of the children of this couple who survive, what is probability that they will be affected by achondroplasia?

The answers based on the given information:

1. Output per worker (Y/L) is given as 100. Capital per worker (K/L) is given as 40,000.

2. Investment per worker (I/L) can be calculated using the savings rate (s). I/L = s * (Y/L). Since the savings rate is 20% (0.20), I/L = 0.20 * 100 = 20.

3. Depreciation per worker can be calculated using the depreciation rate (d) and capital per worker (K/L). Depreciation per worker = d * (K/L). Since the depreciation rate is 4% (0.04), Depreciation per worker = 0.04 * 40,000 = 1,600.

4. Net investment per worker can be calculated by subtracting depreciation per worker from investment per worker. Net investment per worker = (I/L) - Depreciation per worker = 20 - 1,600 = -1,580.

5. Since the net investment per worker is negative, capital per worker is decreasing.

7. If capital per worker is 360,000, net investment can be calculated by multiplying the savings rate by the new output per worker (assuming it stays the same) and then subtracting the depreciation. Net investment = (s * (Y/L)) - (d * 360,000) = (0.20 * 100) - (0.04 * 360,000) = 20 - 14,400 = -14,380.

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Answer:

7

Step-by-step explanation:

Answer:

one solution

Step-by-step explanation:

The formula is an = 32 + (n - 1)(-48), which simplifies to an = (-1/2)^(n-1) × 32.

A formula is a mathematical expression used to calculate the value of a variable based on given values. Formulas can be used to describe relationships between variables, and can be used to represent a wide range of functions.

This is an arithmetic sequence, which means that the difference between consecutive terms is constant. In this sequence, the difference between consecutive terms is -48. Therefore, the explicit formula for the nth term of the sequence is an = (-1/2)^(n-1) × 32, where n is the position of the term in the sequence.

This formula can be derived by looking at the first two terms of the sequence: 32 and -16. The difference between them is 48, which means that the common difference of the sequence is -48. Therefore, the next term in the sequence is -16 - (-48) = 32. This follows the pattern of the general explicit formula for an arithmetic sequence, an = a1 + (n - 1)d, where a1 is the first term in the sequence, n is the position of the term in the sequence, and d is the common difference. So, for this sequence, the formula is an = 32 + (n - 1)(-48), which simplifies to an = (-1/2)^(n-1) × 32.

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f'(2) is equal to 11 calculated by using product rule of differentiation.

The product rule is a formula used to find the derivative of a product of two functions. It states that the derivative of the product of two functions u(x) and v(x) is equal to u(x) times the derivative of v(x) plus v(x) times the derivative of u(x), or mathematically:

d/dx(uv) = u(dv/dx) + v(du/dx)

To find f'(2), we need to use the product rule for differentiation:

f'(t) = u'(t)v(t) + u(t)v'(t)

Substituting the given values, we get:

f'(t) = 5t + 2t^2u(2) + 3t^3u(2)

Since u(2) = 1, 2, −2 and v(t) = t, t^2, t^3, we get:

f'(t) = 5t + 2t^2 + 3t^3

Substituting t = 2, we get:

f'(2) = 5(2) + 2(2^2) + 3(2^3) = 11

Therefore, the answer is f'(2) = 11.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The expression that is equivalent to 5^6 is A.125 x 125

Index forms are defined as mathematical forms of writing numbers that are too large or small in more convenient forms.

Other terms for index forms are called standard forms or scientific notations.

They are also described as numbers or variables that are raised to an exponent.

From the information given, we have that;

5⁶

This is replicating 5 in 6 places, we have the representation as;

5 × 5 × 5 × 5 × 5 × 5

Hence, the expression is 125 x 125

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Answer:

x  = 6.2

Step-by-step explanation:

let ‘x’ denotes the weight of a smaller dog.

“1.2″ + x” be the weight of the larger dog

combined weight = 13.6

smaller dog weight =

x+x+1.2 = 13.6

2x + 1.2 = 13.6

2x = 13.6–1.2

2x = 12.4

x = 12.4/2

x = 6.2 pounds.

Hope you understood it, Happy Learning.

Answer:

y=2x+16

Step-by-step explanation:

finally got it lol

Answer:

1.6f+0.4j-13

Step-by-step explanation:

This is the correct answer hope that helped

The value of x is 0. This means that \(8/10 = 16/20 = 4x+6/4x+11\), so the corresponding sides of triangles abc and def have the same ratio.

The similarity of two triangles can be determined by the ratio of their corresponding sides. In the case of triangles abc and def, the ratio of corresponding sides is \(8/10 = 16/20 = 4x+6/4x+11\).

