what is the probability that one or more of the children is a carrier of the recessive allele? hint: the probability that one or more of the children is a carrier is the same as the sum of all probabilities minus the probability that none of the children is a carrier.

Answer:

The angle marked x can be calculated using the angle sum property of a triangle. Since ∠CBE = 48° and ∠DBC + ∠BCE = 180°, then x = 180° - 48° = 132°.

Answer:Since lines AB and DE are parallel, corresponding angles are congruent. This means that angle x (which is formed by lines AB and DE) is congruent to angle CBE (which is formed by lines DE and BC). Therefore, angle x is also equal to 48 degrees.

x = 48°

The values of F(4; 5) (the incomplete gamma function) and F(5; 4) are 4.41 and 8.904

The value of the incomplete gamma function can be obtained as:

F(4; 5) = ₀∫⁵ t⁴⁻¹ . e^(-t) dt

          = г(4)  ₀∫⁵ (t⁴⁻¹ . e^(-t)) г(4) dt

          = г(4)  [P(T < 5)]    ( the integral is the density function of T ∼ Gamma(4, 1) )

          = (3!) [P(2(1)T < 5(2) (1) )]

          = 6 [P( X²₈ < 10 )]

          = 6 [0.735]

          = 4.41

F(5; 4) = ₀∫⁴ t⁵⁻¹ . e^(-t) dt

          = г(5)  ₀∫⁴ (t⁵⁻¹ . e^(-t)) г(5) dt

          = г(5)  [P(T < 4)]    ( the integral is the density function of T ∼ Gamma(4, 1) )

          = (4!) [P(2(1)T < 4(2) (1) )]

          = 24 [P( X²₁₀ < 8 )]

          = 24 [0.371]

          = 8.904

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The mean, median, and mode for my set of test scores turned out to be the same: 83 · The range of my scores is 42 therefore the five test scores are 58, 83, 83, 90, 100.

This is referred to as the difference between the largest and smallest values, the result of subtracting the sample maximum and minimum.

Range = maximum - minimum

      42  = 100 - x

      x = 100 - 42 = 58

Since the mode and mean is 83 then the set of values = 58, 83, 83, 91, 100/5 = 83

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The difference in area is of about 1445.1 square miles.

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr²

The radius is the distance of the center of the circle to any point on the circumference of the circle.

For the circle with a radius of 18 miles, the area is given as follows:

A = π x 18² = 1017.9 square miles.

For the circle with a radius of 28 miles, the area is given as follows:

A = π x 28² = 2463 square miles.

Hence the difference is of:

2463 - 1017.9 = 1445.1 square miles.

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Answer: 45,60

Step-by-step explanation:

OK

Answer: The one in the middle

Step-by-step explanation:

The one in the middle because of the huge downhill

The rectangular block has a perimeter of 10 units. The triangle's perimeter is 7.5 units.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. Draw a square on a sheet of paper using a pencil. It is a two-dimensional figure. The area of the form on the paper is referred to as its Area.

Here,

area=6 units

length on scale=5-2

=3 units

3*w=6

w=2 units

perimeter=2*(3+2)

=10 units

length of side of triangle=2.5 units

perimeter=2.5+2.5+2.5

=7.5 units

The perimeter of rectangle block is 10 units. The perimeter of triangle is 7.5 units.

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Answer:

Choice C    (1/3b)/7 = 25.50

Step-by-step explanation:

1/3 of budget b =(1/3)b

7 bills at $25.50 per bill = 7 x 25.50

Setting both equation to each other we get
(1/3)b = 7 x 25.50

Dividing by 7:
(1/3b)/7 = 25.50

(a) Confidence interval of 4547 to 8473 steps means the average number of steps taken by employees falls in that range with 95% confidence.

(b) The point estimate was 6510 and  the margin error is 1963

(c) Yes, there  is convincing evidence that the employees of this company are not meeting the guideline, on average

If we take many samples of size 50 and calculate many intervals, about 95% of the interval will capture the true average of steps for an employee in a day.

We are 95% confident that the interval from 4547 to 8473 steps contains the true average steps for employees/day.

Since all plausible values in our interval are under 10,000, there is convincing evidence that the employees are not meeting this guideline, on average.

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The graph of g(x) = -f(x + 4) is the reflection of the graph of f(x) = |x| about the x-axis, translated 4 units to the left.

The graph of f(x) = |x| is a V-shape with the vertex at the origin. The graph of g(x) will have the same V-shape, but with the vertex located 4 units to the left of the origin and reflected about the x-axis.

Therefore, g(x) = -f(x + 4) is the reflection of the graph of f(x) = |x| about the x-axis, translated 4 units to the left. It could be concluded that the correct answer is as given above.

