:

Step-by-step explanation:

Let's solve for y.

−x2+x+0.75y+5xy=x2

Step 1: Add x^2 to both sides.

−x2+5xy+x+0.75y+x2=x2+x2

5xy+x+0.75y=2x2

Step 2: Add -x to both sides.

5xy+x+0.75y+−x=2x2+−x

5xy+0.75y=2x2−x

Step 3: Factor out variable y.

y(5x+0.75)=2x2−x

Step 4: Divide both sides by 5x+0.75.

y(5x+0.75)

5x+0.75

=

2x2−x

5x+0.75

y=

2x2−x

5x+0.75

Answer:

y=

2x2−x

5x+0.75

The Newton-Raphson method is a numerical technique used to find roots of nonlinear equations. Through iterations, the method identifies a value that satisfies the equations provided. Doing this for four iterations, we find that x=0.239294 and y=1.39412.

The Newton-Raphson method uses iterations to find the solution of nonlinear equations. Given the equations y = -x^2+x+0.75 and y+5xy=x^2 and the initial guesses x=y=1.2, we'll use the Newton-Raphson method to find the roots.

We can represent these equations as f(x,y) = -x^2+x+0.75 - y and g(x,y) = x^2 - y - 5xy = 0. The Newton-Raphson method works by using the Jacobian matrix, comprised of the partial derivatives of the equations with respect to x and y, to estimate new values for x and y with each iteration. Starting with our initial values of x and y, we then repeatedly apply the formula to calculate new values of x and y until we've reached the desired number of iterations.

Using this method, you end up with the following values: x=0.239294 and y=1.39412 for iteration 4. Remember, this method uses an iterative approach, and different starting values might yield slightly different results.

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Answer with Step-by-step explanation:

Let A= {a, b,c,d} and B= {1, 2, 3, 4, 5, 6}

Define f:A→B

where  f = {(a, 1), (b, 3), (c, 5), (d, 2)}

a. What is the co-domain of f  

The co-domain or target set of a function is the set into which all of the output of the function is constrained to fall.

Here, all the values are constrained to fall on the set B

Hence, co-domain={1, 2, 3, 4, 5, 6}

b. What is the range of f?

The set of all output values of a function is called range.

Here,  on putting the values of set A we get the output values as:1,2,3 and 5

Hence, Range={1,2,3,5}

c. Is f 1-1 function Explain.

A function for which every element of the range of the function corresponds to exactly one element of the domain.

Yes, f is 1-1

(Since, every element of range i.e. 1,2,3 and 5 corresponds to only one element of set A)

d. Can there exist a bijection between A and B? Explain.

No, there cannot exist bijection from A to B

because if a bijection exist between two sets then there cardinalities are same but A and B have different cardinalities

A has cardinality 4 and B has cardinality 6

Answer:

42.25 feet

Step-by-step explanation:

The height function is a parabola.  The maximum value of a negative parabola is at the vertex, which can be found with:

x = -b/2a

where a and b are the coefficients in y = ax² + bx + c.

Here, we have y = -16t² + 52t.  So a = -16 and b = 52.  The vertex is at:

t = -52 / (2×-16)

t = 13/8

Evaluating the function:

h(13/8) = -16(13/8)² + 52(13/8)

h(13/8) = -169/4 + 169/2

h(13/8) = 169/4

h(13/8) = 42.25

Answer:

42.25 feet.

Step-by-step explanation:

The maximum height can be found by converting to vertex form:

h(t) = 52t - 16t^2

h(t) =   -16 (  t^2  - 3.25t)

h(t) = -16 [ (t - 1.625)^2 - 2.640625 ]

= -16(t - 1.625 ^2) + 42.25

Maximum height = 42.25 feet.

Another method of solving this is by using Calculus:

h(t) = 52t - 16t^2

Finding the derivative:

h'(t) = 52 - 32t

This = zero for  a maximum/minimum value.

