The proportions of blood phenotypes, A, B, AB, and O, in the population of all Caucasians in the United States are approximately .41, .10, .04, and .45, respectively. A single Caucasian is chosen at random from the population. a List the sample space for this experiment. b Make use of the information given above to assign probabilities to each of the simple events. c What is the probability that the person chosen at random has either type A or type AB blood

The coordinate of JK is (-1.7, -0.3)

The coordinate of the points that divides the line segment in the given ratio is calculated as:

\((x, y) = (\frac{ax_1 +bx_2}{a+b} , \frac{ay_1 +by_2}{a + b} )\)

where;

a:b = 7:8

From the image;

(x₁, y₁) = (-6, 5) and,

(x₂, y₂) = (2, -5)

Substitute the given points in the equation above to calculate the coordinates of JK.

\((x, y) = (\frac{7(-6)+8(2)}{7+8} , \frac{7(5) +8(-5)}{7+8} )\\\\(x, y) = (\frac{-26}{15} , \frac{-5}{15} )\\\\(x,y) = (-1.7, -0.3)\)

Thus, the coordinate of JK = (-1.7, -0.3)

Check the image uploaded for the plot of point K

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Answer:

\(5-14i\)

Step-by-step explanation:

\((12-6i)-(7+8i)\\\\12-6i-7-8i\\\\5-14i\)

The solution to the expression to a + bi form is 5 - 14i

From the question, we have the following parameters that can be used in our computation:

(12 - 6i) - (7 + 8i)

Open the brackets

So, we have

(12 - 6i) - (7 + 8i) = 12 - 6i - 7 - 8i

Evaluate the like terms

So, we have

(12 - 6i) - (7 + 8i) = 5 - 14i

Hence, the solution is 5 - 14i

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The number of minutes when they would both paint the same strip of wood is 8 minutes.

The linear equation that represents the total strip of wood that is painted by Henry is: amount of strips already painted + (strips painted per minute x minute)

14 + (3½x m)

14 + 3½m

The linear equation that represents the total strip of wood that is painted by Sandy is: amount of strips already painted + (strips painted per minute x minute)

10 + (4 x m)

10 + 4m

When both people paint the same strip of wood, the two above equations would be equal.

10 + 4m  = 14 + 14 +3½m

4m - 3½m = 14 - 10

0.5m = 4

m = 4 / 0,5 = 8

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The value of the function ƒ(x) at each point is  ƒ(–1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 11, ƒ(3) = 21, the correct option is B.

We are given that;

f(-1)=5 f(0) = 3 f(1) = 5 f(2) = 11 f(3) = 21

Now,

The function ƒ(x) maps each value of x to a corresponding value of y. For example, when x = –1, y = 5, so ƒ(–1) = 5. Similarly, when x = 0, y = 3, so ƒ(0) = 3, and so on. The other options are incorrect because they either reverse the order of x and y, or they do not match the values given in the mapping.

Therefore, by the given domain and range the answer will be ƒ(–1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 11, ƒ(3) = 21.

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The complete question is;

Use the mapping shown above to show the value of the function ƒ(x) at each point. Question options: A) ƒ(1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 11, ƒ(3) = 21B) ƒ(–1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 11, ƒ(3) = 21C) ƒ(–1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 21, ƒ(3) = 11D) ƒ(5) = –1, ƒ(3) = 0, ƒ(5) = 1, ƒ(11) = 2, ƒ(21) = 3.

Step-by-step explanation:

find the y intercept then graph using your slope

Answer:

135

Step-by-step explanation:

use bidmas or bodmas

(9 × 3) 5

brackets first then multiply and if its addition add it or multiplication then times it

The required system has the unique solution (x,y) = (1,0), and the lines x+y=1 and x-y=1 intersect at the point (1,0).

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
The system of linear equations that has exactly one solution is system 3,

x + y = 1
x - y = 1

To see why we can use the fact that a system of linear equations has exactly one solution if and only if the corresponding lines intersect at a single point.

For system 1, the lines y=3 and y=-3 are parallel and never intersect. Therefore, this system has no solution.

For system 2, the lines 3y=4 and 3y=7 are also parallel and never intersect. Therefore, this system has no solution.