To calculate the value of x, we can use the first two ratios and cross-multiply. With 8/10 = 16/20, we get 8*20=16*10, which simplifies to 160=160. Therefore, the first two ratios are equal.

To calculate the value of x using the third ratio, we can use the same method. With 4x+6/4x+11, we get (\(4x+6)*(4x+11)=4x^2+44x+66\). This simplifies to \(4x^2+44x+66=4x^2+44x+66\), so the third ratio is also equal.

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Complete question:

What is the value of x in the ratio 8/10 = 16/20 = 4x+6/4x+11?

Answer:

B) 9/2

Step-by-step explanation:

18 yards would be 54 feet

54:12  Divide both numbers by 6

9:2

For given parametric curve the equations of both tangents at point where it crosses itself are: y = ± (√15x + 2√15)

The graph of parametric curve x = cos t + 2 cos 2t, y = sin t + 2 sin 2t (t ∈ [0, 2π]) is as shown below.

From the graph we can observe that, the curve crosses itself at (-2, 0).

Let x = -2

cos t + 2 cos 2t = -2,

and y = 0

sin t + 2 sin 2t = 0

sin t + 2 (2 sin(t) cos(t)) = 0

sin t + 4 sin t cos t = 0

sin t(1 + 4 cos t) = 0

sin(t) = 0   OR   1 + 4 cos(t) = 0

sin(t) = 0   OR   cos(t) = -1/4

From sin(t) = 0

⇒ t = 0 or t = π,

but for these values of t, cos t + 2 cos 2t = -2 is not true.

This means, the point (-2, 0) must corresponds to cos(t) = -1/4

\(\Rightarrow t=cos^{-1}(\frac{1}{4} )\)

When cos(t) = -1/4,

sin(t) = \(\frac{\sqrt{15} }{4}\)                ..............(by identity sin²(t) + cos²(t) = 1)

And

\(sin(2t) = 2sin(t)cos (t)\\sin(2t) = 2\times \frac{\sqrt{15} }{4} \times (\frac{-1}{4} )\\\\sin(2t) = -\frac{\sqrt{15} }{8}\)

\(\\\\cos(2t)=2cos^2{t} - 1\\\\cos(2t)=2(\frac{-1}{4} )^2 - 1\\\\cos(2t)=\frac{1}{8}-1\\\\ cos(2t)=\frac{-7}{8}\)

Now we find derivative of given parametric equations with respect to t.

for x = cos t + 2 cos 2t,

dx/dt = -sin(t) -4 sin(2t)

y = sin t + 2 sin 2t

dy/dt = cos(t) + 4 cos(2t)

Consider dy/dx

\(= \frac{\frac{dy}{dt} }{\frac{dx}{dt} }\\\\= \frac{cos(t) + 4 cos(2t) }{-sin(t) -4 sin(2t)}\\\\=\frac{\frac{-1}{4}+4~\frac{-7}{8} }{-\frac{\sqrt{15} }{4}-4~\frac{\sqrt{15} }{8} }\\\\=-\sqrt{15}\)

This means, slope m = -√15

We have the point (−2,0)

Using equation of line y=mx+b the y-intercept would be,

0 = -√15 (−2) + b

b = -2√15

So, the equation for this tangent line :

y = -√15x - 2√15

And the equation of other tangent would be,

y = √15x + 2√15

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do you think it could be x+y=800

Answer:

\(\boxed{\mathrm{108 \pi \;cubic\; inches}}\)

3rd Choice

Step-by-step explanation:

Volume of a cylinder V is given by the equation:
\(V = \pi r^2h\\\\\textrm{where r = radius of the cylinder}\\\\\textrm{and, h = height of the cylinder}\\\\\)

\(\textrm{From the diagram we see the diameter of the cylinder = 6 in }\\\\\mathrm{radius = \dfrac{diameter}{2} }\\\\\mathrm {So\; radius = \dfrac{6}{2} = 3\;in}\\\\\)

\(\mathrm{h = 12\;in}\\\\\\\\\mathrm{V= \pi \cdot 3^2 \cdot 12}\\\\\mathrm{V = \pi \cdot 9 \cdot 12}\\\\\mathrm{V = 108 \pi}\)

Answer

Volume of cylinder =  \(\boxed{\mathrm{108 \pi \;cubic\; inches}}\)

Answer:

in the proprety of the number of negs and postive and y the graph -23+y=8 being that the nuber is -15

Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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Answer:

Step-by-step explanation:

Express 2x2 – 3x – 5 as the product of two binomial factors.

factorize the given expression

2x^2 – 3x – 5

2x^2 – 5x+2x – 5

x(2x-5)+ 1 (2x-5)

(2x-5) (x+1)

Hence the expression as the product of two binomial is (2x-5) (x+1)

Answer:

1/8

Step-by-step explanation:

50/100 * 25/100

1/2 * 1/4 = 1/8

The inequality that shows the number of hours Fiona needs to babysit in order to reach her goal is h>9.

