The required probability of the son with normal vision is 0.50 and for the normal blood clotting is 0.
If mutations is present on one of the X chromosome then it is capable of developing the condition which is called X-linked disorder.Generally men are affected by this disorder because they carry one copy of the X chromosome.If women carry one copy of the chromosome, then it is consider that they are carriers of disease and if they have both the copies affected then they are affected by disorder.Colorblind woman with a normal man is in position to produce 2 carrier females and 2 males colorblind.In the condition of a carrier woman with colorblindness marries a hemophilic man, progeny mentioned below phenotypes are produced:Parent phenotype Carrier woman
Affected man (Hemophilic) (colorblindness)
Parents X^h Y XX^C
Gametes X^h, Y X, X^C
Progeny X X^h X^C X^h X^C Y, XY
Total outcome = 100
Favourable outcomes for a son with normal vision is= 50
Probability of a son with normal vision = 50/100
= 0.50
probability of a son with normal blood clotting = 0 / 100
= 0
Therefore, the probability of the son with normal vision and normal blood clotting is 0.50 and 0 respectively.
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does an underdetermined linear system always have infinitely many solutions? if not, give an example.
A linear system that is underdetermined either has no solution or infinitely many solutions. has an infinite number of solutions and is consistent, for example, (x, y, z) = (1, 2, 2), (2, 3, 2), and (3, 4, 2).
If there are more equations than unknowns in a system of linear equations or a system of polynomial equations, it is said to be underdetermined (in contrast to an overdetermined system, where there are more equations than unknowns). The notion of constraint counting can be used to clarify the vocabulary. It is possible to think of each unknown as a potential degree of freedom. One degree of freedom is constrained by each equation that is added to the system.
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– 8g–1+7g2+ – 2g+ – 10g+ – 3g2
Please help me with this
The value of the variable, x is 45 degrees
How to determine the valueWe have that the polygon is one with eight sides, that is, it is a regular octagon.
To determine the interior angle, we have
(n - 2) 180
n is the number of sides
(8-2)180
1080 degrees
Now, divide it by the number of sides
1080/8 = 135 degrees
Note that angles on a straight line is equal to 180
Then,
x + 135 = 180
Collect like terms
x = 180 -135
subtract the values
x = 45 degrees
Hence, the value is 45 degrees
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the mean (average) of 6, 9 and 18 is equal to the mean (average) of 12 and $y$. what is the value of $y$?
Answer:
y = 10
Step-by-step explanation:
[tex]\displaystyle \frac{6+9+18}{3}=\frac{12+y}{2}\\ \\\frac{33}{3}=\frac{12+y}{2}\\ \\11=\frac{12+y}{2}\\ \\22=12+y\\\\10=y[/tex]
3
6+9+18
=
2
12+y
3
33
=
2
12+y
11=
2
12+y
22=12+y
10=y
answer: 10=y
a frustum of cone is filled with ice cream such that the portion above the cone is a hemisphere. define the variables di
The total volume of the ice cream is -4.76 cubic inches.
The volume of the frustum of a cone can be calculated as follows:
V = (1/3) × π × h × (r1² + r2² + r1 × r2), where r1 and r2 are the radii of the top and bottom base of the cone.
And the volume of a sphere can be calculated as follows:
V = (4/3) × π × r³, where r is the radius of the sphere.
To calculate the total volume of the ice cream, we need to subtract the volume of the cone from the volume of the sphere.
Let's first calculate the radii of the top and bottom base of the cone.
r1 = (di/2) = (1.25/2) = 0.625 in.
r2 = (d0/2) = (2.25/2) = 1.125 in.
Now, we can estimate the volume of the cone.
V_cone = (1/3) × π × h × (r1² + r2² + r1 × r2)
= (1/3) × π × 2 × (0.625² + 1.125² + 0.625 × 1.125)
= 6.45 cubic inches.