For system 4, the lines 1/2x+3y=4 and 1/2x+3y=6 are parallel and never intersect. Therefore, this system has no solution.

However, for system 3, we can add the two equations to eliminate y and obtain,
2x = 2
x = 1

Substituting x=1 into one of the original equations, we get:
1 + y = 1
y = 0

Therefore, the system has the unique solution (x,y) = (1,0), and the lines x+y=1 and x-y=1 intersect at point (1,0).

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Answer:

B

Step-by-step explanation:

Let the two numbers be a and b.

The product of the two is 120 and their sum of their squares is 289. In other words:

\(\displaystyle ab = 120 \text{ and } a^2 + b^2 = 289\)

And we want to find the sum of the two numbers.

We can use the perfect square trinomial. Recall that:

\(a^2 + 2ab + b^2 = (a+b)^2\)

From the first equation, multiply by two:

\(2ab = 240\)

Add the two equations together:

\((a^2+b^2)+(2ab) = (289)+(240)\)

Simplify and rewrite:

\(a^2+2ab+b^2 = 529\)

Factor using the perfect square trinomial pattern:

\((a+b)^2 = 529\)

And take the square root of both sides:

\(\displaystyle a + b = \pm\sqrt{529} = \pm23\)

Hence, the sum of the two numbers is 23 or -23.

In conclusion, our answer is B.

When edge D connects with edge X, this net is folded into a cube, which is obtained by folding the given figure in cube.

A cube is a solid shape with six square faces. Each side of a square  has the same side length, so all  faces are the same size.

A cube has 12 sides and 8 vertices. Each vertex refers to the angle where the three edges of the cube meet.

Shape Properties of  Cube  

Thus, when edge D connects with edge X, this net is folded into a cube.

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The perimeter of the rectangle is 62 square units.

The perimeter of a rectangle can be calculated using the formula:

P = 2(L + W)

Where:

L is the length of the rectangle

W is the width of the rectangle

We have:

L = 20 units

W = 11 units

Substituting into the formula:

P = 2(20 + 11)

P = 2(31)

P = 62 square units

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Question in English

What is the perimeter of a rectangle if it is 20 long and 11 wide?

The calculated period of the function is 12

From the question, we have the following parameters that can be used in our computation:

The graph

By definition, the period of the function is calculated as

Period = Difference between cycles or the length of one complete cycle

Using the above as a guide, we have the following:

Period = 13 - 1

Evaluate

Period = 12

Hence, the period of the function is 12

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Answer:

B

Step-by-step explanation:

Inverse means the opposite in effect. The reverse of. Therefore if f(x) is -1,-3 bad you are looking for the inverse which is g(x) is -1,__. It would be 3.

g(1) = 4

The correct answer is an option (D)

"For a function y = f(t), inverse of a function is, \(f^{-1}(y)=t\)"

For given question,

The values in the table define the function f(x).

x   f(x)

-1    -3

1     -1

4     1

6     4

7     6

A function g(x) is the inverse of function f(x).

We need to find the value of g(1).

\(g(1)\\\\=f^{-1}(1)\\\\=4\)

Therefore, g(1) = 4

The correct answer is an option (D)

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Applying the congruent chords theorem, the value of x is: 7.

Length of segment LP is: 6 units.

In geometry, a chord is defined as the line segment that joins two points on the circumference of a circle.

In a circle, if two chords are congruent, then they are equidistant from the center of a circle, according to the congruent chords theorem.

In the circle given, chords JK = LM = 12 units. This means both chords are congruent, therefore, they are equidistant from the center of the circle S.

According to the congruent chords theorem, NS = PS, thus:

8 = 2x - 6

8 + 6 = 2x

14 = 2x

Divide both sides by 2

14/2 = 2x/2

7 = x

x = 7

LP = 1/2(12)

LP = 6 units.

In summary, applying the congruent chords theorem, the value of x is: 7.

Length of segment LP is: 6 units.

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The additional acres that the parks occupy will be 33.75 acres.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, the additional acres that the parks occupy will be:

= (12.5 × 3) - 3.75

= 33.75 acres.

Note that the information is incomplete and the complete information is given below.

