Solve –7x + 23 = 37.

(a) The probability that a randomly chosen nucleotide from the first region is the same as a randomly chosen nucleotide from the second region is 1/4.

(B) The chance that the triple chosen from the first region will be identical to the triple chosen from the second region is 1/4096.

(a) If we assume that there are four possible nucleotides (A, C, G, T) and that each nucleotide is equally likely to occur in each region, then the probability that a randomly chosen nucleotide from the first region is the same as a randomly chosen nucleotide from the second region is 1/4, since there is a 1 in 4 chance that the nucleotide chosen from the first region will be the same as the nucleotide chosen from the second region.

(b) If we again assume that there are four possible nucleotides (A, C, G, T) and that each nucleotide is equally likely to occur in each region, then the probability of choosing a particular three-nucleotide sequence is (1/4)³ = 1/64.

The probability of choosing the same three-nucleotide sequence from both regions is the product of the probabilities of choosing that sequence from each region, or (1/64) x (1/64) = 1/4096. Therefore, the chance that the triple chosen from the first region will be identical to the triple chosen from the second region is 1/4096.

Learn more about Nucleotide Probabilities: Single and Triple here:

https://brainly.com/question/25161031

#SPJ4

This gives us a total of 1,583,616 ft-lbs of work required to pump the water out of the pool.

Amount is a numerical value that refers to the total sum of money or other type of payment due. It is used to quantify the size of a transaction, the cost of goods or services, or any other type of financial transaction. Amounts can be expressed in a variety of different currencies, and they can be negative (owing) or positive (owed).

To calculate the amount of work required to pump all the water from the rectangular swimming pool into a drain at the top edge, we must first calculate the volume of the water in the pool. Volume is calculated by multiplying the length, width, and depth of the pool, which in this case is 20 ft x 20 ft x 8 ft = 3,200 cubic ft. Since the pool is filled to 1 ft below the top, the volume of water is 3,200 ft3 - 20 ft3 = 3,180 ft3.

Next, we must calculate the weight of the water, which is the volume multiplied by the weight density of water (62.4 lb/ft3). The weight of the water in the pool is 3,180 ft3 x 62.4 lb/ft3 = 197,952 lbs.

Finally, to calculate the amount of work required to pump the water from the pool into a drain at the top edge, we must multiply the weight of the water (197,952 lbs) by the height of the drain (8 ft). This gives us a total of 1,583,616 ft-lbs of work required to pump the water out of the pool.

To know more about amount click-
https://brainly.com/question/24795637
#SPJ1

Answer:

63m

Step-by-step explanation:

Alex swims 45m in 1 min .

=> Alex swims 45 m in 60 secs

=> Alex swims 45/60 m in 1 sec

In 1 min & 24 secs ( or 84 secs ) , Alex can swim =

\( \frac{45}{60} \times 84 = 63 \: m\)

The probability of selecting two red marbles without replacement from an urn containing four red marbles and five blue marbles is 12/72, which can be simplified to 1/6.

The probability of selecting the first red marble is 4/9 since there are four red marbles out of a total of nine marbles. After selecting the first red marble, there are now three red marbles left out of a total of eight marbles. Therefore, the probability of selecting a second red marble, without replacement, is 3/8.

To find the probability of both events occurring, we multiply the probabilities together. So the probability of selecting two red marbles without replacement is (4/9) * (3/8) = 12/72.

This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 12. Simplifying gives us 1/6.

Therefore, the correct answer is C. 12/72.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

Answer:

127.3 feet

Step-by-step explanation:

Use Pythagorean Theorem which says

leg^2+leg^2=hyp^2

90^2+90^2= c^2

8100 +8100=c^2

16200 = c^2

sqrt16200 = c

c ~= 127.27922

Round to one decimal place.

c ~= 127.3 feet

OR, use the shortcut of Special Right Triangles, 45°-45°-90° where, the long side (hypotenuse) is the leg•sqrt2

The legs are 90.

So, the long side is 90•sqrt2

~= 127.27922

~= 127.3 feet

see image.

Answer:

all of these are right angled triangle. so u can use pythagoras theorem, h²=p²+b²

longest side is called hypotenious (h)

and u can assume any of the remaining side as p and b as your choice

eg=

1) h=13

p=12

b=?

using pythagrous theroem

h²=p²+b²

13²=12²+b²

169= 144+b²

169-144=b²

25=b²

25 is the square root of 5 so

5²=b²

square root of each side will be cancelled so

b = 5

In this way u can solve your questione.....

Answer:

1.

\( {h}^{2} = {p }^{2} + {b}^{2} \)

\( {13}^{2} \: = {12}^{2} + {b}^{2} \)

\( {b}^{2} = {13}^{2} - {12}^{2} \)

\( {b }^{2} = 169 - 144\)

\( {b}^{2} = 25/tex]

\(b = \sqrt{25} \)

\(b = 5\)

hope this helps you all of your question's is base on the formula given above

mark me as brainliest pls

Answer:

Solve for  x .

x = 68

y = − 24

Step-by-step explanation:

This is the best I can do I hope it helps.