Next, let's calculate the radius of the sphere.
r_sphere = (di/2) = (1.25/2) = 0.625 in.
And finally, we can calculate the volume of the sphere.
V_sphere = (4/3) × π × 0.625³
= 1.69 cubic inches.
So, the total volume of the ice cream is given by:
V_ice_cream = V_sphere - V_cone
= 1.69 - 6.45
= -4.76 cubic inches.
Note: Since the volume of the cone is larger than the volume of the sphere, the total volume of the ice cream will be negative, indicating that it is not possible to fill a frustum of a cone with ice cream in the manner described.
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--The given question is incomplete; the complete question is
"A frustum of a cone is filled with ice cream such that the portion above the cone is a hemisphere. Define the variables di=1.25 in., d0=2.25 in., h=2 in., and determine the volume of the ice cream."--
EX I: Calculate the sector area below.
The sector area for the figure below is 268.19.
What is area of a sector?The quantity of space included within the sector's perimeter is referred to as the sector's area in a circle. A sector always starts at the circle's center. The area of a circle encompassed between its two radii and the arc next to them is known as the sector of a circle. The sector of a circle that most often symbolizes half of a circle is a semicircle.
The area of sector is given by the formula:
A = (pi)r² × α/360
where, r is the radius and α is the angle of the sector.
Substituting the value of r and α in the formula we have:
A = pi (16)² × 120/ 360
A = 268.19
Hence, the sector area for the figure below is 268.19.
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mount everest begins on a plain that is 14,000 feet high, then the summit sits at 29,028 feet. the difference between the height of these two areas is called the .
The elevation gain of Mount Everest is 15,028 feet, a very impressive feat considering it is the highest elevation gain of any mountain in the world.
The difference between the height at the base of Mount Everest, which is 14,000 feet and the summit, which is 29,028 feet is 15,028 feet. This is also known as the elevation gain. It can be calculated using the following formula:
Elevation Gain = Summit Height - Base Height
So in this case, Elevation Gain = 29,028 ft - 14,000 ft
Which gives us: Elevation Gain = 15,028 ft
The elevation gain of Mount Everest is 15,028 feet, a very impressive feat considering it is the highest elevation gain of any mountain in the world. It is also the highest mountain in the world, with the summit standing at an impressive 29,028 feet. This is a testament to the power of nature and the sheer scale of Mount Everest.
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- sports the distance between each base on a baseball infield is 90 feet. the third baseman throws a ball from third base to point p. to the nearest foot, how far did the player throw the ball?
The distance between the third base and the player is 150 feet.
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base, and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle of 90°. The sides of a right triangle (say a, b, and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
In the diagram attached, we can see the locations of the 1st base, 2nd base, 3rd base, and Home plate.
Since these four points form a square of which diagonals are equal in size.
So if we find the distance between the 1st and 3rd base that will be equal to the distance between the Home plate to the second base.
To find the nearest distance,
By applying "Pythagoras' Theorem"
[tex]nearest \ distance =\sqrt{120^2+90^2}\\\\=\sqrt{22500}\\\\=150\ feet.[/tex]
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Bob is thinking about leasing a car. the lease comes with an interest rate of 8%. determine the money factor that will be used to calculate bob’s payment. a. 0.00033 b. 0.00192 c. 0.00333 d. 0.01920 please select the best answer from the choices provided a b c d
The money factor that will be used to calculate bob’s payment is C) 0.00333
Money Factor can be converted to Annual Percentage Rate (APR) and vice versa.
So the money factor can be solved:
APR = 2400 x Money Factor
Money Factor = APR / 2400
Money Factor = 8% / 2400 = 0.0033333
Definition of APRBasically, APR is short for Annual Percentage Rate, which means an annual percentage. APR is widely applied to the money you are going to borrow. Like when you apply for a motor vehicle loan, credit card, consumer loan, loan for education, or home ownership loan.
The APR will display a calculation of the amount of interest that will be charged if you apply for a loan. The lower the APR, the less interest you will have to pay.