What is inequality?

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

Given that,

Fiona wants to earn at least \(\$\)100

She makes \(\$\)11/hour

in order to reach her goal = 100/11 = \(\$\)9.09 .

The inequality that shows the number of hours Fiona needs to babysit in order to reach her goal is h>9.

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The difference quotient `f(x+h)-f(x)` when `h=h*0` is `-x²`. We are given the function, `f(x) = -x²+3x+8` and we need to evaluate the difference quotient `f(x+h)-f(x)` where `h = h*0`.

The difference quotient `f(x+h)-f(x)` can be evaluated by substituting the given function `f(x) = -x²+3x+8` in it.

`f(x+h)-f(x)`= `[-(x+h)²+3(x+h)+8]-[-x²+3x+8]`

= `[-(x²+2xh+h²)+3x+3h+8]+[x²-3x-8]`

= `(-x²-2xh-h²+3x+3h+8)+(x²-3x-8)`

= `-x²+2xh-h²+3h`

Here, we need to simplify the expression `-x²+2xh-h²+3h` given that `h=h*0`.When `h=0`, we have `-x²+2xh-h²+3h` = `-x²+0-0+0` = `-x²`.

Therefore, the difference quotient `f(x+h)-f(x)` when `h=h*0` is `-x²`.

f(x+h)-f(x)`= `[-(x+h)²+3(x+h)+8]-[-x²+3x+8]`

= `[-(x²+2xh+h²)+3x+3h+8]+[x²-3x-8]`

= `(-x²-2xh-h²+3x+3h+8)+(x²-3x-8)`

= `-x²+2xh-h²+3h`

When `h=0`, we have `-x²+2xh-h²+3h` = `-x²+0-0+0` = `-x²`.

Therefore, the difference quotient `f(x+h)-f(x)` calculated when `h=h*0` is `-x²`.

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Julie has $1,000 and wants to invest it. She has three options: 1-year Treasury note paying 4.4% interest, 1-year CD paying 3.9% interest, or money market mutual fund with an average yield of 3.7%. Pros of Treasury note are high interest rate but con is lack of flexibility. Pros of CD are lower risk and predictable return but con is lower interest rate. Pros of money market fund are liquidity and flexibility but con is lower interest rate.

The investment options available to Julie are 1-year Treasury note paying 4.4 percent interest This option offers the highest interest rate among the three options and is a low-risk investment as it is backed by the government. However, the money is locked in for one year, and there may be penalties for early withdrawal.

1-year CD paying 3.9 percent interest This option is also a low-risk investment, but the interest rate is slightly lower than the Treasury note. The money is also locked in for one year, and there may be penalties for early withdrawal.

Money market mutual fund with an average yield of 3.7 percent This option offers a slightly higher return than a savings account, but the risk level is slightly higher. The money can be withdrawn at any time without penalty, making it a more flexible option.

The pros of the Treasury note and CD options are higher interest rates and low-risk investments, while the cons are that the money is locked in for one year, and there may be penalties for early withdrawal.

The pros of the money market mutual fund are flexibility and slightly higher returns, while the cons are slightly higher risk and lower returns compared to the other two options. Julie should weigh the pros and cons of each option based on her personal financial goals and risk tolerance.

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Answer:

Step-by-step explanation:

The total number of tickets is the sum of the number of adult tickets and the number of kid tickets.

  Total tickets, 2 adult tickets and 16 kids tickets: 2 +16 = 18

  Total tickets, a adult tickets and k kids tickets: a +k

_____

Additional comment

The total price is a different matter:

  $12(2) +$7(16) = $136 . . . for 2 adult and 16 kids

  12a +7k . . . for 'a' adults and 'k' kids

Real numbers are numbers that are continous on the number line. They include positive and negative numbers. They can be integers, natural numbers, rational or irrational numbers.

In this exercise the number 1.030030003 is a real number because it can be found on the real number line

It is also a rational number because it is a repeating decimal

Using compound interest formula when the CD matures on Melissa's 14th birthday, there will be $3187.69 available.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

Use the formula for compound interest to calculate the amount of money that will be available when the CD matures -

\(A = P(1 + r/n)^(nt)\)

Where A is the amount of money available when the CD matures, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, the initial principal is $2000, the interest rate is 6%, and the CD will be held for 8 years (from Melissa's 6th to 14th birthday).

