\(\frac{8x+32}{6}\) = x+5

The required requirement of the density curve is should be equal to 1 and the ordinate should not be zero.

Given that,
Two requirements of a density curve are to be determined.

A density curve is defined as a curve on a graph that represents the distribution of values in a dataset.

Here,

The two requirements of a density curve should be,

a. The area under the density curve should be equal to 1.

b. The ordinate of the curve should not be zero i.e. they should always have the vertical height.

Thus, the required requirement of the density curve is mentioned above.

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The observed allele frequencies for the T102C locus are as follows: T allele frequency = 0.388 and C allele frequency = 0.612.


To calculate the observed allele frequencies, we divide the number of occurrences of each allele by the total number of alleles observed.

In this case, the T allele is observed in 108 TT genotypes and 194 TC genotypes, giving a total of 108 + 194 = 302 T alleles. Similarly, the C allele is observed in 194 TC genotypes and 48 CC genotypes, giving a total of 194 + 48 = 242 C alleles.

To calculate the T allele frequency, we divide the number of T alleles by the total number of alleles: 302 T alleles / (302 T alleles + 242 C alleles) = 0.388 (or approximately 0.39).

Similarly, the C allele frequency is calculated as: 242 C alleles / (302 T alleles + 242 C alleles) = 0.612 (or approximately 0.61).

Therefore, the observed allele frequencies for the T102C locus are T allele frequency = 0.388 and C allele frequency = 0.612.

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The maximum volume of the cylinder is 27147.355 cm² at the maximum point.

What is volume of cylinder?

The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula r2h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder. The substance could be a liquid amount or something else that can be evenly put into the cylinder.

The formula for the volume of the cylinder v = \(\pi r^2\)h,

To find the maximum volume of the cylinder we apply the condition of maxima \(\frac{dv}{dr}\)  = 0.

Let r cm be the radius and h cm be the height of the closed cylinder.

Then, Total surface area of the cylinder = \(2\pi r(r+h)\)

                                                   5000      = \(2\pi r^{2} +2\pi rh\)

                                                    h     =    \(\frac{5000-2\pi r^{2} }{2\pi rh}\)............(1)

Volume of the cylinder v = \(\pi r^2h\)

Substitute the value of h  in the above equation

                                      = \(\pi r^2\) × \(\frac{5000-2\pi r^{2} }{2\pi rh}\\\)

                                      = \(\frac{r}{2}\) ×  \(5000-2\pi r^2\)

                                   v = \(2500r-\pi x^{3}\) ..............(2)

Now, for the maximum volume of the cylinder   dv/dr= 0

                                                      \(\frac{d(2500r-\pi x^{3})}{dr}\)         =0

                                                            \(3\pi r^{2} =2500\)

                                                               \(r^{2} =\frac{2500}{3\pi }\)

                                                              r=\(\frac{50}{\sqrt{3\pi } }\)

                                                           r= 27147.355

Hence, The maximum volume of the cylinder is 27147.355 at the maximum point r= \(\frac{50}{\sqrt{3\pi } }\).

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Answer:

it would be C.

Step-by-step explanation:

Solve the equation for  x  by finding  a ,  b , and  c  of the quadratic then applying the quadratic formula.

If Abby is collecting rainfall data, and she finds that one value of the data set is a high-value outlier, then the statement that must be true is "the outlier will pull the mean towards its value."

Outliers are the data points in a distribution that stand out from the rest. In other words, an outlier is a value that is far from the other values in the dataset.

An outlier is a value that is more than 1.5 times the interquartile range (IQR) greater than the upper quartile or less than the lower quartile plus 1.5 times the IQR, which is often referred to as the "1.5*IQR rule."

Here are a few statements that describe the impact of an outlier on a data set:

An outlier does not have an effect on the median value of the data set.

The presence of an outlier in a dataset will raise the range of the dataset.

The presence of an outlier in a dataset will raise the standard deviation of the dataset.

The outlier will pull the mean towards its value, as well as increase the value of the mean.

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complete question:

Abby is collecting rainfall data. She finds that one value of the data set is high-value outlier. Which statement must be true?

1. Abby will use a different formula for calculating the standard deviation

2. The outlier will increase the standard deviation of the data set

3. The spread of the graph of the data will not change

4. Abby will not use the mean when calculating the standard deviation

Answer:

b)The outlier will increase the standard deviation of the data set.

Step-by-step explanation:

e2020

The ratios of vowels to consonants in the words pineapple and strawberry are:

Pineapple: 4:5

Strawberry: 1:4

Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another.