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Every matrix transformation is a linear transformation.a. Trueb. false
True , Every matrix transformation is a linear transformation.
Is there a linear transformation for every matrix operation?
Despite the fact that every linear transformation is a matrix transformation, not all linear transformations are matrix transformations.
Because of this, it's possible that we'll encounter a linear transformation in which we're unable to locate a matrix to carry out the mapping.
What alteration does matrix entail?
In a two-dimensional or three-dimensional space, the transformation matrix converts one vector into another vector, which may be comprehended geometrically.
Stretching, squeezing, rotation, reflection, and orthogonal projection are some of the often utilized transformations.
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given a two-dimensional pore geometry of packed squares as below, plot the porosity as a function of the averaging length scale. the black grains are separated by a distance equal to the grain size in the x and y directions. use a square as the averaging volume and the edge of the square as the averaging length scale. what is the representative elemental volume?
Porosity calculated as ratio of pore to total vol. Plot of porosity vs averaging length scale (edge of square used for averaging). Rep. elemental vol = vol of square used for averaging.
The porosity as a function of the averaging length scale can be calculated as follows:
Define the pore geometry: A two-dimensional pore geometry of packed squares is given, with black grains separated by a distance equal to the grain size in the x and y directions.Select the averaging volume: The averaging volume is defined as a square.Determine the porosity: The porosity is calculated as the ratio of the pore volume to the total volume of the material. In this case, the pore volume is the volume between the black grains and the total volume is the volume of the material.Plot the porosity as a function of the averaging length scale: The averaging length scale is defined as the edge of the square used for averaging. The porosity can be calculated for various values of the averaging length scale and plotted as a function of the averaging length scale.Representative elemental volume: The representative elemental volume is the volume of a single element (e.g. a square in this case) used in the averaging calculation. In this case, the representative elemental volume is equal to the volume of the square used for averaging.Learn more about geometry :
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Victor has saved $89.25 for the bicycle that he wants .the bicycle cost $129.85
The model used by Victor in the linear equation is incorrect,
How to identify Linear Equation Models?The parameters are that;
Victor saved: $89.25
Cost of the bicycle = $129.85
Thus, to find the amount extra that he will need to purchase the bicycle, the equation model should be;
$89.25 + x = $129.85
This can be expressed in words as;
The amount of money he already has saved + the amount of money he still requires = the total price of the bike.
An equation that correctly represents this problem can show the sum of the amount of money he already has and the amount of money he needs equals the total cost of the bicycle
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Complete question is;
Victor has saved $89.25 for the bicycle that he wants. The bicycle costs $129.85. Victor writes the equation below to help him determine the additional amount that he needs to solve to have enough to buy the bicycle.
89.25 + 129.85 = x
Does Victor's equation correctly model the problem?
The measures of the angles of a triangle are in the extended ratio 11:5:4. Find the measures of the angles.
Given that in a △ABC, ∠A:∠B:∠C=11:5:4
Let the angles of the given triangle be 11xo,5xo,4xo.
We know that the sum of the angles of a triangle is 180o
11xo+5xo+4xo=180o⇒20xo=180o
xo=12110o=15o
So, the angles of the triangle are 70o,60o,45o.
write the number as a quotient of integers to show that it is rational300=
The number 300 can be written as 300/1 as a quotient of integers to show that it is rational.
A rational number is a number of the form p/q, where q not equal to 0 and p and q must be co-primes.
To write a number in the form of quotient of integer, we write it as , where p/q.
Here, 300 can be written as 300/1 or 600/2 .
But we should also take care that p and q must be co-primes.
Co-primes are the pairs of numbers that have only one common factor which is 1.
So, 300 can be written as 300/1
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Which fraction is not equivalent to 2/6?
Use the graph to answer the questions:
What does (6, 120) represent?
What ordered pair describes the unit rate?
