assume that a wild-type sequence is 5'agcctac3'. which of the following sequences might be produced by a transversion? correct!

The length of the side DE, that is parallel to the side AC is 6.3 units

Here the line DE is parallel to the side AC of the triangle

In the given triangle

The length of the side BD = The length of the side AD

The length of the side BE = The length of the side EC

That mean the parallel line AC is equally dividing the two side of the triangle

Therefore, the length of the line DE will be be exactly half of the line AC

The length of the side AC = 12.6 units

The length of the side DE = The length of the side AC / 2

Substitute the values in the equation

= 12.6 / 2

= 6.3 unit

Therefore, the length of DE is 6.3 units

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The linear equation parallel to the line that passes through (-6, 1) and (10,0) and that passes through (-7, -2) is:

y = (-1/16)*x - 39/16

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept

If a linear equation crosses through two known points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by:

a = (y₂ - y₁)/(x₂ - x₁)

And two lines are parallel if and only the two lines have the same slope and different y-intercept.

Here we want to find a line that passes through (-6, 1) and (10, 0), the slope of that line is:

a = (0 - 1)/(10 + 6) = -1/16

And we want to find a line with this slope that passes through the point (-7, -2), so we need to have:

-2 = (-1/16)*-7 + b

-2 = 7/16 + b

-2 - 7/16 = b

-32/16 - 7/16 = b

-39/16 = b

So the linear equation is:

y = (-1/16)*x - 39/16

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Answer:

OD=Vertex: (1, -25); intercepts: x= 6,-4

Step-by-step explanation:

y=x²-2x-24

where a = 1,b = –2 and c = –24

to find the vertex we will use this formula

Step 1

(h,k) = (-b/2a, -D/4a), where D = b²–4ac.

(h,k) = (–(–2)/2×1) , –((–2)² – 4 × 1 × –24/4×1)

(h,k)= (2/2) , –(4 + 96)

(h,k) = (1 , –100/4)

(h,k) = (1,–25)

STEP 2

To find x intercept make y = 0

y=x²-2x-24

x² – 2x – 24 = 0

x² –6x + 4x – 24 = 0

x(x –6) +4(x –6) = 0

(x+4)(x–6)=0

x+4 = 0; x = –4

x–6 = 0; x = 6

x = (–4,6)

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The a) equation for the vertical nullcline is y = -4x + 4 and horizontal nullcline is x = -3y + 1. The b) equilibrium points are (0,0) , (0 , 0.8) , (0.75 , 0), and (0.375,0.5)

We have

dx/dt = x(1 - x/3 - y)

dy/dt = y(1 - y/4 - x)

a) To get the equation for vertical nullcline, not on the coordinate axis we take

dy/dt = 0

or, y(1 - y/4 - x) = 0

or, 1 - y/4 - x = 0

or, y/4 = 1 - x

or, y = -4x + 4

Similar;y for horizontal nullcline not on coordinate axis we take

dx/dt = 0

or, (1 - x/3 - y) = 0

or, x/3 = 1 - y

or, x = -3y + 1

b)

To get the equilibrium points of the nullcline system we simply take

Here the x nullcline will intersect y nullcline at

x = 0 and x = 1 - x/3 - y

y = 0 and y = 1 - y/4 - x

therefore we have equilibrium points

for x = 0 and y = 0  at(0,0)

x = 0 and y = 1 - y/4 - x at (0, 4/5)

x =  1 - x/3 - y and y = 0 at (3/4 , 0)

x = 1 - x/3 - y and y = 1 - y/4 - x  at (3/8 , 1/2)

Hence the equilibrium points are (0,0) , (0 , 0.8) , (0.75 , 0), and (0.375,0.5)

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Complete Question

(Image Attached)

Answer:

Step-by-step explanation: Raúl should put a turn of -30° in the walkway after the tree in order to continue in the same direction as before. This is because the negative angle will cancel out the positive angle and the walkway will continue in the same direction as before.

Answer:

10 [tex]\frac{5}{28}[/tex] days

Step-by-step explanation:

There are a lot of places to make mistakes, but I think that I am good.

Make a proportion:

[tex]\frac{Days}{Inches}[/tex] = [tex]\frac{Days}{Inches}[/tex]  Put in the three number that you know and solve for the number of days.