It is not given how many times per year the interest is compounded, so assume it is compounded annually.

Using these values in the formula -

\(A = $2000(1 + 0.06/1)^(1*8)A = $2000(1.06)^8A = $3187.69\)

Therefore, the value is obtained as $3187.69.

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Answer:

\(\tt x=5\)

Step-by-step explanation:

\(\tt 18x-5=13x+4x+1-11\)

\(\tt 18x-17x=15-10\)

\(\tt x=5\)

~

Answer:62.84Step-by-step explanation:pie=3.142c=pie * diameterr=10cmd=2rd=2(10)=20cmc=3.142 * 20c=62.84

Step-by-step explanation:

Answer:

I believe the best answer is 0.45

Answer:

Option 3: 0.45

Step-by-step explanation:

Answer:

\( \huge{ \boxed{ \tt{1 }}}\)

❁ Question : Simplify :

❁ Solution :

First , Use power law of indices.

Remember : If \( \sf{ {a}^{m} }\) is an algebraic term , then

\( \sf{( {a}^{m} ) ^{n} } = {a}^{m \times n} = {a}^{mn} \) , where m and n are positive integers.

➝ \( \sf{ {x}^{a(b - c)} \times {x}^{b(c - a)} \times {x}^{c(a - b)}} \)

➝ \( \sf{ {x}^{ab - ac} \times {x}^{bc - ba} \times {x}^{ca - cb}} \)

Now , Use product law of indices :

Remember : If \( \sf{ {a}^{m} }\) and \( \sf{ {a}^{n}} \) are the two algebraic terms , where m and n are the positive integers then \( \sf{ {a}^{m} \times {a}^{n} = {a}^{m + n}} \)

➝ \( \sf{ {x}^{ab - ac + bc - ba + ca - cb}} \)

Since two opposites adds up to zero , remove them :

➝ \( \sf{ {x} \: ^{ \cancel{ab} \: - \cancel{ac} \: + \cancel{bc} \: - \cancel{ba} \: + \cancel{ca} \: - \cancel{cb} } }\)

➝ \( \sf{ {x}^{0} }\)

Use Law of zero index

Remember : If \( \sf{ {a}^{0}} \) is an algebraic term , where a ≠ 0 , then \( \sf{ {a}^{0} = 1}\)

➝ \( \boxed{ \sf{1}}\)

And we're done !

Hope I helped ! ♡

♪ Have a wonderful day / night ツ

~~

Consequently, the response to the equation 2sin(θ)tan(θ) - 3 = cos(θ) for 0 ≤ θ < 360° is: θ ≈ 83.4° (to one decimal place)

The sine function in mathematics is the relation of the hypotenuse's length to the opposing side's length in a correct triangle. To determine a right triangle's undetermined angle or sides, use the sine formula.

(a) We start with the given equation:

2sin(θ)tan(θ) - 3 = cos(θ)

We know that tan(θ) = sin(θ)/cos(θ), so we can substitute that in to get:

2sin(θ)(sin(θ)/cos(θ)) - 3 = cos(θ)

Simplifying this expression by multiplying both sides by cos(θ), we get:

2sin²(θ) - 3cos(θ) = cos²(θ)

Using the identity sin²(θ) + cos²(θ) = 1, we can substitute sin²(θ) = 1 - cos²(θ) to obtain:

2(1 - cos²(θ)) - 3cos(θ) = cos²(θ)

Simplifying further, we get:

2 - 2cos²(θ) - 3cos(θ) = cos²(θ)

Rearranging terms, we get:

3cos²(θ) + 3cos(θ) - 2 = 0

Therefore, we have shown that the given equation can be written in the form 3cos²(θ) + 3cos(θ) - 2 = 0.

(b) We can solve the equation 3cos²(θ) + 3cos(θ) - 2 = 0 using the quadratic formula:

cos(θ) = [-3 ± √(3² - 4(3)(-2))] / (2(3))

cos(θ) = [-3 ± √(33)] / 6

Using a calculator, we find that cos(θ) ≈ 0.2146 or cos(θ) ≈ -1.5479.

Since 0 ≤ θ < 360°, we know that cos(θ) is positive in the first and fourth quadrants, so we take the positive value of cos(θ):

cos(θ) ≈ 0.2146

To find sin(θ), we can use the identity sin²(θ) + cos²(θ) = 1:

sin(θ) = √(1 - cos²(θ))

sin(θ) ≈ √(1 - 0.2146²) ≈ 0.9763

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