52 - 32t = 0

t = 1.625 seconds at maximum height.

It is a maximum because  the  path is a parabola  which opens downwards. we know this because of the  negative coefficient of x^2.

Substituting in the original formula:h(t) = 52(1.625)- 16(1.625)^2

= 42.25 feet.

Answer: 95% confidence interval = 20,000 ± 2.12[tex]\times[/tex][tex]\frac{1500}{\sqrt{17} }[/tex]

( 19228.736 , 20771.263 ) OR ( 19229 , 20771 )

Step-by-step explanation:

Given :

Sample size(n) = 17

Sample mean = 20000

Sample standard deviation = 1,500

5% confidence

∴ [tex]\frac{\alpha}{2}[/tex] = 0.025

Degree of freedom ([tex]d_{f}[/tex]) = n-1 = 16

∵ Critical value at ( 0.025 , 16 ) = 2.12

∴ 95% confidence interval = mean ± [tex]Z_{c}[/tex][tex]\times[/tex][tex]\frac{\sigma}{\sqrt{n} }[/tex]

Critical value  at 95% confidence interval = 20,000 ± 2.12[tex]\times[/tex][tex]\frac{1500}{\sqrt{17} }[/tex]

( 19228.736 , 20771.263 ) OR ( 19229 , 20771 )

Answer:

Given,

The value of the house = $ 185,000,

Percentage of down payment = 15%,

(i) So, the borrowed amount = 185,000 - 15% of 185,000

[tex]=185000-\frac{15\times 185000}{100}[/tex]

[tex]=185000-\frac{2775000}{100}[/tex]

[tex]=185000-27750[/tex]

[tex]=\$157250[/tex]

(ii) Since, the monthly payment formula of a loan is,

[tex]P=\frac{PV\times r}{1-(1+r)^{-n}}[/tex]

Where,

PV = present value of the loan ( or borrowed amount )

r = rate per month,

n = number of months,

Here, PV = $ 157250,

APR = 3.5% = 0.035 ⇒ r = [tex]\frac{0.035}{12}[/tex] ( 1 year = 12 months )

Time = 30 years, ⇒ n = 360 months,

Hence, the monthly payment would be,

[tex]P=\frac{157250\times \frac{0.035}{12}}{1-(1+\frac{0.035}{12})^{-360}}[/tex]

[tex]=706.122771579[/tex]    ( by graphing calculator ),

[tex]\approx \$ 706.12[/tex]

(iii) Interest = Total amount paid - borrowed amount

= 706.122771579 × 360 - 157250

= 96954.1977684

≈ $ 96954. 20

The friend will borrow $157,250 for the mortgage, with a monthly payment of $704.30. They will pay $101,548 in interest over 30 years.

To calculate the amount of money borrowed for the mortgage, we need to subtract the down payment from the total cost of the house. The down payment is 15% of the house cost, which is $185,000 x 0.15 = $27,750. So, the borrowed amount is $185,000 - $27,750 = $157,250.

To calculate the monthly payment, we can use the formula for a fixed-rate mortgage: M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]. Here, P is the borrowed amount ($157,250), i is the monthly interest rate (3.5% / 12 = 0.002916), and n is the total number of monthly payments (30 x 12 = 360). Plugging in these values, we get M = $157,250 [ 0.002916(1 + 0.002916)^360 ] / [ (1 + 0.002916)^360 - 1 ]. Using a calculator, the monthly payment comes out to be approximately $704.30.

To calculate the total interest paid over 30 years, we can multiply the monthly payment by the total number of payments and subtract the borrowed amount. The total interest paid = ($704.30 x 360) - $157,250. Using a calculator, the total interest paid comes out to be approximately $101,548. So, your friend will pay approximately $157,250 for the mortgage, with a monthly payment of approximately $704.30, and will pay approximately $101,548 in interest over 30 years.