[tex]\frac{7\frac{13}{21} }{10\frac{2}{3} }[/tex] = [tex]\frac{x}{14\frac{1}{4} }[/tex]  Cross multiply and solve for x

10 [tex]\frac{2}{3}[/tex] x = [tex]7\frac{13}{21}[/tex]([tex]14\frac{1}{4}[/tex])  Change everything into improper fractions

[tex]\frac{32}{3}[/tex]x = ([tex]\frac{160}{21}[/tex])[tex]\frac{57}{4}[/tex]  I am going to cross cancel the 160 and 4  They both can be divided by 4 and I am going to cross cancel the 21 and 57.  They are both divisible by 3

[tex]\frac{32}{3}[/tex] x =( [tex]\frac{40}{7}[/tex])[tex]\frac{19}{1}[/tex]

[tex]\frac{32}{3}[/tex] x = [tex]\frac{760}{7}[/tex]  Multiply both sides by [tex]\frac{3}{32}[/tex]

([tex]\frac{3}{32}[/tex])[tex]\frac{32}{3}[/tex]x =([tex]\frac{3}{32}[/tex])[tex]\frac{760}{7}[/tex]  I can cross cancel 32 and 760.  They both can be divided by 8

x = ([tex]\frac{3}{4}[/tex])[tex]\frac{95}{7}[/tex]

x = [tex]\frac{285}{28}[/tex]

x = 10 [tex]\frac{5}{28}[/tex] Days

Answer:

Step-by-step explanation:

Firstly, I presume that the question talks about a rectangle and there is consistency in units i.e.Area is in units^2 and perimeter is in units (else there is no possible solution).

Now, perimeter = 2(L+B) = 40

OR (L+B) = 20.

Also, area = LxB = 100.

Now, LxB = 100 will give you the following values for LxB (Note in a rectangle, L>B or L=B):- (100×1),(50×20),(25x4),(20×5),(10×10).

Only one value gives L+B = 20 viz.L=10 & B=10.

Hope this helps! :)

(This was by another user you can search it up and see.)

According to the profit point of view, compared to smaller firms that export larger companies tend to systematically scan foreign markets to see where export opportunities lie.

What does profit mean?

In math, profit means the excess of returns over expenditure in a transaction or series of transactions.

Here we have given that, compared to smaller firms that export, larger companies tend to to be what.

And for the reason more firms are not proactive is that they are unfamiliar with foreign market opportunities; they simply do not know how big the opportunities actually are or where they might lie. Simple ignorance of the potential opportunities is a huge barrier to exporting

Here we know that, smaller firms, are often intimidated by the complexities and mechanics of exporting to countries where business practices, language, culture, legal systems, and currency are very different from the home market

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The probability of both people being Democrats is 0.243, and the probability of one person being a Republican and one person being a Democrat is 0.486.

To find the probability of each of the following, we can use the formula for the probability of selecting a group of items from a larger group with replacement:

P(A and B) = P(A) * P(B)

Where P(A) is the probability of selecting the first item, and P(B) is the probability of selecting the second item.

Both people are Democrats:

There are 16 Democrats and 31 total people, so the probability of selecting a Democrat is 16/31. Therefore, the probability of selecting two Democrats is (16/31) * (16/31) = 0.243.

One person is a Republican and one person is a Democrat:

There are 15 Republicans and 31 total people, so the probability of selecting a Republican is 15/31. There are 16 Democrats and 31 total people, so the probability of selecting a Democrat is 16/31. Therefore, the probability of selecting one Republican and one Democrat is (15/31) * (16/31) = 0.486.

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The null hypothesis in the given question is 'the mean annual consumption of high fructose corn syrup by a person in the United States is 48.8 pounds' and the alternative hypothesis in the given question is 'the population standard deviation is 3.6 pounds.'

Population mean = 48.8 pounds

Sample size = 120

Sample mean = 49.5 pounds

Population standard deviation = 3.6

α = 0.05

The standardized statistic z is:

z = (Sample mean - Population mean) x (√n / standard deviation)

z = (49.5 - 48.8) x (√120/3.6)

z = 2.13

The standardized statistic P is:

P = 2 - 2 x Φ(z)

P = 2 - 2 x 0.983

P = 0.034

Since, the result we get is statistically significant. We reject the null hypothesis.

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Answer: A

Step-by-step explanation:

D is wrong because its saying 3 times of the flat fee of 52.5 per month.

B is wrong because it is saying 52.5$ per gigabyte

C is wrong because the total amount is not 64.2

The Florida health insurance company can use a variety of predictive methods to predict the annual claims for the sample of 50 customers. These methods include machine learning algorithms such as linear regression and decision trees, as well as statistical methods such as regression analysis and logistic regression.

The company can also use qualitative methods such as interviews and surveys to gain insight into customer needs and preferences. By combining quantitative and qualitative methods, the company can create a more accurate prediction of the annual claims for its sample of 50 customers.The company can calculate its predictions by first gathering data on each of the 50 customers, such as age, gender, health history, lifestyle, and other factors. It can then use this data to create a predictive model that can be used to estimate the annual claims of each customer. These methods include machine learning algorithms such as linear regression and decision trees, as well as statistical methods such as regression analysis and logistic regression. The model can be tested and refined as necessary to ensure it is accurate and reliable. Finally, the company can use the model to make its predictions for the 50 customers.