Use cross multiplication to solve for y
Answer:From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have
x = dozen
y = cookies
This means that
(3, 36) means 3 dozens required 36 cookies
What ordered pair describes the unit rate?
Using the ordered pair in (a):
The unit rate of the pair (3, 36) is 36/3 = 12.
This means that for every 1 dozen change, there is a corresponding 12 cookies change
Step-by-step explanation:
Grade 8 math please help. I’m trying to sleep
The set of points for which y is a function of x is given as follows:
B.
When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
For set B in the context of this problem, we have that:
The input of -3 is mapped to an output of 3.The input of -2 is mapped to an output of 2.The input of -1 is mapped to an output of 1.The input of 1 is mapped to an output of -1.As there are no repeated inputs, this is the set that represents y as a function of x.
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using diagonals from a common vertex, how many triangles could be formed from the polygon pictured below tiiip
5 triangles could be formed from the polygon pictured.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The given figure is an irregular heptagon (7 unequal sides).
Now,
Taking a common vertex A we can draw the triangles as given below.
We see that,
There are 5 triangles that can be drawn.
Thus,
5 triangles can be formed.
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8 cm
7cm
6 cm
What is the surface area, in cm², of the figure?
Answer:
Here you have
Step-by-step explanation:
8 x 7 x 6 = 336 cm²
Calculate the sum of the partial sequence.
[tex]\sum_{n=1}^{75} (12n-9)[/tex]
The required sum of the given partial sequence is 33525.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The sum of the partial sequence.
[tex]= \sum_{n=1}^{75}12n - 9[/tex]
[tex]= \sum_{n=1}^{75}12n - \sum_{n=1}^{75} 9\\= 34200-675\\=33525[/tex]
Thus, The required sum of the given partial sequence is 33525.
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Please help me with this science/math question. I'll tell you the instructions.
We're basically combining science and math.
The letters are elements of the periodic table.
Element's can start with uppercase and lowercase letters together (Sr)
It can just be uppercase to (O)
If both of the letters are capital, they aren't symbols TOGETHER, their separate meaning they have their own element.
So we have the numbers next to the elements symbols (except for 2)
The starting values of each element is one, and we multiple the number that is after the element symbol, not before it.
Once you multiply the element and the number next to it, the element now has a new value, for example
Sr3.
Sr's value is 1.
1x3=3
Sr's new value is 3.
For the parenthesis, both element symbols are capital, which mean they don't belong to the same element, they have different elements. The number 4 isn't after the element symbol P so we don't multiply 4 and P. We multiply 4 and O because 4 is after O.
After we multiply each element's value, we multiply 2 (outside the parenthesis)
We multiply 2 x P which is 2
Then we multiply 2 x 4 since O's new value is 4 because we multiplied it. We'll get 8.
We can't forget about 2 (2 is the starting number from the equation) We multiply the whole equation by 2.
Now this is the part I need help on. I must add the TOTAL number of atoms from each I element. Please help me with this!!! I'd really appreciate it! (tell me step by step as well)
The number of atoms in the compound will be 54 atoms.
How to calculate the number of atomsChemistry's fundamental building block is an atom. It is the smallest fraction of matter into which electrically charged particles cannot be released. It is also the smallest piece of substance with chemical element-like characteristics.
The number of atoms in 2 Sr3(PO4)2 can be determined by counting the number of each type of atom present in the compound. In 2 Sr3(PO4)2, there are:
2 x 3 = 6 Sr atoms
2 x 2 x 4 = 16 P atoms
2 x 2 x 8 = 32 O atoms
So, there are a total of 6 + 16 + 32 = 54 atoms in 2 Sr3(PO4)2.