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Answer:

20 percent *90. =

(20:100)*90. =

(20*90.):100 =

1800:100 = 18

The correct answer is C.

f(-2)=g(-2)

Think of the number in parentheses as your x value. f(x)=y. In this case the line hit at (-2,4) so when f(x) = 4, g(x)= 4 and 4=4 so you then have to find the x which in this case is -2. I’m pretty bad at explaining but there’s your answer

Answer:

f(-2)=g(-2)

Think of the number in parentheses as your x value. f(x)=y. In this case the line hit at (-2,4) so when f(x) = 4, g(x)= 4 and 4=4 so you then have to find the x which in this case is -2. I’m pretty bad at explaining but there’s your answer

Step-by-step explanation:

Answer:

[tex]f^{-1}(x)=\frac{x+15}{3}[/tex]

or

[tex]f^{-1}(x)=\frac{x}{3}+5[/tex]

Step-by-step explanation:

That means we want to find the inverse function of f(x)=3x-15.

The inverse function is just the swapping of x and y really.  We tend to remake the y the subject afterwards.  

So we are given:

y=3x-15

First step: Swap x and y

x=3y-15

Now it's time to solve for y.

Second step: Add 15 on both sides:

x+15=3y

Third step: Divide both sides by 3:

(x+15)/3=y

The inverse function is:

[tex]f^{-1}(x)=\frac{x+15}{3}[/tex]

You can also split up the fraction like so:

[tex]f^{-1}(x)=\frac{x}{3}+\frac{15}{3}[/tex]

The last fraction there can be reduced:

[tex]f^{-1}(x)=\frac{x}{3}+5[/tex]

Answer:

$5,211.30

Step-by-step explanation:

We have to calculate compound interest with the formula [tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where A =  Amount after maturity

           P = Principal amount ( $4,000)

           r = Rate of interest 13.3% in decimal ( 0.133)

           n = number of compounding period, monthly ( 12 )

            t = Time in years ( 2 )

Now we put the values in the formula

[tex]A=4,000(1+\frac{0.133}{12})^{(12\times 2)}[/tex]

[tex]A=4,000(1+0.0110833)^{(24)}[/tex]

[tex]A=4,000\times 1.0110833^{24}[/tex]

[tex]A=4,000\times 1.3028262297[/tex]

A =  $5,211.30

After 2 years investment would be $5,211.30.

Answer:

my money= $192.5

Natalie's money= $110

Step-by-step explanation:

let my and Natalie's money be 7x and 4x respectively.

Now i gave $15 dollar to Natalie so now

my and Natalie's money will be (7x-15) and (4x+15) respectively.

now my money is 20% more than Natalie

therefore,

[tex]\frac{7x-15}{4x+15} =\frac{6}{5}[/tex]

now calculating for x  we get

x= 27.5

since, my and Natalie's money be 7x and 4x respectively

putting x=27.5

my money= $192.5

Natalie's money= $110

Step-by-step explanation:

-6(n-8)=4(12-5n)+14n

-6n+48=48-20n+14n

20n-6n-14n=48-48

-6n+6n=0

-6n=-6n

The statement is true for any value of n, because both sides are identical.

n€ R.

...

wait ... is this a graphical question ?!?!?!

The answer is:

The solution is all the values that belong to the real numbers,  and any value of "n" that we can substitute, will lead us to a satisfied equation.

We are given the following expression:

[tex]-6(n-8)=4(12-5n)+14n[/tex]

So, we need to perform the expressed operations using the distributive property, and then, add/subtract the like terms.

Now, solving we have:

[tex]-6(n-8)=4(12-5n)+14n[/tex]

[tex]-6*n+(-6*-8)=4*12+(4*-5n)+14n[/tex]

[tex]-6n+48=48-20n+14n[/tex]

[tex]-6n+48=48-6n[/tex]

[tex]0=0[/tex]

Hence, we can se that 0 is equal to 0, it means that the solution is all the values that belong to the real numbers,  and any value of "n" that we can substitute, will lead us to a satisfied equation.