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The remaining roots of p(x) is x =  -5 , 4 + 5i , 4 - 5i and the factored form of p(x) =  ( x + 5 ) ( x - ( 4 +  5i ) ( x - ( 4 - 5i )

Given :

The polynomial function p(x)=x³-3 x²+x+205 has x=-5 as a root.

using synthetic division :

x = -5

5     1    -3    1    205

     0     5    10    55

  1     2    11   260

on solving using the quadratic formula or calculator the roots are :

x = -5 , 4 + 5i , 4 - 5i

so quadratic form of p ( x ) = ( x + 5 ) ( x - ( 4 +  5i ) ( x - ( 4 - 5i )

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As a result, the likelihood of a flush (five cards of the same suit) is.198% while the likelihood of getting three cards of the same rank and two cards from any other rank is 0.07612%.

Probability is the study of numerical representations of the likelihood that an event will happen or that a statement is true. An event's probability is a number between 0 and 1, where 0 generally denotes the event's impossibility and 1 typically denotes its certainty.

Here,

a) It is irrelevant what suit the opening card is. Any of the suits may be drawn first, provided that the subsequent four cards are dealt from the same deck and are of the same suit.

After the initial card is drawn, there are only 12 of a given suit left in the deck, which has 13 of each suit in total. The third card, which has 11, the fourth card, which has 10, and the fifth and final card, which has nine, are then the cards that are still available. Each time, one fewer card will be present in the deck as a whole.

(ℎ) = (2 ) ∙ (3 ) ∙ (4ℎ )\s∙ (5ℎ )

(ℎ) = [tex]\frac{12}{51} *\frac{11}{50} *\frac{10}{49} *\frac{9}{48}[/tex]

(ℎ) =11880 / 5997600

(ℎ)= 33/16660 = .00198 .198%

c) The likelihood of three identical cards and two cards from one other rank.

Considering that the cards have 13 ranks

So, P =  [tex]\frac{13}{52} *\frac{12}{51} *\frac{11}{50} *\frac{10}{49}[/tex]

P = 267696/351655200

P=0 .0007612 or 0.07612 %

As a result, the likelihood of a flush (five cards of the same suit) is.198% while the likelihood of getting three cards of the same rank and two cards from any other rank is 0.07612%.

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On solving the provided question, P = 0.037 reject H o,P-value < 0.05 ( level of significance )

If there is no statistical significance between two variables, the null hypothesis is that there isn't any. The researcher or experimenter generally aims to refute or undermine the theory. An alternate explanation is that the two variables have a statistically significant association.

based on P value -

P = 0.037 reject H o

P-value < 0.05 ( level of signifance )

we are 95% y confidence that the average age of divorced man is how different than it was in 1989.

we would have concluded that the average age is not different wher, it really was different.

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Answer:

t ≥ 5

Step-by-step explanation:

In the tank now: 19

Fill rate per minute: 6

Number of minutes: t

Amount filled in t minutes: 6t

Total amount in tank after t minutes: 6t + 19

Amount desired: at least 49 liters

At least 49 liters means "greater than or equal to 49"

Inequality:

6t + 19 ≥ 49

Subtract 19 from both sides.

6t ≥ 30

Divide both sides by 6.

t ≥ 5

After changing  the denominators to rename these fractions  the sum is 5/6 .

Given :

If necessary, use / for the fraction bar(s).

We still need to find a way to add these fractions. Now you try.

Change the denominators to rename these fractions and find their sum.

To find sum we need to find LCM of denominators .

Least common multiple :

Least Common Multiple ( LCM ) is a method to find the smallest common multiple between any two or more numbers.

so = 1 / 2 + 1 / 3

LCM of 2 and 3 is 6

= 1 * 3 + 1 * 2 / 6

= 3 + 1 * 2 / 6

= 3 + 2 / 6

= 5 / 6

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Answer:

The total driving distance from Austin, TX to Seattle, WA is 2,128 miles

Step-by-step explanation:

Answer:

i believe it is a 2,116.4 mile drive.

Step-by-step explanation:

Answer:

-4 im pretty sure

Step-by-step explanation:

= -4

= -4

The total expected waiting time including the morning and the evening time is 41/3

given that your waiting time for a bus in the morning is uniformly distributed on [0, 8], whereas waiting time in the evening is uniformly distributed on [0, 10] independent of morning waiting time.

