The probability that at least one of the three children gets the disease from their mother is 97.3%.
To find the probability that at least one child gets the disease from their mother when a female carrier of the gene has three children, we can follow these steps:
1. Define the probabilities:
- Probability that a child gets the disease from their mother (given): [tex]\( P(D) = 0.70 \)[/tex].
- Probability that a child does not get the disease from their mother: [tex]\( P(D^c) = 1 - P(D) = 0.30 \)[/tex].
2. Identify the total number of children:
- Number of children: [tex]\( n = 3 \)[/tex].
3. Calculate the probability that none of the children get the disease:
- For all three children to not get the disease, the probability is [tex]\( (P(D^c))^n = (0.30)^3 \)[/tex].
4. Find the probability that at least one child gets the disease:
- The probability that at least one child gets the disease is the complement of the probability that none of the children get the disease.
- Thus, [tex]\( P(\text{at least one child gets the disease}) = 1 - P(\text{none of the children get the disease}) \)[/tex].
Let's do the calculations step by step.
Step-by-Step Calculations:
1. Calculate the probability that none of the children get the disease:
[tex]\[ P(\text{none of the children get the disease}) = (P(D^c))^3 = (0.30)^3 \][/tex]
2. Perform the exponentiation:
[tex]\[ (0.30)^3 = 0.30 \times 0.30 \times 0.30 = 0.027 \][/tex]
3. Calculate the probability that at least one child gets the disease:
[tex]\[ P(\text{at least one child gets the disease}) = 1 - P(\text{none of the children get the disease}) = 1 - 0.027 = 0.973 \][/tex]
Conclusion:
The probability that at least one child gets the disease from their mother is [tex]\( 0.973 \)[/tex], or 97.3%.
Which equation demonstrates the distributive property?
A) 3 (2 + 8) = 3 (8 + 2)
B) 3 (2 + 8) = 3 × 2 + 3 × 8
C) (3 × 2) × 8 = 3 × (2 × 8)
D) 3 × (2 × 8) = 3 × (8 × 2)
22.6 is an outlier for which of the following sets of data?
1. 22.6, 21.5, 23.7, 22.6, 28.9, 22.6, 20.9
2. 2.4, 5.3, 3.5, 22.6, 1.8, 2.1, 4.6, 1.9
3. 20.5, 20.8, 21.6, 22.6, 23.7, 24.5, 25.1
4. 13.6, 31.7, 25.8, 22.6, 18.9, 21.6, 30.5
Step-by-step explanation: B
help me, please............
3 times the complement of an angle is 30 more than the supplement of the original angle. What is the measure of the angle? 15° 30° 60° 90°
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Which is true about the statements
The graph of f(x) has a vertex of (–4, 6).
The graph of f(x) is horizontally stretched.
The graph of f(x) opens upward.
The graph of f(x) has a domain of x <=–6.
Answer: B) The graph of f(x) is horizontally stretched.
Step-by-step explanation: We are given an absolute function [tex]f(x)=-\frac{2}{3} |x+4|-6[/tex].
The standard equation of an absolute function is [tex]f(x)= a|x-h|+k[/tex].
Where (h,k) is the vertex of the absolute function.
If we compare [tex]f(x)=-\frac{2}{3} |x+4|-6[/tex] and [tex]f(x)= a|x-h|+k[/tex], we can see a=[tex]-\frac{2}{3}[/tex], h= -4 and h= -6.
Therefore, vertex of the given function is (-4,-6).Because we have value of a is a negative number so it would open down.An absolute function always have domain " All real numbers".Therefore, first, third and fourth options are incorrect.
So, the second option would only be applicable.
B) The graph of f(x) is horizontally stretched.What is the following difference? 11 square root 45 - 4 square root 5
Answer:
[tex]29\sqrt{5}.[/tex]
Step-by-step explanation:
The difference is
[tex]11\sqrt{45}-4\sqrt{5}[/tex]
To simplify let's try to covert [tex]\sqrt{45}[/tex] in terms of [tex]\sqrt{5}[/tex]:
45 = 9*5, then [tex]\sqrt{45} = \sqrt{9*5} = \sqrt{9}\sqrt{5} = 3\sqrt{5}[/tex]. So,
[tex]11\sqrt{45}-4\sqrt{5} = 11(3\sqrt{5})-4\sqrt{5} = 33\sqrt{5} -4\sqrt{5} = 29\sqrt{5}.[/tex]
Find two consecutive whole numbers that 101 lies between
We can see here that the two consecutive whole numbers that 101 lies between are 100 and 102.
