Approximately 1 in 28 people of Ashkenazi Jewish descent are Tay-Sachs carriers. In randomly sampling one man and one woman from this population, what is the probability neither is a Tay-Sachs carrier? What is the probability both are carriers?

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Answer:

There is a value of [tex]c[/tex] in (-1, 1), [tex]c = 0.577[/tex].

Step-by-step explanation:

Let [tex]f(x) = x^{3}+2\cdot x[/tex] for [tex]x \in[-1,1][/tex], we need to prove that [tex]f(x)[/tex] is continuous and differentiable to apply the Mean Value Theorem. Given that [tex]f(x)[/tex] is a polynomical function, its domain comprises all real numbers and therefore, function is continuous.

If [tex]f(x)[/tex] is differentiable, then [tex]f'(x)[/tex] exists for all value of [tex]x[/tex]. By definition of derivative, we obtain the following expression:

[tex]f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]

[tex]f'(x) = \lim_{h \to 0} \frac{(x+h)^{3}+2\cdot (x+h)-x^{3}-2\cdot x}{h}[/tex]

[tex]f'(x) = \lim_{h \to 0} \frac{x^{3}+3\cdot x^{2}\cdot h+3\cdot x\cdot h^{2}+h^{3}+2\cdot x+2\cdot h-x^{3}-2\cdot x}{h}[/tex]

[tex]f'(x) = \lim_{h \to 0} \frac{3\cdot x^{2}\cdot h+3\cdot x\cdot h^{2}+h^{3}+2\cdot h}{h}[/tex]

[tex]f'(x) = \lim_{h \to 0} 3\cdot x^{2}+ \lim_{h \to 0} 3\cdot x \cdot h+ \lim_{h \to 0} h^{2}+ \lim_{h \to 0} 2[/tex]

[tex]f'(x) = 3\cdot x^{2}+2[/tex] (Eq. 2)

The derivative of a cubic function is quadratic function, which is also a polynomic function. Hence, the function is differentiable at the given interval.

According to the Mean Value Theorem, the following relationship is fulfilled:

[tex]f'(c) = \frac{f(1)-f(-1)}{1-(-1)}[/tex] (Eq. 3)

If we know that [tex]f(-1) = -3[/tex], [tex]f(1) = 3[/tex] and [tex]f'(c) = 3\cdot c^{2}+2[/tex], then we expand the definition as follows:

[tex]3\cdot c^{2}+2 = 3[/tex]

[tex]3\cdot c^{2} = 1[/tex]

[tex]c = \sqrt{\frac{1}{3} }[/tex]

[tex]c \approx 0.577[/tex]

There is a value of [tex]c[/tex] in the interval (-1, 1), [tex]c = 0.577[/tex].

Answer:

10) m: 6

    b: 5

    y= 6x +5

12)  m: -2

     b: -1

     y= -2x-1

14)  m: 1

     b: 0

     y= x

Step-by-step explanation:

The slope-intercept form is the form y=mx+b

m is the slope. You can find it by finding two points that the line intersects, and counting the number of units between them.

Remember the slope is "rise over run", so, the difference in y over the difference in x.

b is the y-intercept. You can find it by looking at where the line crosses the y-axis.

Hope this helps you out!

Answer:

y = -1/8x + 1

Step-by-step explanation:

Line perpendicular to 8 is -1/8

If the line were to start at the origin, then y- intercept would be 0, and it would pass through the point (-8, 1) To pass through point (-8, 2), add 1 to y in the first example.

Answer:

4/15

Step-by-step explanation:

Make both fractions have equal denominators:

2 x3      ----->   6/15

5 x3

                                            6/15 + 5/15 = 11/15 --->  15/15 - 11/15 = 4/15

1 x5      ------>  5/15

3 x5

Answer:

1/5 - 4

Step-by-step explanation:

First add -15,  8 and 3 to simplify.

And add 2/5 and -1/5

Now you should have 1/5 - 4

Answer:

The equation of the line that is parallel to given line and passes through the point (-8, -3) is: [tex]y = 5x+37[/tex]

Step-by-step explanation:

Given equation of line is:

[tex]y=5x-3[/tex]

The general form of equation of line in slope-intercept form is written as:

[tex]y = mx+b[/tex]

Here m(co-efficient of x) is the slope of the line and b is the y-intercept.