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The solution of the system of equation is (1, 0). Therefore, the answer is b.

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

We are asked to solve the system of equation by substitution method.

Hence,

y = x - 1

3x + 2y = 3

Using substitution method, let's substitute the value of y in equation(ii)

3x + 2(x - 1) = 3

3x + 2x - 2 = 3

5x  = 3 + 2

5x = 5

x = 5 / 5

x = 1

Let's find the value of y in the equation.

y = 1 - 1

y = 0

Therefore,

x = 1 and y = 0

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Answer:

3570

Step-by-step explanation:

Find the prime factorization of 105

105 = 3 × 5 × 7

Find the prime factorization of 170

170 = 2 × 5 × 17

Multiply each factor the greater number of times it occurs in steps 1 or 2 above to find the LCM:

LCM = 2 × 3 × 5 × 7 × 17

LCM = 3570

(x,y)⇒(x+5,y+10) is the translation rule for A'B, which is a translation of AB.

A translation is a geometric transformation in Euclidean geometry that moves every point in a figure, shape, or space by the same distance in the same direction. A translation may alternatively be thought of as adding a constant vector to each point or changing the coordinate system's origin. A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction. A translation in mathematics moves a form left, right, up, or down but does not turn it. The translated (or picture) shapes appear to have the same size as the original shape, showing that they are congruent. They've just moved in one or more directions.

Here,

A translation is a sort of transformation in which every point in a figure moves the same distance in the same direction. Slides are another term for translations. A translation can be described with words like "moved up 3 and over 5 to the left" or using notation.

The translation rule for A'B is a translation of AB is (x,y)⇒(x+5,y+10).

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Answer:

24x+96

Step-by-step explanation:

so we could use Distributive property

which means -12time -2x+-12times-8

                                   =24x+96

i hope is helpful

The line y = ax + b is parallel to the line y = 2x - 6 and passes through the point (1, -7), the value of a and b is 2 and -9 respectively.

The equation of line:

y = 2x - 6

We firstly find the slope of the equation by comparing the equation by y = mx + c.

On comparing m = 2

The point is (1, -7).

So x(1) = 1 and y(1) = -7

The formula of slope intercept form is:

y - y(1) = m(x - x(1))

Now putting the value:

y - (-7) = 2(x - 1)

y + 7 = 2x - 2

Subtract 7 on both side, we get

y = 2x - 9

On comparing the equation from y = ax + b, we get

a = 2 and b = -9

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The complete question is:

The line y = ax + b is parallel to the line y = 2x - 6 and passes through the point (1, -7). Find the value of a and b.

Answer: D) 15.7

Step-by-step explanation:

Start with the formula C=2 πr

Then solve for r r=C2π = 98.62·π = 15.69(7)204

The radius of the circle is 15.7 mm.

The route or boundary that encircles any shape in mathematics is defined by the shape's circumference.

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.

We have,

The circumference of Circle = 2πr

Also, The circumference of a circle is 98.596 millimeters.

So, circumference of Circle = 2πr

98.596 = 2πr

98.596 = 6.28r

r= 98. 596 / 6.28

r = 15.7 mm

Thus, the radius is 15.7 mm.

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By using the Angle Sum Property, we can find that m angle a = 180 - (3(x - 5) + x 25) = 180 - 4x + 25

We can use the Angle Sum Property to solve this problem. The Angle Sum Property states that the sum of the measures of the angles in a triangle is equal to 180°. We can use this to write the equation 180 = m angle bdc + m arc bc + m angle a. Since we have the values for m angle bdc and m arc bc, we can plug them in and rearrange the equation so that m angle a is the only unknown. We get 180 = 3(x - 5) + x 25 + m angle a. Subtracting 3(x - 5) + x 25 from both sides, we get m angle a = 180 - (3(x - 5) + x 25). Simplifying, we get m angle a = 180 - 4x + 25, which is the final answer.

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Sample average: To calculate the sample average, add up all the measurements and divide by the number of measurements.

42.4 + 65.7 + 29.8 + 58.7 + 52.1 + 55.8 + 57.0 + 68.7 + 67.3 + 67.3 + 54.3 + 54.0 = 751.4

Sample average = 751.4 / 12 = 62.62

Sample standard deviation steps:

Subtract the sample average from each measurement to find the deviations.

Square each deviation.

Add up the squared deviations.

Divide the sum by the number of measurements minus one (n-1).

Take the square root of the result.

Sample standard deviation = sqrt(sum of squared deviations / (n-1))

Dot diagram: A dot diagram, also known as a dot plot, is a simple graphical representation of a set of data where each data point is represented by a dot on a number line. To create a dot diagram, plot each measurement as a dot on a number line with the corresponding value.