To find two consecutive whole numbers that 101 lies between, we can start by finding the smaller whole number.
Since 101 is greater than 100, the smaller whole number would be 100.
To find the larger whole number, we can add 2 to the smaller whole number:
100 + 2 = 102
Thus, we see here that 100 and 102 are the two consecutive numbers where 101 lies between. As we see above, we see the process of finding the numbers.
Consecutive numbers are numbers that follow each other in order without any gaps and have a difference of 1 between each number. In other words, they are numbers that come one after another in a sequence.
Use inductive reasoning to find the next term in the sequence 1, 2, 4, 7, 11, 16… what is the next term?
a. 18
b. 19
c. 22
d. 26
Bernadette is at the turtle tank. There are 32 green (g) and yellow (y) turtles in the tank. There are 3 times as many yellow turtles as green turtles. Using the guess and check method, determine how many yellow turtles are in the tank.
Answer:
24
Step-by-step explanation:
The turtle tank has 24 yellow turtles, computed using the guess and check method.
What is the guess and check method?The guess and check method is the process of guessing a solution to the given conditions that will be satisfying all the conditions.
How to solve the question?In the question, we are informed that Bernadette is at the turtle tank, which has 32 green and yellow turtles in the tank. We are also informed that there are 3 times as many yellow turtles as green turtles.
Assuming the number of green turtles to be g, and the number of yellow turtles to be y, we can write the equation g + y = 32, as the total number of turtles is given to be 32.
Now, we are told that the number of yellow turtles is 3 times the number of yellow turtles.
Thus, we can say that y = 3g.
Substituting this in the equation, we get g + 3g = 32, or, 4g = 32.
We are asked to solve this equation by the guess and check method.
If we guess g to be 7, the equation is not satisfied as we get 28 = 32.
If we guess g to be 9, the equation is not satisfied as we get 36 = 32.
If we guess g to be 8, the equation is satisfied as we get 32 = 32.
Thus, the correct value for g is 8.
Thus, y = 3g = 3*8 = 24.
Thus, the turtle tank has 24 yellow turtles, computed using the guess and check method.
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He first three terms of a geometric sequence are as follows. 10 , 30 , 90 find the next two terms of this sequence.+
The next two terms of the given geometric sequence is 810.
The first three terms of a geometric sequence are 10, 30, 90.
What is a geometric sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.
The formula to find nth term of the geometric sequence is [tex]a_n = ar^{n - 1[/tex].
Where, a = first term of the sequence, r= common ratio and n = number of terms.
Here, the common ratio is 30/10 = 90/30 = 3
Now, [tex]a_4=10\times 3^{4-1}[/tex]
= 10 × 3³
= 270
[tex]a_5=10\times 3^{5-1}[/tex]
= 810
Therefore, the next two terms of the given geometric sequence is 810.
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Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle A?
Enter your answer in the box.
°
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1) An Egyptian pyramid has a square base that measures 80 meters on each side. If the height of the pyramid is 30 meters, what is the slant height of the pyramid?
2) A room in a bank is shaped like the rectangular prism shown below. The room has a security system that is triggered by two laser beams which stretch from Point A to D and Point B to C. How many total feet of laser beams are there?
*A 3-D rectangle 15 ft. length the back rectangle 12 ft. width the side 35 ft. width front*
Answer:
1) the slant height of the pyramid is 50 meters.
2) there are (approximately) a total of 80 ft of laser beams.
Step-by-step explanation:
1) The height of the pyramid (30 m) and half of the length of its base (40 m) form a rectangular triangle, where the slant height is its hypotenuse (H). From Pythagorean theorem:
H^2 = 30^2 + 40^2
H = √2500
H = 50 m
2) In the figure attached the rectangular prism is shown (point E was added).
The length of the laser beams is the addition of the segments AD to segment CB (which are equal).
We can make a rectangular triangle between points ECD. From Pythagorean theorem:
ED^2 = EC^2 + CD^2
ED = √(12^2 + 35^2)
ED = 37 ft
We can make a rectangular triangle between points AED. From Pythagorean theorem:
AD^2 = EA^2 + ED^2
AD = √(15^2 + 37^2)
AD ≈ 40
Then, there are (approximately) a total of 80 ft of laser beams.