Comparing the given equation with the general form we get

m = 5

Two parallel lines have same slope so the slope of any line parallel to given line will also be 5.

Let m1 be the slope of required line parallel to y=5x-3

Then m1=5

Putting in general form

[tex]y = m_1x+b[/tex]

[tex]y=5x+b[/tex]

To find the value of b(y-intercept) the given point has to be put in the equation from which the line passes.

The point is (-8,-3)

[tex]-3 = 5(-8)+b\\-3 = -40+b\\b = -3+40\\b = 37[/tex]

Putting the value of b and m1, we get

[tex]y = 5x+37[/tex]

Hence,

The equation of the line that is parallel to given line and passes through the point (-8, -3) is: [tex]y = 5x+37[/tex]

Complete question :

Harry fills up his Jeep with gasoline and notes that the odometer reading is 23,568.7 miles. The next time he fills up his Jeep, he pays for 12.6 gallons of gasoline. He notes his odometer reading is 23,706.3 miles. How many miles per gallon did he get?

Answer:

10.9 miles per gallon

Step-by-step explanation:

Given that :

Odometer reading when filled up with gasoline = 23,568.7 miles

Odometer reading with 12.6 gallons of gasoline = 23,706.3 miles

Miles per gallon gotten :

(Current Odometer reading - reading when filled up) / gallon of gasoline

(23706.3 - 23568.7) / 12.6

= 10.920634

= 10.9 miles per gallon

Answer:

[tex]x=325[/tex]°

Step-by-step explanation:

[tex]360-35=325[/tex]

The answer above mine is correct... ^^;

Answer:

60%

Also known as 330 students

Step-by-step explanation:

Plz mark brainliest!!!

Answer:

Work shown below!

Step-by-step explanation:

If 40% of students take the bus, then 60% of 550 students don't take the bus;

[tex]\frac{60}{100}*\frac{550}{1} =6*55=330[/tex]

330 students do not take the bus

Answer: Quadrant 4

Step-by-step explanation:

Answer:

no nobody can help you

Step-by-step explanation:

Answer:

9.375

Step-by-step explanation:

Answer:

Danny paid 2.87$ per gallon of gasoline

Step-by-step explanation: 17.22 divided by 6

Answer:

36

Step-by-step explanation:

50800-30000=10800/300=36

:)

Answer:

0.25

Step-by-step explanation:

La parte decimal de un número decimal exacto está compuesta por una cantidad finita de términos.

Ejemplos:

15.125

0.1

3.0000001

Si en sus factores sólo aparecen 2, 5 o ambos, la fracción es decimal exacta.

Answer:-2/3

-3-2 1/3

which is also

-3 -7/3

which is also

-9/3-7/3

which is

-2/3

Answer:

80 :)

Step-by-step explanation:

Answer:

r=0

Step-by-step explanation:

the line passes through the origin which means there is no y-intercept

Answer:

42

Step-by-step explanation:

from the trigonometric identity

[tex]sin \beta =cos(90 -\beta )[/tex]

if [tex]\beta[/tex]=48 hence

[tex]90-48=42[/tex]

hence

[tex]sin48=cos42[/tex]

Answer:

Step-by-step explanation:

g(x) = 4x + 3

h(x) = 3x + 3

g(x) + h(x) = 7x + 6

Answer:

f(-5) = -3

Step-by-step explanation:

f(x) = x + 2

Let x = -5

f(-5) = -5 + 2

      -3

Answer:

80

Step-by-step explanation:

-5+6/3(2)+9^2

−5+(2)(2)+92

−5+4+92

−1+92

−1+81

= 80

Answer:

3

Step-by-step explanation:

x^2=7/3x+2

3^2=7/3(3)+2

9=7+2

9=9

Answer:

150 years.

Step-by-step explanation:

Just divide 54750 by 365.

Use a calculator.

Answer:

First one

Step-by-step explanation:

Answer:

Hey! No need to fret ok so you are doing 7/6 the answer is 1.16 what do we know about this that is true.

Step-by-step explanation:

You are correct only the sum which is 1.16 is irrational because the product of the numbers is rational. Hope I help have a good day please put me for brainliest Thank You!

Answer:

I think the answer is C it may not be right but I think it is