Tay-Sachs disease is a genetic disorder that is usually fatal in young children. If both parents are carriers of the disease, the probability that their offspring will develop the disease is approximately 0.25. Suppose that a husband and wife are both carriers and that they have four children. If the outcomes of the four pregnancies are mutually independent, what are the probabilities of the following events?
a. All three children will develop Tay–Sachs disease.
b. Only one child will develop Tay–Sachs disease.
c. The third child will develop Tay–Sachs disease, given that the first two did not.

Answer:

The answer is 1/9 and 1/2

Answer:

a) The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).

b) 30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week.

This means that [tex]n = 77, \pi = \frac{30}{77} = 0.3896[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 - 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.2982[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 + 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.481[/tex]

The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).

Question b:

30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.

Answer:

-30u+20w+10

Step-by-step explanation:

multiple each term inside the parenthesis by -5. remember negative times negative = positive

qualitative

Step-by-step explanation:

b cos the question is in quality format

Answer:

cutee!

SUP???

Hiii friend :]

cuteee~!

prettyyy

Answer:

Step-by-step explanation:

Use the change-of-base rule.

Answer:

1/4

Step-by-step explanation:

that is the answer

I found the constant which was -3

a = 1/4

b=-1

Answer:

the value of a in the function's equation is 1/4

Step-by-step explanation:

Plato answer

Answer:

13.9 (if x is the Hypotenuse)

Step-by-step explanation:

which one is the Hypotenuse (the side opposite of the 90 degree angle) ?

because that determines the calculation.

if x is the Hypotenuse then Pythagoras looks like this

x² = 7² + 12² = 49 + 144 = 193

x = sqrt(193) = 13.9

if 12 is the Hypotenuse, then it looks like this

12² = 7² + x²

144 = 49 + x²

95 = x²

x = sqrt(95) = 9.75

Answer:

5 bags of cement are required.

Step-by-step explanation:

Since to make concrete, the ratio of cement to sand is 1: 3, if cement and sand are sold in bags of equal mass, to determine how many bags of cement are required to make concrete using 15 bags of sand the following calculation must be done:

Cement = 1

Sand = 3

3 = 15

1 = X

15/3 = X

5 = X

Therefore, 5 bags of cement are required.

Answer:

B

Step-by-step explanation:

B is the correct answer

9514 1404 393

Answer:

  (b)  0 = -78

Step-by-step explanation:

Subtracting 6 times the first equation from the second will give ...

  (4x +15y) -6(2/3x +5/2y) = (12) -6(15)

  0 = -78

Answer:

the answer is b

Step-by-step explanation:

Step-by-step explanation:

Given:

[tex]\vec{\textbf{F}}(x, y, z) = ye^z\hat{\textbf{i}} + xe^z\hat{\textbf{j}} + xye^z\hat{\textbf{k}}[/tex]

A vector field is conservative if

[tex]\vec{\nabla}\textbf{×}\vec{\text{F}} = 0[/tex]

Looking at the components,

[tex]\left(\vec{\nabla}\textbf{×}\vec{\text{F}}\right)_x = \left(\dfrac{\partial F_z}{\partial y} - \dfrac{\partial F_y}{\partial z}\right)_x[/tex]

[tex]= xe^z - ye^z \neq 0[/tex]

Since the x- component is not equal to zero, then the field is not conservative so there is no scalar potential [tex]\phi[/tex].

Answer:

Step-by-step explanation:

r is the common ratio.

Third term minus first term is 48.

a₃ - a₁ = 48

a₃ = a₁r²

a₁r² - a₁ = 48

a₁(r²-1) = 48

r²-1 = 48/a₁

Fourth term minus second term is 144.

a₄ - a₂ = 144

a₂ = a₁r

a₄ = a₁r³

a₁r³ - a₁r = 144

a₁r(r²-1) = 144

r²-1 = 144/(a₁r)

48/a₁ = 144/(a₁r)

r = 3

:::::

r²-1 = 48/a₁

a₁ = 6

:::::

a₆ = a₁r⁵ = 1458

(i) The common ratio for the given condition is 3.

ii) The first term of the sequence is 6.

iii) The 6th term of the sequence​ is 1458.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity,

It is given that a  is a geometric progression such that the 3rd term minus a first term is 48. The 4th term minus the 2nd term 144.

Each number following the first in a geometric sequence is multiplied by a particular number, known as the common ratio.

