about 2% of the population has a particular genetic mutation. 300 people are randomly selected. find the standard deviation for the number of people with the genetic mutation in such groups of 300.

Answer:

$470

Step-by-step explanation:

%30 of 470 = $141

Answer: $470

I hope it help

The perimeter of the rug is 37.2

The first line says that the rug is twice as long as its width. If the width is taken as w and length is taken as l, we get an equation l= 2w. Since it is a rectangle, the area of the rectangle will be (length*width) which is equal to l*w.

Since l=2w, area = 2w*w = 2w^2. This is given equally to 76.88.

2w^2 = 76.88

w^2 = 38.44

w = 6.2

l = 2w = 2*6.2 = 12.4

Now, perimeter of rectangle is 2w+2l = 2*6.2 + 2*12.4 = 37.2

Hence the perimeter of the rug is 37.2

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Answer:

Step-by-step explanation:

The street was 900m long when the speed is 15m/s and, the time is 60 seconds.

To calculate speed, divide the distance traveled by the time it took to complete the voyage, so speed = distance divided by time. To determine the distance, multiply the speed by the passage of time. These equations can be reduced as s=d/t, where s represents speed, d represents distance, and t represents time.

Distance divided by time equals speed. Distance = time * speed

To solve for speed or rate, utilize the speed formula, s = d/t, which implies speed equals distance divided by time. To solve for time, utilize the time formula, t = d/s, which implies time equals distance divided by speed.

Given,

Speed of the biker who travels down the street=15m/s

Time taken=60seconds

Distance=?

We know that,

Distance=Speed× Time

Distance=15×60

Distance=900m

Therefore, the street was 900m long

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The number 1/8 represent the fraction of full sheet of paper the teacher asked each student to color.

The information given are;

The information given are

= 1/4 of 1/2x

= 1/4 × 1/2x

= 1/8x

So therefore, the student colored 1/8 of the original piece of paper.

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Answer:

60 [tex]in^{2}[/tex]

Step-by-step explanation:

Volume = the area of the base times the height.

Base:

[tex]\frac{lengthxwidth}{2}[/tex]

[tex]\frac{3x4}{2}[/tex]

6  multiply this by the height of 10

Volume = 60 [tex]in^{3}[/tex]

Answer:

-------------------------------

From the figure

A. alternate interior angles:  1

B. same side exterior: 4

C. vertical: 4 and 3

D. same side interior: 3

E. obtuse angle: 1

F. adjacent angle pairs: 1 and 2

G. alternate exterior: 2

H. corresponding: 4

I. complimentary:

parallel lines refer too lines that would never meet. When there is a pair of parallel lines with a transversal line like in the figure some angle theorems come into play  

some of the are used in the in the problem and definition of some them include

adjacent angles refer to angles that are next to each other, such angles are being demarcated by a line to the other angle. in the figure angle 1 and 2 alternate angles

Obtuse angles refers to angles that are more than 90 degrees but less than 90 degrees

vertical angles are angles opposite to each other, formed when two lines meet

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The equation of the line that passes through the point (-4, 3) and slope of 3/4 is y = 3x/4+6.

According to the question,

We have the following information:

We have the point (-4,3) and a slope of 3/4.

We know that the following formula is used to find the equation passing through any point:

(y-y') = m(x-x') where m is the slope and in this case, y' = 3 and x' = -4

y-3 = 3/4{x-(-4)}

y-3 = 3/4 (x+4)

Multiplying 3/4 into the bracket:

y-3 = 3x/4 + 3

Moving -3 from the left hand side to the right hand side:

y = 3x/4+3+3

y = 3x/4+6

Hence, the equation of the line that passes through the point (-4, 3) and slope of 3/4 is y = 3x/4+6.

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Answer:

By comparing both the figures there is a difference of 6

[tex]x + 1 = 24 - 6 \\ x = 24 - 6 - 1 \\ x = 17[/tex]

The value of the correlation coefficient is 0.625.

Correlation coefficients quantify the strength of a relationship between two variables. A correlation coefficient is a number ranging from -1 to 1 that indicates the degree and direction of a relationship between variables. It is a statistical notion that aids in the establishment of a relationship between predicted and actual values collected in a statistical experiment.

In this case, the slope of the model was 2.5 centimeters per pH level, and the standard deviation of the sample of plant heights was 4 centimeters.

The correlation coefficient will be:

= Slope / Standard Deviation

= 2.5 / 4

= 0.625

The coefficient is 0.625.