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Find the slopes of all four sides: J(-4,-1), K(-7,-4), L((2, -10), M(5, -7)
Slopes of all four sides are 1, -2/3, 1 and -2/3.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given points are J(-4,-1), K(-7,-4), L((2, -10), M(5, -7)
For JK, Slope=-4 - (-1)) / (-7 - (-4)) = -3 / -3 = 1
For KL, slope= (-10 - (-4)) / (2 - (-7)) = -6 / 9 = -2/3
For LM, slope= (-7 - (-10)) / (5 - 2) = 3 / 3 = 1
For MJ, Slope=(-1 - (-7)) / (-4 - 5) = 6 / -9 = -2/3
Hence, slopes of all four sides are 1, -2/3, 1 and -2/3.
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Solve the inequality -8 < 32.
-8x < 32
?
on both sides. ?
the inequality.
x>-4 is the solution of the inequality -8x < 32
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is -8x < 32
Minus eight times of x less than thirty two.
We need to solve for x which is a variable.
Divide both sides by 8
-x<4
x>-4
Hence, x>-4 is the solution of the inequality -8x < 32
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a ski resort charges $55 for renting a snowboard or skis and $11 per hour for a lift ticket. If julian spent a total of $121, how many hours was you there
If a ski resort charges $55 for renting a snowboard or skis and $11 per hour for a lift ticket. If julian spent a total of $121. The number of hours is 6.
How to find the number of hour?Let's call the number of hours Julian spent at the ski resort "h".
We know that:
55 (the cost of the equipment rental) + 11h (the cost of the lift ticket) = 121 (the total amount Julian spent).
So we can subtract 55 from both sides to isolate the lift ticket cost:
11h = 121 - 55 = 66
Finally, we divide both sides by 11 to find the number of hours:
h = 66 / 11 = 6
Therefore, Julian was at the ski resort for 6 hours.
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Mr. and Mrs. Torres have three pretty daughters, Jane, Jade and Jem. Jane is twice old as Jade, and Jem is 5 years younger than Jane. If n represents the age of Jade and the sum of their ages is 55, then ;
1. Who among the children is the youngest?
2, Write an expression representing the age of Jane.
3. Who among the children is the oldest?
4. How old is Jade?
5. Write an equation representing the sum of ages of Jane, Jade, and Jem.
1. The youngest is Jade she is 12 years old.
2. The expression representing the age of Jane is:- Jane = 2 x Jade
3. The oldest age is Jane she is 24 years old.
4. The age of Jade is 12 years.
5. The expression for the sum of the ages will be:-
Jane + Jade + Jem = 55
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Mr and Mrs Torres have three pretty daughters, Jane, Jade and Jem. Jane is twice old as Jade, and Jem is 5 years younger than Jane. If n represents the age of Jade and the sum of their ages is 55.
From the given data following equations can be made:-
Jane = 2 x Jade
Jem = Jane - 5
Jane + Jade + Jem = 55
From the three equations the following equation can be made:-
2 Jade + Jade + 2Jade - 5 = 55
4Jade - 5 = 55
4Jade = 60
Jade = 60 / 5 = 12 years
Jane = 2 x Jade = 2 x 12 = 24 years
Jem = Jane - 5 = 24 - 5 = 19 years
The answers can be written as:-
1. Jade, who is 12 years old, is the youngest.
2. Jane's age is represented by the formula Jane = 2 x Jade.
3. Jane, who is 24 years old, is the oldest.
4. Jade is twelve years old.
5. Jane + Jade + Jem = 55 will be the formula for the total age.
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consider sequences that consist entirely of $a$'s and $b$'s and that have the property that every run of consecutive $a$'s has even length, and every run of consecutive $b$'s has odd length. examples of such sequences are $aa$, $b$, and $aabaa$, while $bbab$ is not such a sequence. how many such sequences have length 14?
The number of such sequences of strings of length 14 is 172.
Let [tex]$a_n$[/tex] and [tex]$b_n$[/tex] denote, the number of sequences of length n ending in A and B, respectively.
If a sequence ends in an A, then it must have been formed by appending two A's to the end of a string of length (n-2).
If a sequence ends in a B, it must have either been formed by appending one Bs to a string of length (n-1) ending in an A, or by appending two Bs to a string of length (n-2) ending in a B.