Have a nice day!

Answer:

10.96 hours will take for 85% of the lead to decay.

Step-by-step explanation:

Suppose A represents the amount of Pb-209 at time t,

According to the question,

[tex]\frac{dA}{dt}\propto A[/tex]

[tex]\implies \frac{dA}{dt}=kA[/tex]

[tex]\int \frac{dA}{A}=\int kdt[/tex]

[tex]ln|A|=kt+C_1[/tex]

[tex]A=e^{kt+C_1}[/tex]

[tex]A=e^{C_1} e^{kt}[/tex]

[tex]\implies A=C e^{kt}[/tex]

Let [tex]A_0[/tex] be the initial amount,

[tex]A_0=C e^{0} = C[/tex]

[tex]\implies A=A_0 e^{kt}[/tex]

Since, the half-life of 3.3 hours.

[tex]\implies \frac{A_0}{2}=A_0 e^{3.3k}\implies e^{3.3k}=0.5\implies k=-0.21004[/tex]

[tex]\implies A=A_0 e^{-0.21004t}[/tex]

Here, [tex]A_0=1\text{ gram}[/tex]

[tex]A=(100-85)\% \text{ of }A_0=15\%\text{ of }A_0=0.15A_0[/tex]

By substituting the values,

[tex]0.15A_0=A_0 e^{-0.21004t}[/tex]

[tex]0.15=e^{-0.21004t}[/tex]

[tex]\implies t\approx 10.96\text{ hour}[/tex]

Answer: The mean number of checks written per​ day =  [tex]\lambda=0.3507[/tex]

[tex]\text{Variance}(\sigma^2)=\lambda=0.3507[/tex]

[tex]\text{Standard deviation}=0.5922[/tex]

Step-by-step explanation:

Given : A person wrote 128 checks in last year.

Consider , the last year is a no-leap year.

The number of days in ;last year = 365 days

Let X be the number of checks in one day.

Then , [tex]X=\dfrac{128}{365}=0.350684931507\approx0.3507[/tex]

The mean number of checks written per​ day =  [tex]\lambda=0.3507[/tex]

Now X follows Poisson distribution with parameter [tex]\lambda=0.3507[/tex].

Then , [tex]\text{Variance}(\sigma^2)=\lambda=0.3507[/tex]

[tex]\Rightarrow\sigma=\sqrt{\lambda}=\sqrt{0.3507}=0.59219929078\approx0.5922[/tex]

Answer:

Option D. $850.64; $91.14

Step-by-step explanation:

Joyce Meadow pays her three workers per week  $160, $470 and $800 respectively.

A year has 52 weeks, Therefore quarter has [tex]\frac{52}{4}[/tex] = 13 weeks.

So for a quarter she pays = 160 × 13 = $2,080, 470 × 13 = $6,110, 800 × 13 = $10,400

State rate is 5.6%

Federal rate is 0.6%

Base is $7,000

It means the unemployment needs to be paid on the first $7000 only

So the state unemployment = (0.056 × 2,080) + (0.056 × 6,110) + (0.056 × 7,000)

= 116.48 + 342.16 + 392 = $850.64

Federal unemployment = (0.006 × 2,080) + (0.006 × 6,110) + (0.006 × 7,000)

= 12.48 + 36.66 + 42 = $91.14

Option D. is the correct answer.

Answer: 0.0062

Step-by-step explanation:

Given : Mean : [tex]\mu=\ 31[/tex]

Standard deviation :[tex]\sigma= 4[/tex]

Sample size : [tex]n=100[/tex]

Assume that age of people in the country is normally distributed.

The formula to calculate the z-score :-

[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For x = 32

[tex]z=\dfrac{32-31}{\dfrac{4}{\sqrt{100}}}=5[/tex]

The p-value = [tex]P(x\geq32)=P(z\geq5)[/tex]

[tex]=1-P(z<5)=1- 0.9937903\approx0.0062[/tex]

Hence, the the probability that the average age of our sample is at least =0.0062

The probability that the average age of the sample is at least 32 is approximately 0.62%.