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The length of the line segment MN given that the ratio of KL:LM:MN = 2:3:1 is; 9

We are told that the points K, L, M and N all lie on the same line segment.

Since the points lie on the same line segment, then it means that they are collinear points.

We are told that the ratio of the segments, KL:LM:MN = 2:3:1.

This means that we can find the length of MN since we are also given the total length of the whole segment, KN = 54.

Length of MN = (Individual ratio of MN ÷ the total ratio value of the 3 given segments) × length of the whole segment

Individual ratio of MN = 1

Total ratio value of the 3 given segments = 2 + 3 + 1 = 6

Length of whole segment, KN = 54

Length of MN = (1/6) * 54

Length of MN = 9

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Answer:

Step-by-step explanation:

3b(2x - z^3)  = 2h - 7gx      Distribute 3b

6bx - 3bz^3 = 2h - 7gx      Add 3bz^3 to both sides

6bx = 3bz^3 + 2h - 7gx    Add 7gx to both sides

6bx + 7gx = 3bz^3 + 2h     Factor left side, factor out a gcf of x

x(6b + 7g) = 3bz^3 + 2h     Divide both sides by (6b + 7g) to isolate x

x = (3bz^3 + 2h)/ (6b + 7g)

Answer:

2 3/5

Step-by-step explanation:

First, change all terms to improper fraction

We have;

13/2÷5/2

13/2 ×2/5

13/5

Change to mixed fraction, we have;

2 3/5

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The simplest simplified form of the given expression is 3 9/10.

First, let us understand the mixed number;

A mixed number is made up of three components: a whole number, a numerator, and a denominator. The numerator and denominator are both components of the appropriate fraction that results in the mixed number.

Change all the given terms to improper fractions, we will get;

6 1/2 = (6 * 2 + 1) / 2 = 13 / 2

1 2/3 = (1 * 3 + 2) / 3 = 5 / 3

We are given;

13/2 ÷ 5/3

= 13/2 × 3/5

= 39/10

Change to mixed fraction, we will get;

39/10 = 3 9/10

Thus, the simplest simplified form of the given expression is 3 9/10.

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1st image

angle 5 is 31 degrees alternate interior angles

2nd image

angle8=angle9, alternate interior angles

Answer:

125=16t², t²=125/16=√7.8125=2.7951 ,hence t=3secounds

Answer:

The second plan ($15.00 for 15 songs) offers the lowest cost per song.

Step-by-step explanation:

The objective is to find the plan that provides the lowest cost per song.  "Lowest cost per song" is basically $/song.  So let's compare the two plans by calculating the cost per song.

Plan 1:  $9.60/(8 songs)    = $1.20/song

Plan 2: $15.00/(15 songs) =  $1.00/song

The second plan ($15.00 for 15 songs) offers the lowest cost per song.

The value of x is 5 for the given equation 5/3 = x/3.

So, the equation is:

Now, solve for x as follows:

Therefore, the value of x is 5 for the given equation 5/3 = x/3.

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Correct question:

Solve for x. 5/3= x/3

The quadratic function has only maximum value :

[tex]F(x)_{min}[/tex] = 30

x = 3

There is no minimum value of the quadratic function.

Given,

In the question:

The quadratic function is given as:

F(x) =  [tex]-3x^2+18x +3[/tex]

Determine whether the following quadratic function has a maximum or a minimum value. Then find  the maximum and minimum value of the function.

Now, According to the question:

The quadratic function is given as:

F(x) =  [tex]-3x^2+18x +3[/tex]

Take out the leading coefficient

F(x) = -3[tex](x^2-6x)+3[/tex]

Complete the square:

F(x) = [tex]-3(x^2+(2(-3))x + (-3)^2)+(3-(-3)^2))[/tex]

Express the function in vertex form

F(x) = [tex]-3(x-3)^2+30[/tex]

To  find the maximum value

[tex]F(x)_{min}[/tex] = 30

x = 3

For Minimum value:

F(x) = [tex]-3x^2 +18x +3[/tex]

Rewrite the function by completing the square

F(x) = [tex]-3(x-3)^2+30[/tex]

The graphs always open downwards

So, There is no minimum value of the quadratic function.

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Answer: x=4

Step-by-step explanation: simplify expression and divide polynomials

Answer: 9

Step-by-step explanation:

        Finding the zeros is the same as solving. Then, we will add the two solutions together.