3x^3 + 2x^2 + 11x - 20 + (10/(-x-7)), This corresponds exactly to the result of polynomial long division.

Algebraic expressions called polynomials include constants and indeterminates.

Polynomials can be thought of as a type of mathematics. Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.

A specific kind of expression is a polynomial. A mathematical statement without the equals symbol (=) is called an expression.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.

Any polynomial must have variable exponents that are non-negative integers.

Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

According to our question-

-3x3 + 2x2 + 11x - 20 + (10/(-x-7)) = 3x4 + 19x3 - 25x2 - 57x + 150

In order to perform synthetic division, we must first remove the minus sign from the divisor and write out

-7 | -3 -19 25 57 -150

| 21 -14 -77 140

-3 2 11 -20 -10

obtain that

3x4 + 19x3 - 25x2 - 57x + 150 / (-x-7) is equivalent to 3x4 - 19x3 - 25x2 - 57x + 150 / (x+7) is equivalent to 3x3 + 2x2 + 11x - 20 + (10/(-x-7)).

Hence, 3x^3 + 2x^2 + 11x - 20 + (10/(-x-7)), This corresponds exactly to the result of polynomial long division.

learn more about polynomials click here:

https://brainly.com/question/2833285

#SPJ1

Answer:See below and attached

Step-by-step explanation:

Given numbers

4.2×10^-6, 2.1×10^-3, 3.1×10^-2, 3.2×10^-5, 3.5×10^-4, 5.8×10^-3, 5.2×10^-4

Greater than 3.1×10^-3

3.1×10^-2, 5.8×10^-3

Between 3.1 × 10^-3  and 4.3 × 10^-5

2.1×10 ^-3, 3.5×10^-4, 5.2×10^-4

Less than 4.3 × 10^-5

4.2×10^-6, 3.2×10^-5

Step-by-step explanation

:

Answer:

$585

Step-by-step explanation:

simply find 13% of 4500. 0.13 x 4500 is $585

Answer:

isosceles right

Step-by-step explanation:

hope this was helpful

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

To know more about annual rate click here

brainly.com/question/6026546

#SPJ4

Explanation

we can easily solve this by checking the equation

It is writen in slope- y intercept fom

hence

I hope this helps you

Answer:

33

Step-by-step explanation:

−16−35+18+x=0

-51+18+x=0

-33+x=0

x=33

gathmathcom

Answer:

May be -4 will be the answer

Step-by-step explanation:

2x+3+5x-2

7x+1

x =

1

_

7

I hope you understand the answer . I am sorry for writing it in weird way

answer is 1 by 7

A half life is the amount of time it takes for half of a radioactive substance to decay.

Yes, that is correct. The half-life of a radioactive element is the amount of time it takes for half of the initial amount of the element to decay. Therefore, the larger the initial amount of the element, the longer the half-life will be. This is because there are more atoms that need to decay in order for the half-life to occur. Conversely, if the initial amount of the element is small, the half-life will be shorter because there are fewer atoms that need to decay.

learn more about "half-life":- https://brainly.com/question/1160651

#SPJ11

The area of the sector is π square meters.

Length of arc \(= (90/360)* 2π(2m) = πm\)

To find the area of the sector and the length of the arc, we need to use the formulas:

Area of sector = ( Θ/360 x π\(r^2\)

Length of arc = (θ/360) x 2πr

Given radius (r) = 2m and angle (θ) = 90 degrees, we can plug these values into the formulas to get:

Area of sector = \((90/360) * \pi (2m)^2\)

\(= (1/4) * \pi * 4m^2\)

\(= \pi m^2\)

Therefore, the area of the sector is π square meters.

Length of arc = (90/360) x 2π(2m)

= (1/4) x 4πm

= πm

Therefore, the length of the arc is π meters.

To know more about the area of sector visit:

https://brainly.com/question/7512468

#SPJ1

The set of side measurements that could be used to form a right triangle is

√2, 3, √11 .

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is given that:

The side length of the triangle is shown in the option:

As we know,

Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

Using Pythagoras' theorem:

From option(B):

√2, 3,0 and √11

(√2)² + 3² = (√11) ²

2+ 9 = 11 (True)

Thus, the set of side measurements that could be used to form a right triangle is

√2, 3, √11 .

To Learn more about the right-angle triangle here:

brainly.com/question/3770177

#SPJ1

The smallest distance of the line to the point is of:

5.36 units.

Suppose the line is defined as follows:

ax + by + c = 0.

The coordinates of the points are as follows:

(x0,y0).

Then the shortest distance of the point to the line is:

D = |a(x0) + b(y0) + c|/sqrt(a²+b²).

In this problem, the line goes through these two points:

(2/7, 3) and (-2,11).

The slope is given by the change in y divided by the change in x, hence:

m = (11 - 3)/(-2 -2/7) = -3.5.

Then:

y = -3.5x + b.

When x = -2, y = 11, hence the intercept is calculated as follows:

11 = -3.5(-2) + b

11 = 7 + b

b = 4.

Then the line is:

y = -3.5x + 4.