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A city is building 3 parks in a new subdivision. Each park will be 1.25 acres. How many total acres will the 3 parks be? 3.75 acres

The city acquired more land next to the subdivision. If it decides to make each park 12.5 acres, how many additional acres would the parks occupy?

Answer:

Triangle x = 30. Pentagon x = 50

Step-by-step explanation:

For the triangle,

Find the angle which is beside x in the triangle,

let's name that angle y, so 55 + 55 + y = 180 ( we find 55 by subtracting both angles 125 from 180)

110 + y = 180

Y = 180 - 110

y = 70

Now that we have find Y, we can easily find x by subtracting 70 from 180 which would be, 70 + X = 180

x = 180 - 70

x = 30

For the pentagon,

Again find the angle which is beside x in the pentagon,

let's name that y again, 90 + 120( by subtracting 60 from 180) + 110( by subtracting 70 from 180)  + 90 + y = 540

210 + 200 + y = 540

410 + y = 540

y = 540 - 410

y = 130

Now that we have find y, we can easily find x by subtracting 130 from 180 which would be, 130 + x = 180

x = 180 - 130

x = 50

Hope this helps!

Answer:

you have to simplify and then the coeffitant of that will be in ur so its b.

Step-by-step explanation:

The csc(theta) = 1/sin(theta) = 1/(-2/√13) = -√13/2. So, the cosecant of theta is -√13/2.

To find the cosecant (csc) of theta when a point (-3, -2) lies on its terminal side, we need to determine the hypotenuse (r) of the right triangle formed by this point.

Using the Pythagorean theorem, r^2 = (-3)^2 + (-2)^2. So, r^2 = 9 + 4 = 13, and r = √13.

The csc(theta) is the reciprocal of sin(theta). Sin(theta) is calculated as the ratio of the opposite side (y-coordinate) to the hypotenuse, or sin(theta) = -2/√13.

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(200 - 100√2) / 16 is the rectangular form of the product c1*c2 for an equilateral triangle's vertices.

A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.

Here,

An equilateral triangle is a triangle with three equal sides. If 3-2i, 6-i, and c form the vertices of an equilateral triangle, then the distance between 3-2i and 6-i is equal to the distance between 3-2i and c.

The distance between two complex numbers a + bi and c + di can be found using the formula:

√((c - a)² + (d - b)²)

So, the distance between 3-2i and 6-i is:

√((6 - 3)² + (-1 - (-2))²) = √((3)² + (1)²) = √(9 + 1) = √10

And the distance between 3-2i and c is:

√((c - 3)² + (c - (-2))²) = √((c - 3)² + (c + 2)²)

Since these distances must be equal, we have:

√((c - 3)² + (c + 2)²) = √10

Squaring both sides:

(c - 3)² + (c + 2)² = 10

Expanding both sides:

c² - 6c + 9 + c² + 4c + 4 = 10

Combining like terms:

2c² + 10c + 5 = 10

Subtracting 10 from both sides:

2c² + 10c - 5 = 0

This is a quadratic equation, which can be solved using the quadratic formula:

c = (-b ± √(b² - 4ac)) / 2a

Where a = 2, b = 10, and c = -5. Plugging these values into the formula:

c = (-10 ± √(10² - 4 * 2 * -5)) / 2 * 2

c = (-10 ± √(100 + 40)) / 4

c = (-10 ± √(140)) / 4

c = (-10 ± 10√2) / 4

So there are two complex solutions, c1 = (-10 + 10√2) / 4 and c2 = (-10 - 10√2) / 4.

The product of these two solutions is:

c1 * c2 = ((-10 + 10√2) / 4) * ((-10 - 10√2) / 4)

= (100 - 100√2 + 100) / 16

= (200 - 100√2) / 16

(200 - 100√2) / 16 is the answer in rectangular form for the product c1*c2 for the vertices of an equilateral triangle.

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Answer:

867.08

Step-by-step explanation:

first you do 2x6 squared add 2x17 squared

Answer:

225%

Step-by-step explanation:

54 = 24 of x

54 = .24x

Divide both side by the same number

54/.24 = .24x/.24

= 225%

[RevyBreeze]

The answers are:

Part A: The two values of x are: x > 8 or x < -24

Part B: Closed circles at -24 as well as 8 on the number line.