For pineapple:

There are 4 vowels (a, i, e, and a) and 5 consonants (p, n, p, p, and l).

Thus, the ratio of vowels to consonants in the word " pineapple" is:

4:5

For strawberry:

There are 2 vowels (a and e) and 8 consonants (s, t, r, w, b, r, r and y).

Thus, the ratio of vowels to consonants in the word "strawberry" is:

2:8 = 1:4

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The deepest that Lucy dove is 5 feet when Antonia dove at least 7 times as deep as Lucy did.

According to the question,

We have the following information:

On a snorkeling trip, Antonia dove at least 7 times as deep as Lucy did. If Antonia dove 35 feet below the ocean's surface.

Let's take the feet Lucy dove is x feet.

So, we have the following expression:

Antonia dove 7x times.

7x = 35

x = 35/7 (7 was in multiplication on the left hand side. So, it is in the division on the right hand side.)

x = 5 feet

Hence, Lucy dove 5 feet below the ocean's surface.

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Answer:

y-6=22(x-5) or y=22x-104

Step-by-step explanation:

Slope-point form is y-y1=m(x-x1)

x1=5

y1=6

m=22

Now plug it all in

y-6=22(x-5)

You can leave it that way or simplify it down to y=22x-104 if you'd like

Hope this helps!

The term that best describes the investment is $1,250 invested at 4% compounded interest. The Option A is correct.

We will use compound interest: A = P(1 + r/n)^(nt) formula to get the annual total investment. In this case, P = $1,250, r = 0.04, n = 1 and t = 1.

Plugging the values, we get:

A = 1250(1 + 0.04/1)^(1*1)

A = 1250(1.04)

A = $1,300

Therefore, term that best describes the investment is $1,250 invested at 4% compounded interest.

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Answer:

114.666666666666667

Step-by-step explanation:

The critical points are (0, 0) and (1/2, 1/8).

To find the critical points of the function f(x, y) = 8x^3 + y^3 - 6xy + 2, we need to find the points where the partial derivatives of f with respect to x and y are equal to zero.

a.) Finding the critical points:

∂f/∂x = 24x^2 - 6y = 0

∂f/∂y = 3y^2 - 6x = 0

From the first equation, we have:

24x^2 - 6y = 0

4x^2 - y = 0

y = 4x^2

Substituting y = 4x^2 into the second equation:

3(4x^2)^2 - 6x = 0

48x^4 - 6x = 0

6x(8x^3 - 1) = 0

This gives two possible cases:

6x = 0, which implies x = 0.

8x^3 - 1 = 0, which implies 8x^3 = 1 and x^3 = 1/8. Solving this equation, we find x = 1/2.

For x = 0, we can substitute it back into y = 4x^2 to find y = 0.

So, the critical points are (0, 0) and (1/2, 1/8).

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The quotient is 1111. The process continues until the result is less than the divisor.

To perform the division using the restoring-division algorithm with the given divisor and dividend, follow these steps:

Step 1: Initialize the dividend and divisor

Divisor: 00011

Dividend: 1011

Step 2: Append zeros to the dividend

Divisor: 00011

Dividend: 101100

Step 3: Determine the initial guess for the quotient

Since the first two bits of the dividend (10) are greater than the divisor (00), we can guess that the quotient bit is 1.

Step 4: Subtract the divisor from the dividend

101100 - 00011 = 101001

Step 5: Determine the next quotient bit

Since the first two bits of the result (1010) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

Step 6: Subtract the divisor from the result

101001 - 00011 = 100110

Step 7: Repeat steps 5 and 6 until the result is less than the divisor

Since the first two bits of the new result (1001) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100110 - 00011 = 100011

Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100011 - 00011 = 100001

Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100001 - 00011 = 011111

Since the first two bits of the new result (0111) are less than the divisor (00011), we guess that the next quotient bit is 0.

011111 - 00000 = 011111

Step 8: Remove the extra zeros from the result

Result: 1111

Therefore, the quotient is 1111.

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Answer:

1/2

Explanation:

Given a geometric progression with the following:

• The first term, a= -8

• The 6th term = -1/4

The nth term of a geometric progression is obtained using the formula:

Substitute the given values:

We solve the equation for r:

Next, take the 5th root of both sides:

The common ratio of the geometric progression is 1/2.