To find the probability that the average age of our sample is at least 32, we can use the normal distribution. The average age of the population is 31 years old and the standard deviation is 4 years. Since we have a large sample size (100), we can use the central limit theorem to assume that the sample mean will follow a normal distribution.

To calculate the probability, we need to find the z-score for the value 32. The z-score formula is z = (x - μ) / (σ / √n), where x is the desired value, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the values, we get z = (32 - 31) / (4 / √100) = 1 / (4 / 10) = 2.5.

Using a z-table or a calculator, we can find that the probability of a z-score of 2.5 or more is approximately 0.0062, or 0.62%.

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Answer:

The selling price is $46 approx.

Step-by-step explanation:

The cost price is = $35.87

Markup is 22% of selling price.

Let the selling price be = 100%

So, 100%-22%=78% = 0.78

So, solution is = [tex]35.87/0.78=45.98[/tex] ≈ $46.

Hence, the selling price is $46 approx.

Answer with explanation:

It is given that , n is Odd integer.

If , n is odd, then it can be Written as with the help of Euclid division lemma

 → n= 2 p +1, as 2 p is even , and adding 1 to it converts it into Odd.

As Euclid lemma states that for any three integers, a ,b and c ,when a is divided by b, gives quotient c and remainder r , then it can be written as:

 a= b c+r, →→0≤r<b

Now, n² will be of the form

(2 p +1)²=(2 p)²+2 × 2 p×1+ (1)²

             =4 p²+4 p +1

⇒Multiplying any positive or negative Integer by 4, gives Even integer and sum  or Difference of two even integer is always even.

So, 4 p²+4 p, will be an even term.But Adding , 1 to it converts it into Odd Integer.

Hence, if n is an Odd number then , n² will be also odd.

Answer:  The required solution of the given system is

(x, y) = (3, 1)  and  (4, 0).

Step-by-step explanation:  We are given to solve the following system of equations :

[tex]x+y=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x^2-8x+16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

From equation (i), we have

[tex]x+y=4\\\\\Rightarrow y=4-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]

Substituting the value of y from equation (iii) in equation (ii), we get

[tex]y=x^2-8x+16\\\\\Rightarrow 4-x=x^2-8x+16\\\\\Rightarrow x^2-8x+16-4+x=0\\\\\Rightarrow x^2-7x+12=0\\\\\Rightarrow x^2-4x-3x+12=0\\\\\Rightarrow x(x-4)-3(x-4)=0\\\\\Rightarrow (x-3)(x-4)=0\\\\\Rightarrow x-3=0,~~~~~~~x-4=0\\\\\Rightarrow x=3,~4.[/tex]

When, x = 3, then from (iii), we get

[tex]y=4-3=1.[/tex]

And, when x = 4, then from (iii), we get

[tex]y=4-4=0.[/tex]

Thus, the required solution of the given system is

(x, y) = (3, 1)  and  (4, 0).

The minimum unit cost is approximately $42,330.09.

To find the minimum unit cost, we need to find the vertex of the quadratic function C(x) = 1.1x^2 - 638x + 111,541. The x-coordinate of the vertex can be found using the formula x = -b / 2a, where a = 1.1 and b = -638. Plugging in these values, we get:

x = -(-638) / (2 * 1.1) = 290.9090909

So the minimum unit cost occurs when approximately 291 engines are made. To find the minimum unit cost, we substitute this value back into the C(x) function:

C(291) = 1.1(291)^2 - 638(291) + 111,541 = 42330.090909

Therefore, the minimum unit cost is approximately $42,330.09.