Need help on questions 1, and 2 please
Kohl's sells casual shirts for $9 and polo shirts for $18.00. Total sales were $1,080, and customers bought 4 times as many casual as polo shirts. How many casual shirts did Kohl's sell?
a. 40
b. 12
c. 20
d. 60
When you add two rational numbers, each number can be written as a?
When you add two rational numbers, each number can be written as a
✔ fraction .
Step-by-step explanation:
When you add two rational numbers, each number can be written as a fraction.
What is a rational number?A Rational number can be defined as any number which can be represented in the form of p/q where q ≠ 0. It can be made by dividing an integer by an integer.
For the given situation,
The sum of two rational numbers is rational.
The closure property of addition of rational number states that if we add two rational number, then the sum of these two rational number will also be a rational number.
Adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication.
Hence we can conclude that when you add two rational numbers, each number can be written as a fraction.
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The masses of four planets in a solar system outside the Milky Way are given below. Mass of Planet A: 5.97 × 10 24 kg; Mass of Planet B: 3.30 × 10 23 kg; Mass of Planet C: 1.89 × 10 27 kg; Mass of Planet D: 4.87 × 10 24 kg What is the order of these planets from least to greatest mass?
Planet C; Planet B; Planet D; Planet A Planet C; Planet A; Planet D; Planet B Planet B; Planet D; Planet A; Planet C Planet A; Planet D; Planet B; Planet C\
The order of the planets from least to greatest mass is Planet B, Planet D, Planet A, Planet C.
To determine the order of the planets from least to greatest mass, we need to compare the given masses:
Mass of Planet A: 5.97 × 1024 kg
Mass of Planet B: 3.30 × 1023 kg
Mass of Planet C: 1.89 × 1027 kg
Mass of Planet D: 4.87 × 1024 kg
These masses help us rank the planets:
Planet B: 3.30 × 1023 kg
Planet D: 4.87 × 1024 kg
Planet A: 5.97 × 1024 kg
Planet C: 1.89 × 1027 kg
Therefore, the order of the planets from least to greatest mass is Planet B, Planet D, Planet A, Planet C.
Find the zeros K(x) = -x²+ 2x + 15 EXPLAIN EVERY STEP!
the distance light travels in one second (one light-second) is about 1.86 x 10^5 miles. Saturn is about 475 light-seconds from the sun. About how many miles from the sun is saturn?
Answer:
Step-by-step explanation:
Given that the distance light travels in one light second about
[tex]1.86(10^5) miles[/tex]
Distance of Saturn from Sun = Time taken for travel x speed
Here speed = [tex]1.86 x 10^5[/tex]
Time taken = 475 light seconds
Hence distance = [tex]1.86 x 10^5x475\\=883.5x10^5\\=8.835x10^7[/tex] miles
write the polynomial in standard form. Then name the polynomial based on it's degree and number of terms
6 - 12x + 13x^2 - 4x^2
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please help me and explain it
Find the volume of the prism. 1,728 cu. in. 864 cu. in. 288 cu. in.
Volume of cube is given by the formula :
[tex] Volume = a * a * a [/tex]
Where a is edge of the cube.
We are given edge of cube as 12 inches.
Plugging the value of edge in given formula:
[tex] Volume = 12 * 12 * 12 [/tex]
Volume = 1728 cubic inches.
Answer : Volume of cube is 1728 cubic inches.
Volume of cube is given by the formula :
[tex] Volume = a * a * a [/tex]
Where a is edge of the cube.
We are given edge of cube as 12 inches.
Plugging the value of edge in given formula:
[tex] Volume = 12 * 12 * 12 [/tex]
Volume = 1728 cubic inches.
Answer : Volume of cube is 1728 cubic inches.
Let f(x)=x2+14x+48. What are the zeros of the function? Enter your answers in the boxes.
Answer:x= -6 and -8
Step-by-step explanation: I took the test
Use the diagram to complete the statement. Given JKL, sin(38) equals—
(Diagram is a right triangle. Angle K is 52 degrees and angle L is 38)
cos(38)
cos(52)
tan(38)
tan(52)
Answer:
Answer is b
Step-by-step explanation:
Jacey obtains a 30-year 6/2 ARM at 4% with a 2/6 cap structure in the amount of $224,500. What is the monthly payment during the initial period?