As the third term minus the first term is 48.

a₃ - a₁ = 48

a₃ = a₁r²

a₁r² - a₁ = 48

a₁(r²-1) = 48

r²-1 = 48/a₁

The fourth term minus the second term is 144.

a₄ - a₂ = 144

a₂ = a₁r

a₄ = a₁r³

a₁r³ - a₁r = 144

a₁r(r²-1) = 144

r²-1 = 144/(a₁r)

48/a₁ = 144/(a₁r)

r = 3

r²-1 = 48/a₁

a₁ = 6

a₆ = a₁r⁵ = 1458

Thus the common ratio for the given condition is 3, the first term of the sequence is 6 and the 6th term of the sequence​ is 1458.

Learn more about the sequence here:

brainly.com/question/21961097

#SPJ2

Answer:

E &F

Step-by-step explanation:

The rules of a 30-60-90 Triangle is E, and F is just a different value of numbers (but the same ratio).

Answer:

1/64

Step-by-step explanation:

4^ (-11/3) ÷ 4 ^ (-2/3)

We know a^b ÷a^c = a^(b-c)

4 ^(-11/3 - - 2/3)

4^(-11/3 +2/3)

4^(-9/3)

4^ -3

We know a^-b = 1/a^b

1/4^3

1/64

Answer:

A one solution

Step-by-step explanation:

4(x - 5) = 3x + 7

Distribute

4x - 20 = 3x+7

Subtract 3x from each side

4x-3x-20 = 3x+7-3x

x -20 = 7

Add 20 to each side

x -20+20 = 7+20

x = 27

There is one solution

Answer:

Step-by-step explanation:

Let's simplify that before we make the decision, shall we? We'll get rid of the parenthesis by distribution and then combine like terms.

4x - 20 = 3x + 7 and combining like terms and getting everything on one side of the equals sign:

1x - 27 = 0. Since that x has a power of 1 on it (linear), that means we have only 1 solution. If that was an x², we would have 2 solutions; if that was an x³, we would have 3 solutions, etc.

Answer:

A proportion equation is something like:

[tex]\frac{A}{B} = \frac{x}{C}[/tex]

Where A, B, and C are known numbers, and we want to find the value of x.

Now we want two cases where in one of the numerators we have a mixed number, where a mixed number is something like:

1 and 1/3

which actually should be written as:

1 + 1/3

1) a random problem can be:

[tex]\frac{1 + 1/3}{4} = \frac{x}{5}[/tex]

We can see that the numerator on the left is a mixed number.

First, let's rewrite the numerator then:

1 + 1/3

we need to have the same denominator in both numbers, so we can multiply and divide by 3 the number 1:

(3/3)*1 + 1/3

3/3 + 1/3 = 4/3

now we can rewrite our equation as:

[tex]\frac{4/3}{4} = \frac{x}{5}[/tex]

now we can solve this:

[tex]\frac{4/3}{4} = \frac{4}{3*4} = \frac{x}{5} \\\\\frac{1}{3} = \frac{x}{5}[/tex]

now we can multiply both sides by 5 to get:

[tex]\frac{5}{3} = x[/tex]

Now let's look at another example, this time we will have the variable x in the denominator:

[tex]\frac{7}{12} = \frac{3 + 4/7}{x}[/tex]

We can see that we have a mixed number in one numerator.

Let's rewrite that number as a fraction:

3 + 4/7

let's multiply and divide the 3 by 7.

(7/7)*3 + 4/7

21/7 + 4/7

25/7

Then we can rewrite our equation as

[tex]\frac{7}{12} = \frac{25/7}{x}[/tex]

Now we can multiply both sides by x to get:

[tex]\frac{7}{12}*x = \frac{25}{7}[/tex]

Now we need to multiply both sides by (12/7) to get:

[tex]x = \frac{25}{7}*\frac{12}{7} = 300/49[/tex]

Answer:

b) By analyzing data, we may be able to identify connections and relationships in our data.

Step-by-step explanation:

Answer:

t is less than or equal to $52, or t <= $52

Step-by-step explanation:

If you can't have more than $52, then use less than symbol (<). The sentence doesn't state that a ticket shouldn't cost $52, so it's safe to assume that you can have exactly $52.

Answer:

(-2, 13) (-1,8) (0, 5) (1, 4) (2, 5) (3, 8)

(2.4 , 6) or (-0.4, 6)

Step-by-step explanation:

Graph y = 6 on top of y = [tex]x^{2}[/tex] -2x + 5 and use the points where the two lines meet.