3.5x + y - 4 = 0. (standard format, a = 3.5, b = 1).

The coordinates of the point are as follows:

(x0,y0) = (-3,-5).

Then the shortest distance is:

D = |3.5(-3) + 1(-5) - 4|/sqrt(3.5²+1²).

D = 19.5/sqrt(3.5²+1²).

D = 5.36 units.

More can be learned about the distance between line and point at https://brainly.com/question/28783035

#SPJ1

Answer:

true

true

True

true

False

Step-by-step explanation:

Answer:

8885

Step-by-step explanation:

5(870)+7(465)+8(160)=8885

Program State Model describes a precise mathematical description of the semantics of an executing program.

This model is used to illustrate how the program executes and to determine its behavior. It is composed of three components: states, transitions, and actions. A program state is a snapshot of the program's state at a particular point in its execution. It includes the values of variables and other resources. Transitions are the changes that occur between states, and are caused by the execution of instructions. Finally, actions are the operations that are performed by the program as it transitions from one state to the next. All of these components together provide a mathematical model for understanding the behavior of a program.

Learn more about model here

https://brainly.com/question/29810500

#SPJ4

Answer:

Step-by-step explanation:

subtract 2 from both sides

Answer:

divide both sides by 3

Step-by-step explanation:

The probability that more than one of the tested bottles is contaminated is found using the method of combination. It is expressed as a decimal as \(0.1679\) fraction as \(\frac{168}{1000}\).

A pharmacist receives a shipment of \(25\) bottles, of which \(4\) are contaminated. They test \(3\) of the bottles. We want to find the probability that more than 1 of the tested bottles is contaminated.
There are two possibilities to consider: Two or all the three of the tested bottles are contaminated. We can find the probabilities of each case and then sum them.
Case 1: Two of the tested bottles are contaminated.
We can choose 2 contaminated bottles out of \(4\) in \({{^{4}C_2}\) ways, and \(1\) non-contaminated bottle out of the remaining \(21\) in \({{^{21}C_1}\) ways. This will be the required favorable outcome. The total number of ways or the sample space to select \(3\) bottles is \({{^{25}C_3}\). The probability of this case is:
\(\frac{{^{4}C_2\times ^{21}C_1}}{^{25}C_3}
Case 2: All the three tested bottles are contaminated.
We can choose 3 contaminated bottles out of \(4\) in \(^{4}C_3\) ways. The probability of this case is:
\(\frac {{^{4}C_3}}{{^{25}C_3}}\)
Now, we sum the probabilities of both cases:
P(More than 1 contaminated)\(=\frac{({^{4}C_2\times ^{21}C_1)+^{4}C_3}}{^{25}C_3}\)
Using the combination formula and simplifying, we get:
P(More than 1 contaminated)\(=0.1679\).
Thus, the probability that more than 1 of the tested bottles is contaminated is approximately 0.1679, or as a fraction, as 168/1000.

Learn more about Combination theory here:

https://brainly.com/question/28065038

#SPJ11

Answer:

66 students

Step-by-step explanation:

To find how many played bass instruments, multiply 120 by 0.55

120(0.55)

= 66

So, 66 students played bass instruments

The number of oranges that are expected to weigh more than 4 oz is:

1400 - (1400 × 0.0228)≈ 1368.

The mean weight of the oranges growing in an orchard is 8 oz and standard deviation is 2 oz, the distribution of the weight of oranges can be represented as normal distribution.

From the batch of 1400 oranges, the number of oranges is expected to weigh more than 4 oz can be found using the formula for the Z-score of a given data point.

\(z = (x - μ) / σ\)

Wherez is the Z-score of the given data point x is the data point

μ is the mean weight of the oranges

σ is the standard deviation

Now, let's plug in the given values.

\(z = (4 - 8) / 2= -2\)

The area under the standard normal distribution curve to the left of a Z-score of -2 can be found using the standard normal distribution table. It is 0.0228. This means that 0.0228 of the oranges in the batch are expected to weigh less than 4 oz.

To know more about normal distribution  visit :

https://brainly.com/question/23418254

#SPJ11

Answer:

Find the indicated sum for each geometric series.

{1875+750+300+⋯+3.072}

Answer: 3122.952

Step-by-step explanation:

{1875+750+300+⋯+3.072}

r=0.4 3.072=1875(0.4)n−1

0.0016384=(0.4)n−1

7=n−1→n=8

Sn=1875(1−(0.4)8)1−0.4=3122.952

I think is like this.

It reaches a high of 51.8 degrees Fahrenheit. There is a 59.4 degree F range. 12.6 degrees Fahrenheit is the standard deviation. The average temperature is 33.8°F. The median temperature is 35.6 °F. IQR is 60.8 degrees Fahrenheit.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem. The study of gathering, analyzing, interpreting, presenting, and organizing data in a particular way is the focus of the mathematic branch known as statistics. The process of gathering data, classifying it, presenting it in a way that makes it understandable, and then conducting additional analyses of the data is known as statistics.

To know more about statistics,

https://brainly.com/question/16765198

#SPJ4