Answer:

Step-by-step explanation:

hope this helps. pls mrk me branliest :)

Answer:

1)24.25

2)21

Step-by-step explanation:

1) (a/4)^2=(20/4)^2=25

b/2/8=6/8=3/4

25-3/4

=100/4-3/4

=97/4

=24.25

2)2(x-y)^2=2(3)^2=18

x-y=3

=18+3

=21

Hope this helps!

From the given suspects information, D is lying and C is the one who actually cheated. So, correct option is D.

To determine who is lying and who cheated, we need to analyze the statements and check for inconsistencies.

Let's analyze each statement:

A said: C won't cheat unless B cheated.

This statement implies that if C cheated, then B must have also cheated. If C is telling the truth, then B is also telling the truth.

B said: Either A or B cheated.

This statement implies that either A or B cheated, but not both. If B is telling the truth, then A must be lying, as both cannot be true.

C said: B didn't cheat, I cheated.

This statement implies that C cheated, but B did not cheat. If C is telling the truth, then B is lying.

D said: B cheated.

This statement implies that B cheated. If D is telling the truth, then B is also telling the truth.

Based on the analysis, we can conclude that C is lying because if C cheated, then B must have cheated according to A's statement. This means that B is telling the truth.

Therefore, the correct answer is:

d) D lied, C cheated.

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Answer:

6x² - 12x - 18

the factors are -18 and 6

6x² - 18x + 6x - 18

6x(x - 3) + 6 (x - 3)

(6x + 6) or (x - 3)

the factors are:

(6x + 6) or (x - 3)

Option (A) is the correct option and on simplifying the expression by combining like terms we get,

24 - 3p.

Here, we have,

Given, the expression 6(4 - 2p) + 9p

On simplifying, we get

24 - 12p + 9p

24 - 3p

So, on simplifying the given expression, we get

24 - 3p

Hence, Option (A) is the correct option and on simplifying the expression by combining like terms we get,

24 - 3p

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The average velocity for the [3,4] is 27m/s and for [4,5] is 37m/s

The average velocity can be found by taking the derivative of the position function and evaluating it at the midpoint of the interval.

The average velocity on the interval [3,4] is given by (s(4) - s(3)) / (4 - 3), which is equal to (s(4) - s(3)) / 1. Using the position function, s(t) = 5t^2 - 8t + 13, we find that s(4) = 5(4²) - 8(4) + 13 = 61 and s(3) = 5(3²) - 8(3) + 13 = 34. Therefore, the average velocity on the interval [3,4] is (61 - 34) / 1 = 27 m/s.

The average velocity on the interval [4,5] is given by (s(5) - s(4)) / (5 - 4), which is equal to (s(5) - s(4)) / 1. Using the position function, s(t) = 5t² - 8t + 13, we find that s(5) = 5(5²) - 8(5) + 13 = 98 and s(4) = 5(4²) - 8(4) + 13 = 61. Therefore, the average velocity on the interval [4,5] is (98 - 61) / 1 = 37 m/s.

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Answer:

Step-by-step explanation:

it is related as all integers are rational numbers

The required solution is integers are rational numbers.

It is required to find the solution.

Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.

Solution:

They are related because most of the integer numbers are similar to rational numbers. Also, when subtracting, it is basically like adding a negative number which is a integer. They are related because the equations have both integer and rational numbers in it.

∴It is related as all integers are rational numbers.

Therefore, the required solution is integers are rational numbers.

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Answer:

answer my question

Step-by-step explanation:

20 boxes of strawberries and 6 boxes of blueberries were purchased by Melissa.

We can use these two equations to solve for x and y:

x + y = 26 (equation 1)

3x + 1.25y = 67.50 (equation 2)

We can multiply equation 1 by 1.25 and subtract it from equation 2 to get rid of y:

3x + 1.25y = 67.50

-1.25x - 1.25y = -32.5

1.75x = 35

x = 20

Substituting x = 20 into equation 1, we get:

20 + y = 26

y = 6

A mathematical definition of an equation is a claim that two expressions are equal and joined by the equals sign "=".

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

A condition on a variable is what an equation in algebra is. It can only be satisfied if the variable has a specific value. That means that only the value of x = 9 may satisfy the equation 2x - 5 = 13.

From the question:

Let x represent the number of boxes Melissa purchased of strawberries, and y represents the number of boxes Melissa purchased of blueberries.

All in sum, Melissa purchased 26 boxes of berries, thus x + y = 26.

A box of strawberries costs $3, hence the price of x boxes of strawberries is $3.