Given:

y = x² - 9x - 10

Solving by Quadradic Formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

[tex]\displaystyle x=\frac{-(-9)\pm\sqrt{(-9)^2-4(1)(-10)} }{2(1)}[/tex]

[tex]\displaystyle x=\frac{9\pm\sqrt{81+40} }{2}[/tex]

[tex]\displaystyle x=\frac{9\pm\sqrt{121} }{2}[/tex]

[tex]\displaystyle x=\frac{9+11}{2},\;\;x=\frac{9-11}{2}[/tex]

x = 10, -1

Adding them together:

10 + -1 = 9

The way that one number in the second equation be changed so the system has only one solution is;  to divide each term by 2 to get the coefficient of y as 5.

There are different methods to solve simultaneous equations such as;

We are given the equations as;

3x + 5y = 4

16x + 10y = 4

Now, we want to perform an operation whereby we make the second equation be changed so the system has only one solution. This method is the elimination method.

The elimination method is the process that we use to eliminate one of the variables in the system of linear equations with the aid of the addition or subtraction methods as well as multiplication or division of coefficients of the variables.

Now, since we have 5y in the first equation, the first step to carry out on the second equation is to divide each term by 2 to get the coefficient of y as 5.

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Answer:

Jane paints faster if I may be correct

Step-by-step explanation:

in order to be able to decide each case we need the slopes of all involved lines.

and that means we need to bring all of the equating into a "y = ..." form, because then the slope is always the factor of x.

parallel lines have the same slope.

the slopes of perpendicular lines (intercept at a right angle) have the y/x ratio turned upside-down and a flipped sign : -x/y.

"neither" is everything else.

our reference line

x + 2y = 6

2y = -x + 6

y = -1/2 x + 3

so, the reference slope is -1/2.

y = -1/2 x - 5 is parallel (same slope).

-2x + y = -4

y = 2x - 4 perpendicular (2/1 vs. -1/2)

-x + 2y = 2

2y = x + 2

y = 1/2 x + 1 neither

x + 2y = -2 parallel (as the structure except for the constant part is the same as our reference line).

2y = -x - 2

y = -1/2 x - 1

Answer:

  A)  n > 0

Step-by-step explanation:

You want the solution and graph for -8n +18 > -6(3n -3).

Eliminating parentheses, we have ...

  -8n +18 > -18n +18

Subtracting 18 gives ...

  -8n > -18n

Adding 18n, we have ...

  10n > 0

Finally, dividing by 10 gives ...

  n > 0

The graph is attached.

The equation of the line in the slope intercept form is y = (-1/2)x + 60

From the given graph,

Choose two points

(0, 60) and (40, 40)

The slope of the line the change in y coordinates with respect to the change in x coordinate of the function

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the value in the equation

= [tex]\frac{40-60}{40-0}[/tex]

= -20/40

= -1/2

From the graph we can say that,

y intercept of the line = 60

The slope intercept form is

y = mx + b

where m is the slope of the line

b is the y intercept

y = (-1/2)x + 60

Hence, the equation of the line in the slope intercept form is y = (-1/2)x + 60

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It is equivalent to 8^x/3

acc to our question-

to write a square root into fraction. To do that, you just have to apply the formula :

x^power/root

Then, here it gives . 8^x/3

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To find the parallel line of y =3z+6 passing through the slope intercept points (-2,5).

For a line to be parallel to another line, by definition it must have the same slope.

Because the equation is in the slope-intercept form we can use the slope of the line.

The slope- intercept form of a linear equation is :

y=mx+b

Where m is the slope and b is the y− intercept value.

Therefore, for the given equation, the slope is 3.

Now we can use the point slope formula to determine the equation for the parallel line.

The point - slope formula states: (y−y1)=m(x−x1)

Where m is the slope and (x1,y1) is a point the line passes through.

Substituting the slope from the given line and the given point gives:

y−5=3(x+2)

Transforming this to the slope-intercept form by solving for y gives:

y−5=3x+6

y−5+5=3x+6+5

y=3x+11

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The probability that a designer does not prefer red is 0.77.

Probability (event) = favorable outcome / total outcome

Total primary color designers = 400.

The number of opinions for red = 92

The probability for designer prefer red = 92 /100

The probability for designer prefer red = 0.23

Then, the probability that a designer does not prefer red = 1 - 0.23

The probability that a designer does not prefer red = 0.77

Thus, the probability that a designer does not prefer red color = 0.77.

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The correct question along with table is attached-