Answer:

Step-by-step explanation:

cotθ = cosθ/sinθ = 2/3

sinθ = 3/√(2²+3²) = 3/√13

cscθ = 1/sinθ = √13/3

Answer:

[tex]a = 4, -4[/tex]

Step-by-step explanation:

Step 1:  Plug in -4 for c

[tex]-a^{2} + c^{2}[/tex]

[tex]-a^{2} + (-4)^{2}[/tex]

[tex]-a^{2} + 16[/tex]

Step 2:  Solve for a

[tex]-a^{2}+16-16=0-16[/tex]

[tex]-a^{2}/-1 = -16/-1[/tex]

[tex]a^{2} = 16[/tex]

[tex]\sqrt{a^{2}} = \sqrt{16}[/tex]

[tex]a = 4, -4[/tex]

Answer:  [tex]a = 4, -4[/tex]

Answer:

Step-by-step explanation:

7/18=7/18

it cant be divided agian

1/3=1/3

it cant be divded agian

1/5=1/5

it cant be divded agian

1/10=1/10

it cant be divded agian

3 1/2=3/2

2 5/9 =10/9

i am not sure if this is what you wanted ...

Answer:

The correct answer is "[tex]2.633< \sigma < 4.480[/tex]".

Step-by-step explanation:

Given:

n = 21

s = 3.3

c = 0.9

now,

[tex]df = n-1[/tex]

    [tex]=20[/tex]

⇒ [tex]x^2_{\frac{\alpha}{2}, n-1 }[/tex] = [tex]x^2_{\frac{0.9}{2}, 21-1 }[/tex]

                  = [tex]31.410[/tex]

⇒ [tex]x^2_{1-\frac{\alpha}{2}, n-1 }[/tex] = [tex]10.851[/tex]

hence,

The 90% Confidence interval will be:

= [tex]\sqrt{\frac{(n-1)s^2}{x^2_{\frac{\alpha}{2}, n-1 }} } < \sigma < \sqrt{\frac{(n-1)s^2}{x^2_{1-\frac{\alpha}{2}, n-1 }}[/tex]

= [tex]\sqrt{\frac{(21-1)3.3^2}{31.410} } < \sigma < \sqrt{\frac{(21.1)3.3^2}{10.851} }[/tex]

= [tex]\sqrt{\frac{20\times 3.3^2}{31.410} } < \sigma < \sqrt{\frac{20\times 3.3^2}{10.851} }[/tex]

= [tex]2.633< \sigma < 4.480[/tex]

Answer:

9/10

Step-by-step explanation:

3/8 ÷5/12

Copy dot flip

3/8 * 12/5

Rewriting

3/5 * 12/8

3/5 * 3/2

9/10

Answer:

0.26684

Step-by-step explanation:

Given that :

Mean, μ = 62.5

Standard deviation, σ = 1.96

P(Z ≥ 63.72)

The Zscore = (x - μ) / σ

P(Z ≥ (x - μ) / σ)

P(Z ≥ (63.72 - 62.5) / 1. 96) = P(Z ≥ 0.6224)

P(Z ≥ 0.6224) = 1 - P(Z < 0.6224)

1 - P(Z < 0.6224) = 1 - 0.73316 = 0.26684

Answer:

It is a ray because there are two points with a line passing through them which is extenging on one side but not on the other.

Answer:

f(0) = 6

Step-by-step explanation:

Complete question:

The function f (x) is given by the set of ordered pairs 1,0 (-10,2), (0,6) (3,17) (-2,-1) which equation is true

f(-10)=1

f(2)=-10

f(0)=6

f(1)=-10

Given the coordinate (x, y). This shows that the input function is x and the output function is y, i.e. f(x) = y

From the pair of coordinates given, hence;

f(1) = 0

f(-10) = 2

f(0) = 6

f(3) = 17

f(-2) = -1

From the following options, this shows that f(0) = 6 is correct

Answer:

f(0) = 6

Step-by-step explanation:

EDGE

Answer:

This answer is 2487

which will be the third one

Hope this help

Answer:

x=60

Step-by-step explanation:

There are different ways to find x but this is what I found easiest.

To solve first note that AOD and CFB are vertical angles; this means that they are congruent. AOD consists of two angles with the measurements of 90 and x. CFB consists of two angles with the measurements of 30 and 2x. So, to find x set add the adjacent angles and set them equal to the other pair of angles. The equation would be [tex]90+x=30+2x[/tex]. First, subtract x from both sides; this makes the equation [tex]90=30+x[/tex]. Then, subtract 30 from both sides. This gives the final answer, x=60.