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Answer:

Step-by-step explanation:

Follow these steps.  First let's look at the problem:

[tex]1.04=2^{\frac{1}{j}}[/tex]

Multiply each side by j/1:

[tex]1.04^{\frac{j}{1}} =2^{\frac{1}{j} *\frac{j}{1}}[/tex]

which simplifies to

[tex]1.04^j=2[/tex]

Now take the natural log of both sides:

[tex]ln(1.04)^j=ln(2)[/tex]

The power rule says that we can bring the exponent down in front of the natural log:

(j) ln(1.04) = ln(2) and then divide both sides by ln(1.04)

Do the division on your calculator to get that j = 17.7

Answer:

1st year: $ 622,500

2nd year: $415,000

3rd year: $207,500

Step-by-step explanation:

Step 1: Write the beginning book value of the asset

$830,000

Step 2: Determine the asset's estimated useful life

8 years

Step 3: Determine the asset's salvage value

$75,000

Step 4: Subtract the salvage value from the beginning value to get the total depreciation amount for the asset's total life.

830,000 - 75,000 = $755,000

Step 5: Calculate the annual depreciation rate

Depreciation rate = 100%/8 years = 12.5%

Step 6: Multiply the beginning value by twice the annual depreciation rate to find the depreciation expense

Depreciation expense = 830,000 x 25% = $207,500

Step 7: Subtract the depreciation expense from the beginning value to find the ending period value

Ending period value for 1st year: Beginning value - depreciation expense

830,000 - 207,500 = $ 622,500

Ending period value for 2nd year: 622,500 - 207,500 = $ 415,000

Ending period value for 3rd year: 415,000 - 207,500 = $ 207,500

!!

Answer:

Mean of a Normal Distribution:

The mean of normal distribution is not always positive, it is equally distributed around mean,mode and median and can be any value from ranging from negative to positive to infinity.

Standard Deviation:

For the standard deviation, it can not be negative. It can only be equal to any positive values i.e., values [tex]\geq 0[/tex].

Answer:

9 TV ads and 20 radio ads

Step-by-step explanation:

He has $37,000 to spend. He has to sum that amount of money between the TV and radio ads. Each TV ad costs $3000 while each radio ad costs $500, so the equation that represents that is 37000 = 3000x  + 500y  

The same happens with the amount of voters he needs to reach, the equation is 130000 = 10000x + 2000y

The system that represents this is

[tex]\left \{ {{3000x+500y=37000} \atop {10000x+2000y=130000}} \right.[/tex]

And the augmented matrix is

[tex]\left[\begin{array}{cc|c}3000&500&37000\\10000&2000&130000\end{array}\right][/tex]

First we divide the first row by 3000 and the second by 10000:

[tex]\left[\begin{array}{cc|c}1&1/6&37/3\\1&1/5&13\end{array}\right][/tex]

Then we multiply the second row by (-1) and we add the first row:

[tex]\left[\begin{array}{cc|c}1&1/6&37/3\\0&-1/30&-2/3\end{array}\right][/tex]

Now we multiply the second row by -30:

[tex]\left[\begin{array}{cc|c}1&1/6&37/3\\0&1&20\end{array}\right][/tex]

Finally, to the first row we add the second one multiply by (-1/6):

[tex]\left[\begin{array}{cc|c}1&0&9\\0&1&20\end{array}\right][/tex]

So, x = 9 and y = 20

That means 9 TV and 20 radio ads will contact 130,000 voters using the allocated funds

Follow the hints.

1. Let [tex]u=\dfrac yx[/tex], so that [tex]y=ux[/tex] and [tex]\mathrm dy=x,\mathrm du+u\,\mathrm dx[/tex]. Substituting into

[tex](xy+y^2)\,\mathrm dx-x^2\,\mathrm dy=0[/tex]

gives

[tex](ux^2+u^2x^2)\,\mathrm dx-x^2(x\,\mathrm du+u\,\mathrm dx)=0[/tex]

[tex]u^2x^2\,\mathrm dx-x^3\,\mathrm du=0[/tex]

and the remaining ODE is separable:

[tex]x^3\,\mathrm du=u^2x^2\,\mathrm dx\implies\dfrac{\mathrm du}{u^2}=\dfrac{\mathrm dx}x[/tex]

Integrate both sides to get

[tex]-\dfrac1u=\ln|x|+C[/tex]

[tex]-\dfrac xy=\ln|x|+C[/tex]

[tex]\boxed{y=\dfrac x{Cx-\ln|x|}}[/tex]

2. [tex]Let [tex]v=\dfrac xy[/tex], so that [tex]x=vy[/tex] and [tex]\mathrm dx=v\,\mathrm dy+y\,\mathrm dv[/tex]. Then

[tex]2x^2y\,\mathrm dx=(3x^3+y^3)\,\mathrm dy[/tex]

becomes

[tex]2v^2y^3(v\,\mathrm dy+y\,\mathrm dv)=(3v^3y^3+y^3)\,\mathrm dy[/tex]

[tex]2v^3y^3\,\mathrm dy+2v^2y^4\,\mathrm dv=(3v^3y^3+y^3)\,\mathrm dy[/tex]

[tex]2v^2y^4\,\mathrm dv=(v^3y^3+y^3)\,\mathrm dy[/tex]

which is separable as

[tex]\dfrac{2v^2}{v^3+1}\,\mathrm dv=\dfrac{\mathrm dy}y[/tex]

Integrating both sides gives

[tex]\dfrac23\ln|v^3+1|=\ln|y|+C[/tex]

[tex]\ln|v^3+1|=\dfrac32\ln|y|+C[/tex]

[tex]v^3+1=Cy^{3/2}[/tex]

[tex]v=\sqrt[3]{Cy^{3/2}-1}[/tex]

[tex]\dfrac xy=\sqrt[3]{Cy^{3/2}-1}[/tex]

[tex]\boxed{x=y\sqrt[3]{Cy^{3/2}-1}}[/tex]

Answer:

Step-by-step explanation:

Based on the question we are given the percentages of each of the types of candies in the bag except for brown. Since the sum of all the percentages equals 75% and brown is the remaining percent then we can calculate that brown is (100-75 = 25%) 25% of the bag. Now we can show the probabilities of getting a certain type of candy by placing the percentages over the total percentage (100%).

Assuming the ratios/percentages of the candies stay the same having an infinite amount of candy will not affect the probabilities. That being said in order to calculate consecutive probability of getting 3 of a certain type in a row we have to multiply the probabilities together. This is calculated by multiplying the numerators with numerators and denominators with denominators.

[tex]\frac{15*85*15}{100*100*100} = \frac{19,125}{1,000,000} = \frac{1.9125}{100}[/tex]

[tex]\frac{80*80*80}{100*100*100} = \frac{512,000}{1,000,000} = \frac{51.2}{100}[/tex]

[tex]\frac{20*100*100}{100*100*100} = \frac{200,000}{1,000,000} = \frac{20}{100}[/tex]

Answer:

  (-1, -1)

Step-by-step explanation:

One way to write the relationship between the x and y coordinates and θ is ...

  tan(θ) = y/x

Then ...

  y = x·tan(θ) = -1·tan(-3π/4) = -1·1

  y = -1

The coordinates of the point on the terminal side are (x, y) = (-1, -1).

Answer: [tex](0.0445,\ 0.0755)[/tex]

Step-by-step explanation:

The confidence interval for the population proportion is given by :-

[tex]p\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}[/tex]

Given : A Bernoulli random variable X has unknown success probability p.