Sum of both waiting times = X+Y

Where X = morning wait time is U(0.8) and

Y = evening wait time is U(0,10)

Since X and Y are independent

Var(x+y) = Var(x)+Var(y)

Var(x) = (8^2 - 0^2)/12 = 16/3

Var(Y) = (10^2 - 0^2)/12 = 25/3

Var(x+y) = 16/3 + 25/3

= (16 + 25)/3

= 41/3

Therefore, the total expected value of waiting time including the morning and the evening time is 41/3.

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42) The functions  F and G  are G(x) = (2x - 1)/ (3x + 4) and F(x) = √x

43) The functions  F and G  are G(x) = 3x² - 4 and F(x) = 1/x⁻³.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Given composite function is

H(x) =  (fog)(x).

42)

H(x) =√[(2x - 1)/ (3x + 4)]

Rewrite the above equation

H(x) =√[G(x)] where G(x) = (2x - 1)/ (3x + 4)

H(x) = F(G(x)) where F(x) = √x

42)

H(x) =1/(3x² - 4)⁻³

Rewrite the above function

H(x) =1/[G(x)]⁻³ where G(x) = 1/(3x² - 4)

H(x) = F(G(x)) where F(x) = 1/x⁻³

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Answer: D & C

Step-by-step explanation:

The net Income of the business is represented as

Net profits or income = Net sales revenue (gross income) – Cost of goods and services sold – Administration, operating, marketing, and advertising costs, taxes, interests, and other expenses.

Here C is an option because we need to take operating expenses into consideration but if you consider cost of goods brought into store as operating then option changes to D.

D represents the sales which helps us determine the net income of the business.

Answer:

$18

Step-by-step explanation:

15 : 100 = x : 15

x =  15 · 15 / 100

x = 225 / 100

x = $ 2.25 (tips)

5 : 100 = x : 15

x = 15 · 5 / 100

x = 75 / 100

x = $ 0.75 (tax)

15 + 0.75 + 2.25 = $18

a) The number of seventh graders that participated in the competition was of 223.

b) The number of eight graders that participated in the competition was of 208.

c) The total number of students that participated in the competition is of 431.

The amounts in this problem are obtained applying the proportions given by the fractions.

For item a, we have that the amount is 5/8 of 3/5 of 595, hence the total amount is obtained as follows:

5/8 x 3/5 x 595 = 223 students.(rounding to the nearest integer).

For eight graders in item b, we have that 7/8 of 2/5 of 595 students participated, hence the number of students that participated in the competition is given as follows:

7/8 x 2/5 x 595 = 208 students. (rounding to the nearest integer).

Then the total number of students that participated in the competition is given by the sum of these amounts as follows:

223 + 208 = 431 students.

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For the given circle the value of cotθ is -√30/√19.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The terminal side of an angle θ.  

The standard position intersects the unit circle at (√30/7, -√19/7).

We need to find the value of cotθ.

Suppose that θ is an angle in standard position whose terminal side intersects the unit circle at (√30/7, -√19/7)

cotθ=x/y

=-√30/7/√19/7

=-√30/7×7/√19

=-√30/√19

Hence, the value of cotθ is -√30/√19 for the given circle.

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Answer:

14772

Step-by-step explanation:

Let X and Y be IID Unif(0, 1). the distance between X and Y.Expected value: 0 and Standard deviation: [tex]$\sqrt{\frac{1}{3}}$[/tex]

Expected value:

E(X-Y)

= E(X) - E(Y)

= 0 - 0

= 0

Standard deviation:

Var(X-Y) = Var(X) + Var(Y) = 1 + 1 = 2

SD(X-Y) = [tex]$\sqrt{2}$[/tex]

= [tex]$\sqrt{\frac{1}{3}}$[/tex]

The expected value of X-Y is the difference of the expected values of X and Y, which are both 0 since they are both IID Unif(0, 1). The variance of X-Y is the sum of the variances of X and Y, which are both 1. Since the standard deviation is the square root of the variance, the standard deviation of X-Y is the square root of 2.

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x= 6;

y= 4.

[tex](1)7x-8y=10\\\\ (2)x-8y=-26\\[/tex]

[tex](1)7x-8y=10\\-\\ (2)x-8y=-26\\--------\\\\6x+0y=36\\ \\6x=36[/tex]

[tex]\frac{6x}{6} =\frac{36}{6} \\ \\x=6[/tex]

For this solution, we are going to use equation 2 to get the value of "y".

[tex](6)-8y=-26\\\\-8y=-26-6\\ \\-8y=-32\\ \\\frac{-8y}{-8} =\frac{-32}{-8} \\ \\y=4[/tex]

If the answers are correct, both equations should return the same value in both sides of the equal (=) sign.

[tex]7(6)-8(4)=10\\ \\42-32=10\\ \\10=10[/tex]

That's correct.

[tex](6)-8(4)=-26\\ \\6-32=-26\\ \\-26=-26[/tex]

That's correct.

Hence, the answers are correct.