Inequalities are mathematical formulas with two sides that are unequal. In an inequality, we evaluate two numbers rather than two equations. In place of the equal sign, a less than (less than or equal to), larger than (greater than or equal to), or not equal to sign is used.

The following steps are missing for the inequalities:

Solving the inequalities,

Part A:

|1/4x+2|+4 >= 8

|1/4x+2|>=4

Now when we remove the sign fom the inequality, there would be 2 values:

(1/4) x + 2 > 4 or (1/4) x + 2 < -4

Now subtracting 2 from both side:

\((\frac{1}{4} )x > 2\ or\ (\frac{1}{4} )x < -6\)

Divide both the sides by 4:

4(1/4) x > 4(2) or 4(1/4) x < 4(-6)

Now we get two values of x:

x > 8 or x < -24

Part B:

Closed circles at -24 as well as 8 on the number line. Draw a thick line from -24 to the left arrow and a thick line from 8 to the right arrow.

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The character in Seedfolks to whom Paul Fleischman assigned the most personal perspective on gardening is:

The plot reveals a formerly lonely setting that would be gradually turned into a bubbling garden by the characters.

Kim, a nine-year-old Vietnamese girl was assigned the most personal perspective because she planted her Lima beans in the garden to strike a connection with her late father who she did not know on a personal basis.

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Answer:

a edge 2023

Step-by-step explanation:

The probability of rolling a number greater than 3 is 1/2 or 0.5.

When rolling a standard cube, there are six possible outcomes, corresponding to the six faces of the cube. Each face has a number from 1 to 6.

To find the probability of rolling a number greater than 3, we need to determine the number of favorable outcomes (rolling a number greater than 3) and divide it by the total number of possible outcomes (rolling any number from 1 to 6).

The favorable outcomes for rolling a number greater than 3 are: 4, 5, and 6. So, there are three favorable outcomes.

The total number of possible outcomes is six since there are six faces of the cube.

Therefore, the probability of rolling a number greater than 3 is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 3 / 6

Probability = 1/2

Hence, the probability of rolling a number greater than 3 is 1/2 or 0.5.

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The probability that the mean of a sample of 90 computers would be greater than 117.13 months, if the quality control manager is correct, is approximately 0.9955 or 99.55%.

The sampling distribution of the sample mean follows a normal distribution with a mean of 120 and a standard deviation of 10/sqrt(90) = 1.0541 months (using the formula for the standard deviation of the sample mean).

To find the probability that the mean of a sample of 90 computers would be greater than 117.13 months, we can standardize the sample mean using the formula:

z = (sample mean - population mean) / (standard deviation of sample mean) = (117.13 - 120) / 1.0541 = -2.6089

Using a standard normal distribution table or calculator, we can find that the probability of obtaining a z-score greater than -2.6089 is approximately 0.9955.

Therefore, the probability that the mean of a sample of 90 computers would be greater than 117.13 months, if the quality control manager is correct, is approximately 0.9955 or 99.55%.

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Answer:

Answer is 6 and 2/3. That’s it

Step-by-step explanation:

The length of JN of the second triangle is  \(6\frac{2}{3}\).

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

As the two triangles BTL and PJN are similar because the corresponding two angles are given equal in the question.

Thus, the ratios of the side are equal.

\(\frac{BT}{JP} = \frac{LT}{JN}\)

\(\frac{6}{8} =\frac{5}{JN}\)

\(JN =\frac{20}{3}\)

\(JN= 6\frac{2}{3}\)

Therefore, the length JN of the triangle comes out to be \(6\frac{2}{3}\).

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The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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The answer choice which belongs in the green box and is the longest side of the triangle as required is; 11.06.

It follows from the task content that since the sum of angles in a triangle is; 180°, the missing angle measure is; 180 - 51 - 109° = 20°.

Consequently, it follows from the sine law that;

4 / sin 20° = x / sin 109°

x = 4 sin 109° / sin 20°

x = 11.06.

Ultimately, the number that belongs in the green box is; 11.06.

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Answer:

Step-by-step explanation:

THE ANSWER TO YOUR QUESTION IS C.