This is a useful tool to visualize the distribution of the data and to see the general pattern, such as the presence of outliers, skewness, or clusters.

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Three fifth of the vegetable in Alia garden are tomatoes so number of tomatoes are 3/5x in Alias garden.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

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Answer:

below

Step-by-step explanation:

Use right triangle Pythagorean theorem

L^2 = 8^2 + 4^2

L^2 = 80

L = sqrt (80)   units      <====exact

             approx is sqrt(80) =~8.94 units

For the given matrix, Cartesian products to elements is verified,

(a) (1,2)

A X A: This set contains all possible ordered pairs where x is a member of set A and y is also a member of set A. The element (1,2) does not belong to this set because 1 is a member of set A, but 2 is not.

B X A: This set contains all possible ordered pairs where x is a member of set B and y is a member of set A. The element (1,2) does not belong to this set because 2 is a member of set B, but 1 is not.

A X B: This set contains all possible ordered pairs where x is a member of set A and y is a member of set B. The element (1,2) belongs to this set because 1 is a member of set A and 2 is a member of set B.

B X B: This set contains all possible ordered pairs where x is a member of set B and y is also a member of set B. The element (1,2) does not belong to this set because 1 is not a member of set B.

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Answer:

The properties of multiplication are distributive, commutative, associative, removing a common factor and the neutral element.

Step-by-step explanation:

The distributive, commutative, associative, removes a common factor, and neutral element characteristics of multiplication.

According to the associative property, grouping symbols can be altered during addition or multiplication without affecting the outcome.

A + (b + c) = A + (b + c) is how this is expressed. In order to multiply a number by all of the distinct addends of another number, one must use the distributive property of multiplication.

A mathematical principle known as the associative property states that the product of a multiplication problem is unaffected by the way the factors are organized.

You can arrange the addends in multiple ways without changing the result, according to the associative property of addition. You can reorder the addends and the result won't change, according to the commutative property of addition.

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Answer:

"In

In a 30-60-90 triangle, the sides are in a ratio of 1:√3:2.

So, the hypotenuse of the triangle is 62 = 12 ft long.

The longer leg of the triangle is 6√3 = 10.8 ft long (to the nearest tenth of a foot)

The probability that at least 3 of them will be carrying a reusable water bottle is 74.6%

Here it is given that probability of people who carry at least 1 reusable water bottle is p = 0.58.

A random sample of n = 5 people is selected.

This data follows a binomial distribution, with success denoted by a person carrying t least 1 reusable water bottle. The probability mass function of the binomial distribution is,

[tex]P(X=x)=(^n_x)P^x(1-P)^n^-^x; x=0,1,2,...0 < P < 1[/tex]

Compute the probability that at least 3 of them will be carrying a reusable water bottle as follows:

P (X ≥ 3) =P(X=3)+P(X=4)+P(X=5)

[tex]P(X\geq 3)=(^5_3)0.58^3(1-058)^5^-^3+(^5_4)0.58^4(1-058)^5^-^4+(^5_5)0.58^5(1-058)^5^-^5[/tex]        

P(X≥3)=0.449538048+0.237646416+0.0656356768

P(X≥3)=0.746821224

The percentage is,0.746821224 × 100 = 74.6%.

Thus, the probability that at least 4 of them will be carrying a reusable water bottle is 74.6%.

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The value for $\frac{0.\overline{72}}{0.\overline{27}}$ as a common fraction in lowest terms is 2.666

To convert repeating decimals to fractions, we can use the following method:

Let's call the repeating decimal 0.72... = x, and the repeating decimal 0.27... = y.

Then 10x = 7.2... and 10y = 2.7...

Subtracting the original expressions from the above:

10x - x = 7.2... - 0.72...

=> 9x = 7

=> x = 7/9

And similarly,

10y - y = 2.7... - 0.27...

=> 9y = 2

=> y = 2/9

Therefore,

0.72... / 0.27... = x / y = (7/9) / (2/9) = 7/2 = 3.5

A repeating decimal is a decimal that has a repeating pattern of digits after the decimal point. To convert a repeating decimal to a fraction, we need to identify the repeating pattern and convert it to a fraction. This is done by multiplying both the numerator and denominator by a power of 10 that makes the repeating part an integer.

Then, the resulting fraction can be simplified to its lowest terms. In this case, the repeating decimals 0.72... and 0.27... can be converted to the fractions 7/9 and 2/9 respectively, and dividing the two results in a fraction of 7/2 can be simplified to 3.5.