Blueberries cost $1.25 a box, thus 1.25 dollars are spent on y boxes of blueberries.

In total, Melissa spent $67.50, therefore 3x + 1.25y = 67.50.

x + y = 26 (equation 1)

3x + 1.25y = 67.50 (equation 2)

3x + 1.25y = 67.50

-1.25x - 1.25y = -32.5 (multiplying equation 1 by 1.25 and changing its sign)

1.75x = 35

x = 20

Substituting x = 20 into equation 1, we get:

20 + y = 26

y = 6

Melissa consequently purchased 6 boxes of blueberries and 20 boxes of strawberries.

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The solution is Option B.

The system of inequalities is x² - 2y ≥ 7000 and 2x + 5y < 1000

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the first inequality equation be represented as A

Let the second inequality equation be represented as B

Now , value of a company’s stock is represented by the expression x² - 2y

And , company’s goal is to maintain a stock value of at least $ 7,000

So , the inequality is x² - 2y ≥ 7000

And , the company’s purchases are modeled by 2x + 5y

Also , the company's purchases should be below $ 1,000

So , the inequality is 2x + 5y < 1000

Hence , the inequalities are solved

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Answer:

≈78.539816 ft²

≈78.54 ft²

Step-by-step explanation:

Since the logo is in the shape of a circle, the area can be found with the formula:

To find r, divide the diameter of the circle by 2 (r stands for radius, the length from the center of the circle to the edge):

Now that all variables are known, complete the equation to find the area:

Answer:

1.36

2.-60

3.30

hope this helps

Answer:

U did not add a picture but if u do I will help.

Step-by-step explanation:

It should be 8 to the right and 12 to the left which should end at -4

Answer:

The answer is 4?? tell me if it's wrong or not.

An equation is formed of two equal expressions. The equation of the ellipse is,

⇒ [(x-6)²/49] + [(x-2)²/9] = 1.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

As it can be seen that the centre of the ellipse is at (6,2). Also, the major radius is equal to 7 units, while the minor radius is equal to 3 units. The general equation of the ellipse is given as,

(x - h)²/a² + (y - k)²/b² = 1

(x - 6)²/7² + (y - 2)²/3² = 1

[(x-6)²/49] + [(x-2)²/9] = 1.

Hence, the equation of the ellipse is,

⇒ [(x-6)²/49] + [(x-2)²/9] = 1 .

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Answer:

the answer is A on edge :)

Step-by-step explanation:

good luck <3

Answer:FGJ is 71º

Step-by-step explanation:

Since 1 (HGJ(35º) and 2 (FGH(36º) added together is 71º and both 1 and 2 are in FGJ that means FGJ is 71º

Hope this helped!If you are reading this hope you have a wonderful day and may  your dreams come true!

Tell me if it’s wrong :(

Good luck

\(\dfrac{2ax+3}{ax+3}=-1\)

Rewrite -1 as a fraction

\(\dfrac{2ax+3}{ax+3}=\dfrac{-1}{1}\)

Cross multiply

\(2ax+3=-1(ax+3)\)

Distribute the -1

\(2ax+3=-ax-3\)

Add both sides by ax

\(3ax+3=-3\)

Subtract both sides by 3

\(3ax=-6\)

Divide both sides by 3a

\(x=-\dfrac{6}{3a}\)

Simplify

\(=-\dfrac{2}{a}\)

That's the value of x respect to a. Let me know if you need any clarifications, thanks!

Answer:

Step-by-step explanation:

\(\frac{2ax+3}{ax+3} =-1\\2ax+3=-ax-3\\2ax+ax=-3-3\\3ax=-6\\x=-\frac{2}{a}\)

Answer:

Step-by-step explanation:

QA = QC = 5.9    ⇒    PA = 27.4 - 5.9 = 21.5

PB = PA = 21.5

CR = BR = 12.2

So, the perimeter:

P = 27.4 + 5.9 + 2×12.2 + 21.5 = 79.2

The perimeter of the triangle PQR is 79.2 units.

Perimeter of a straight sided figures or objects is the total length of it's boundary.

Given a triangle PQR.

An incircle is drawn inside the triangle.

We know that the length of the tangents which are drawn from an exterior point to the circle are equal.

Using this property and the given lengths,

PQ = 27.4

PR = (27.4 - 5.9) + 12.2 = 33.7

QR = 5.9 + 12.2 = 18.1

Perimeter of the triangle = 27.4 + 33.7 + 18.1 = 79.2 units

Hence the perimeter is 79.2 units.

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