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As cars passed a checkpoint, the following speeds were clocked and recorded. Speed (mph): 55 62 61 54 68 72 59 61 70
What are the minimum, first quartile, median, third quartile, and maximum of the data set? Show your work.
We have ---- > 55, 62, 61, 54, 68, 72, 59 ,61, 70
In total 9 numbers
step 1
order the numbers from smallest to largest
54,55,59,61,61,62,68,70,72
1) What is the minimum of the data set ?
The lowest number is the minimum------------ > 54
2) What is the median of the data set ?
Find the number that is in the middle
54,55,59,61,61,62,68,70,72
The middle number is 61. That is the median.
Find the middle of each half. Since these numbers are between 2 numbers, you average the numbers (add then divide by 2).
55+59=114/2=57 This is the first quartile.
68+70=138/2=69 This is the third quartile
3) What is the first quartile of the data set ?
the answer is 57
4) What is the third quartile of the data set ?
the answer is 69
5) What is the maximum of the data set ?
The highest is the maximum------------ > 72
Answer:
Minimum = 54
Maximum = 72
Median = 61
First quartile = 57
Third quartile = 69
Step-by-step explanation:
Data : 55 62 61 54 68 72 59 61 70
Arrange the data is ascending order
54 , 55, 59, 61,61 ,62 , 68,70 ,72
So, minimum = 54
Maximum = 72
Median is the mid value .
There are nine observations.
So, 5th observation is the median
So, Median = 61
First quartile = It is the median of data of the left side data of the median .
Left side data : 54 , 55, 59, 61
There are four observations
Median = [tex]\frac{\frac{n}{2}th+(\frac{n}{2}+1)th}{2}[/tex]
Median = [tex]\frac{\frac{4}{2}th+(\frac{4}{2}+1)th}{2}[/tex]
Median = [tex]\frac{2th+3rd}{2}[/tex]
Median = [tex]\frac{55+59}{2}[/tex]
Median = [tex]57[/tex]
First quartile = 57
Third quartile = It is the median of data of the right side data of the median .
Right side data : 62 , 68,70 ,72
There are four observations
Median = [tex]\frac{\frac{n}{2}th+(\frac{n}{2}+1)th}{2}[/tex]
Median = [tex]\frac{\frac{4}{2}th+(\frac{4}{2}+1)th}{2}[/tex]
Median = [tex]\frac{2th+3rd}{2}[/tex]
Median = [tex]\frac{68+70}{2}[/tex]
Median = [tex]69[/tex]
Third quartile = 69
Hence minimum is 54 , maximum is 72 ,median is 61 , first quartile is 57 and third quartile is 69
Nicholas used a $10 bill to pay for a granola bar that only costs p dollars. How much change did Nicholas receive from the cashier?
Is it possible to place 158 books on three shelves so that the first shelf has 8 less books than the second and 5 more books than the third shelf?
Yes, it is possible to place 158 books on three shelves with the given conditions. The distribution will be 49 books on the first shelf, 57 books on the second, and 52 books on the third shelf.
To solve this problem, let's use algebra. Let x represent the number of books on the second shelf. According to the given conditions, the first shelf would have x - 8 books, and the third shelf would have x - 5. The total number of books on all three shelves is 158, and the equation representing the total number of books is:
x + (x - 8) + (x - 5) = 158
Combining like terms:
3x - 13 = 158
Adding 13 on both sides:
3x = 171
Dividing both sides by 3:
x = 57
Therefore, the second shelf has 57 books, the first shelf has 49 books (57 - 8), and the third shelf has 52 books (57 - 5).
It is possible to place the books on the three shelves as required, and the answer is yes, with the distribution being 49 books on the first shelf, 57 books on the second, and 52 books on the third.
PLZ HELP!!!! 43 POINTS!!!!! Koji is installing a rectangular window in an office building. The window is 8 2/3 ft wide and 5 3/4 ft high. The formula for the area of a rectangle is A=bh. What is the area of the window?
I need more math help, the!
Cement truck A can pour 200 cubic ft of concrete in 20 minutes. It only takes truck B 15 minutes to do the same job. If they both work together,how long will it take them to pour the 200 cubic feet?
I need help setting up the problem and solving it, thank you!