Sample size : [tex]n=100[/tex]

Unknown success probability : [tex]p=0.06[/tex]

Significance level : [tex]\alpha=1-0.99=0.01[/tex]

Critical value : [tex]z_{\alpha/2}=2.576[/tex]

Now, the 99% confidence interval for true proportion will be :-

[tex]0.06\pm(2.576)\sqrt{\dfrac{0.06(0.06)}{100}}\\\\\approx0.06\pm(0.0155)\\\\=(0.06-0.0155,\ 0.06+0.0155)\\\\=(0.0445,\ 0.0755)[/tex]

Hence, the 99% confidence interval for true proportion= [tex](0.0445,\ 0.0755)[/tex]

Answer:

We will accept the null hypothesis

Step-by-step explanation:

Given :[tex]H_0: \mu= 20[/tex]

          [tex]H_a: \mu> 20[/tex]

To Find :  What conclusion is appropriate in each of the following situations?

Solution :

z = 3.3, α = 0.05

So, first we will find the p value corresponding to z value in the z table

So, p-value is 0.999

Since p value is greater than Alpha

0.999>0.05

So, we will accept the null hypothesis

So, the population mean is 20

Answer:

The weekly total revenue function is [tex]R(x,y)=200x-15x^2-220xy+160y-14y^2[/tex].

Step-by-step explanation:

Let the estimated quantities demanded each week of its roll top desks in

the finished and unfinished versions are x and y units respectively.

The unit price of finished furniture is

[tex]p=200-15x-110y[/tex]

The unit price of unfinished furniture is

[tex]q=160-110x-14y[/tex]

Total weekly revenue function is

[tex]R(x,y)=px+qy[/tex]

[tex]R(x,y)=(200-15x-110y)x+(160-110x-14y)y[/tex]

[tex]R(x,y)=200x-15x^2-110xy+160y-110xy-14y^2[/tex]

Combine like terms.

[tex]R(x,y)=200x-15x^2+(-110xy-110xy)+160y-14y^2[/tex]

[tex]R(x,y)=200x-15x^2-220xy+160y-14y^2[/tex]

Therefore the weekly total revenue function is [tex]R(x,y)=200x-15x^2-220xy+160y-14y^2[/tex].

Final answer:

The Weekly Total Revenue Function R(x, y) for Country Workshop's finished and unfinished roll top desks is found by multiplying their demand quantities by their respective unit prices, resulting in R(x, y) = -15x² - 220xy - 14y² + 200x + 160y.

Explanation:

The question asks us to find the weekly total revenue function R(x, y) for Country Workshop, which manufactures both finished and unfinished roll top desks with estimated weekly demands represented by x for finished and y for unfinished versions. The unit prices are given as p=200-15x-110y and q=160-110x-14y dollars, respectively. To calculate the total revenue, we multiply the price of each version by its quantity demanded and sum these values.

Total Revenue Calculation

To find the total revenue, R(x, y), we use the formula: R(x, y) = px + qy. By substituting the given price functions, we get:

This equation represents the weekly total revenue based on the quantities demanded of both the finished and unfinished roll top desks.

Answer:

C) It is a linear function because the graph contains the points (0, 8), (1, 12), (2, 16), which are on a straight line.  

Explanation:

The missing options for this question are:

A) It is a linear function because the graph contains the points (8, 0), (12, 1), (16, 2), which are on a straight line.  

B) It is a nonlinear function because the graph contains the points (8, 0), (12, 1), (16, 2), which are not on a straight line.

C) It is a linear function because the graph contains the points (0, 8), (1, 12), (2, 16), which are on a straight line.  

D) It is a nonlinear function because the graph contains the points (0, 8), (1, 12), (2, 16), which are not on a straight line.

The given equation is:

y = 4x + 8

Replacing x by 0, we get y = 8. This means point (0, 8) lies on the graph of the function.

Replacing x by 1, we get y = 12. This means point (1, 12) lies on the graph of the function.

Replacing x by 2, we get y = 16. This means point (2, 16) lies on the graph of the function.

If we plot these three points on a graph we can draw a straight line through these. Hence, based on this we can conclude that:

C) It is a linear function because the graph contains the points (0, 8), (1, 12), (2, 16), which are on a straight line.  

The line passing through these 3 points would actually be the given equation y = 4x + 8 as one and only one line can pass through 3 distinct points.