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The first equation into the second to eliminate [tex]y[/tex] and solve for [tex]x[/tex]

[tex]$$\begin{gathered}-x+4\left(\frac{1}{4} x-3\right)=-4 \\\Rightarrow \\-x+x-12=-4 \\\Rightarrow \\-12=-4 \\\Rightarrow \\x=3\end{gathered}$$[/tex]

At infinite solutions, both sides are equal. For example, 6x + 2y - 8 = 12x +4y - 16. Simplifying an equation with an infinite-solution formula or method results in an infinite solution, because both sides are the same. Infinity represents infinity or infinity. It is usually represented by the “∞” symbol.

Some equations have infinitely many solutions. In these equations any value of the variables makes the equation true. When you try to solve an equation to get a variable or number equal to itself, you find that the equation has infinitely many solutions. 

This system of linear equations can be graphed on a [tex]$x-y$[/tex] plane. The first equation represents a line with slope [tex]\frac{1}{4}[/tex] and [tex]$y$[/tex]-intercept [tex]-3[/tex]. The second equation represents another line with slope [tex]-1[/tex] and [tex]$y$[/tex]-intercept [tex]-4[/tex]. The intersection point of the two lines is the solution to the system of linear equations.

To find the solution, we can substitute the first equation into the second to eliminate [tex]y[/tex] and solve for [tex]x[/tex]

[tex]$$\begin{gathered}-x+4\left(\frac{1}{4} x-3\right)=-4 \\\Rightarrow \\-x+x-12=-4 \\\Rightarrow \\-12=-4 \\\Rightarrow \\x=3\end{gathered}$$[/tex]

We can then use either equation to find the value of [tex]y[/tex]

[tex]$$\begin{gathered}y=\frac{1}{4} x-3 \\\Rightarrow \\y=\frac{1}{4} \cdot 3-3 \\= \\y=-2\end{gathered}$$[/tex]

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The process of converting a decimal number to its base 7 equivalent is explained below.

The radix point is the point that separates the whole number part of a number from its fractional part in a numerical system.

The process of converting a decimal number to its base 7 equivalent starts by dividing the decimal number by 7. The remainder from this division will be the first digit after the radix point in the base 7 equivalent.

We continue this process by dividing the quotient obtained in the previous step by 7 until we get a quotient of 0. The remainders obtained from each division will be the digits after the radix point in the base 7 equivalent, in the reverse order.

To get the integer part, we keep dividing the decimal number by 7 until we get a quotient of 0. The remainders obtained from each division will be the digits in the integer part of the base 7 equivalent, in the reverse order.

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Answer:

142

Step-by-step explanation:

6 day av 144 / day so total =144*6

first 3 day av 132 so total =132*3

next 2 days av 163 so total =163*2

144*6= 132*3+163*2+final day

so final day = 142

The results for systems under rotational motion are listed below:

First section:

Part A - The angular speed of the large gear is 90π radians per minute.

Part B - The linear velocity of the large gear is 27π centimeters per minute.

Part C - The linear velocity of the smaller gear is 27π centimeters per minutes.

Part D - The angular speed of the smaller gear is 27π / 8 radians per minute.

Part E - The angular speed of the smaller gear is 27 / 16 revolutions per minute.

Second section:

Part A - The angular speed of the LP is 200π / 3 radians per minute.

Part B - The angular velocity of the LP is 200π / 3 radians per minute.

In the first part of this question we find the case of rigid transmission system under rotational motion, two gears that transmits power and whose angular speed ratio is shown below:

ωL / ωS = rS / rL

Where:

And the linear velocity (v), in centimeters per minute, is calculated by this formula:

v = rL · ωL = rS · ωS

Part A - How many radians per minute is the large gear turning?

R/ The angular speed is:

ωL = 45 rev / min × 2π rad / rev

ωL = 90π rad / min

Part B - What is the linear velocity of the teeth on the large gear?

v = (0.3 cm) · (90π rad / min)

v = 27π cm / min

Part C - What is the linear velocity of the teeth on the smaller gear?

v = 27π cm / min

Part D - How many radians per minute is the smaller gear turning?

ωS = v / rS

ωS = (27π cm / min) / (8 cm)

ωS = 27π / 8 rad / min

Part E - How many revolutions per minute is the smaller gear turning?

nS = 27π / 8 rad / min × (1 / 2π rev / rad)

nS = 27 / 16 rev / min

The second part uses the same kinematic equation used in the previous part:

Part A - How many radians per minute is this:

ω = (33 + 1 / 3 rev / min) × (2π rad / rev)

ω = 200π / 3 rad / min

Part B - Find the angular velocity:

The angular velocity is independent from radius of rotation, thus:

ω = 200π / 3 rad / min

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