Thus, we get the recursions as follows -
[tex]a_n &= a_{n-2} + b_{n-2}[/tex]
[tex]b_n &= a_{n-1} + b_{n-2}[/tex]
By counting further, we find that [tex]$a_1[/tex]= 0, [tex]b_1[/tex] = 1, [tex]a_2[/tex] = 1, [tex]b_2[/tex] = 0.
Similarly, we will get the following table -
Therefore, the number of such strings of length 14 is [tex]$a_{14} + b_{14}[/tex] = 80 + 92 = 172.
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Evaluate: (1) 3p +5(2q+p)+3p-6q
(2) Z+8-6(z-2a)+5z
The values are evaluated to give;
1. 11p + 4q
2. -12a + 8
What is an algebraic expression?An algebraic expression is an expression that is composed of terms, coefficients, variables, factors and constants.
From the information given, we have that;
3p +5(2q+p)+3p-6q
expand the bracket, we get;
3p + 10q + 5p + 3p - 6q
collect and add the like terms
11p + 4q
Then,
Z+8-6(z-2a)+5z
expand the bracket
z + 8 - 6z - 12a + 5z
collect and add the like terms
-12a + 8
Hence, the expression are 11p + 4q and -12a + 8
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Please help >_<
If t = <2, -10> and v = <-3, −1> find t + v.
A. <-1, -11>
B. <-1, -9>
C. <5, -11>
D. <5, -9>
The correct option regarding the addition of vectors t and v is given as follows:
A. <-1, -11>.
How to add the vectors?The standard notation of a vector is given as follows:
<x,y>.
In which:
x is the horizontal component of the vector.y is the vertical component of the vector.To add two vectors, we add the elements at the same component.
Then the addition of vectors t and v is given as follows:
t + v = <2, -10> + <-3, - 1> = <2 - 3, -10 -1> = <-1, -11>.
From the result obtained above, the correct option in the context of this problem is given by option A.
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Choose the correct solution graph for the inequality -9x> 54
Answer:
x < -6
Step-by-step explanation:
-9x > 54
Divide both sides by -9, this process will switch the inequality sign:
[x < -6]
Please help!!
When answering please number them
The rationalized surds are;
1) 20 + 5√3/13
2) 12√7 - 24/7
3) 6√2 + 6√3/5
What is the conjugate of a surd?
The surd has to do with an irrational number. In this case we are asked to find the value of the following surds.
1) The conjugate of the denominator is; 4 + √3 and the rationalize we have;
5/4 - √3 * 4 + √3/4 + √3
20 + 5√3/16 + 4√3 - 4√3 - 3
20 + 5√3/13
2) The conjugate of the denominator is; √7 - 2
To rationalize we have;
12/√7 + 2 * √7 - 2/√7 - 2
12√7 - 24/7 -2√7 + 2√7
12√7 - 24/7
3) The conjugate of the denominator is √2 + √3
To rationalize we have;
6/√2 - √3 * √2 + √3/√2 + √3
6√2 + 6√3/2 + √6 - √6 + 3
6√2 + 6√3/5
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Dominick’s grandfather gave him $300 to start his college savings account. Dominick’s grandfather also gives him $75 each month to add to the account. Dominick’s mother gives him $40 each month, but has been doing so for 3 fewer months than Dominick’s grandfather. Write a simplified expression for the amount of money Dominick has received from his grandfather and mother after m months.
Simplified expression for the amount is 5(36+23m) .
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
Step 1: Form an equation for the amount of money Troy has received after m months.
If the total months that Troy's grandfather has given him money is m, then the number of months that Troy's mother has given him money is m - 3.
⇒ Total amount in account = 300 + 75m + 40(m - 3)
= 300 + 75m + 40m-120
=180 + 115m
=5(36+23m)
Hence, Simplified expression for the amount is 5(36+23m) .
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