In a class of 20 students:
11 have a brother
9 have a sister
6 have neither
Fill in the Venn Diagram.

Answer:

a. The mean mark for the test was 20.667.

b. The mean mark as a percentage is 51.6%.

Step-by-step explanation:

a. Calculate the mean mark for the test.

b. Express the mean mark as a percentage.

Answer:

A

Step-by-step explanation:

Angles 1 and 3 are congruent since they are vertical angles.

Angle 7 is congruent to angle 3 since they are corresponding angles.

Angle 5 is congruent to angle 1 since they are corresponding angles.

Answer: A

If the given differential equation is

[tex]\cos^2(x) \sin(x) \dfrac{dy}{dx} + \cos^3(x) y = 1[/tex]

then multiply both sides by [tex]\frac1{\cos^2(x)}[/tex] :

[tex]\sin(x) \dfrac{dy}{dx} + \cos(x) y = \sec^2(x)[/tex]

The left side is the derivative of a product,

[tex]\dfrac{d}{dx}\left[\sin(x)y\right] = \sec^2(x)[/tex]

Integrate both sides with respect to [tex]x[/tex], recalling that [tex]\frac{d}{dx}\tan(x) = \sec^2(x)[/tex] :

[tex]\displaystyle \int \frac{d}{dx}\left[\sin(x)y\right] \, dx = \int \sec^2(x) \, dx[/tex]

[tex]\sin(x) y = \tan(x) + C[/tex]

Solve for [tex]y[/tex] :

[tex]\boxed{y = \sec(x) + C \csc(x)}

which follows from [tex]\tan(x)=\frac{\sin(x)}{\cos(x)}[/tex].

Answer:

34 years

Step-by-step explanation:

f = s + 28          Eq. 1

f+8 = 3(s+8)      Eq. 2

f = father age

s = son age

replacing Eq. 1 on Eq. 2

(s+28) + 8 = 3(s+8)

s + 36 = 3*s + 3*8

s + 36 = 3s + 24

36 - 24 = 3s - s

12 = 2s

12/2 = s

s = 6

from the Eq. 1

f = 6 + 28

f = 34

Check

from the Eq. 2

34+8 = 3(6+8)

42 = 3*14

Answer:

To calculate the area that Marcus needs to paint we must calculate the area of the window and subtract it from the total area of the wall.

To calculate the area of a rectangular wall we must use the following formula:

Where a is the length of the height, and b is the length of the width.

Next, we need to calculate the area of the window. If it is a square or rectangular window we use the same formula "area = a × b".

If the window is circular we use this formula:

Once we know the area of the wall and the area of the window, we subtract the area of the window from the area of the wall and we will know what is the total area that Marcus must paint.

Note: This question is incomplete because some information is missing. However I can answer it based on my general prior knowledge.

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The plot represent the data A box plot titled Scores of Participants and labeled Scores uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35.

The box extends from 17 to 24 on the number line.

A line in the box is at 23 The whiskers end at 12 and 28.

A box plot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.

Given:

12 points

21 points

29 points

17 points

24 points

23 points

28 points

According to the given data,

A box plot titled Scores of Participants and labeled Scores uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35.

The box extends from 17 to 24 on the number line.

A line in the box is at 23 The whiskers end at 12 and 28.

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Answer:

D

Step-by-step explanation:

factor the denominators of both fractions

x² - 16 ← is a difference of squares

= (x - 4)(x + 4)

8x + 2x² ← factor out 2x from each term

= 2x(4 + x) = 2x(x + 4)

then expression is

[tex]\frac{x^2}{(x-4)(x+4)}[/tex] + [tex]\frac{9x}{2x(x+4)}[/tex]

with LCD of 2x(x + 4)(x - 4)

The area of the surface of the pool is 7322.64 m².

The area of rectangle is product of length and its breadth.

i.e., length * breadth

Given: Length = 100 m, Width = 52 m and Diameter = 52 m

Area of rectangle,

= 100 × 52

= 5200 m²

Now,

Area of semicircle = 1/2 × πr²

=1/2 × 3.14 × 26²

= 1061.32 m²

Hence, area of the surface of the pool is

= 1061.32 + 1061.32 + 5200

= 7322.64 m²

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5200 square meters, 1061, 7322

Answer:

I think it's 1.17 - -3.85

The solution of the given expression is [tex][p^{2}(p-y)^{y-1} (p-y)^{y-2} -2p(p-y)^{y} (p-y)^{y-2} +7(p-y)^{y} (p-y)^{y-1}]/ (p-y)^{y} (p-y)^{y-1}(p-y)^{y-2}[/tex]

Given [tex]p^{2} /(p-y)^{y} -2p/(p-y)^{y-1} +7/(p-y)^{y-2}[/tex]

We have to solve the above expression.

We know that expression is a combination of numbers, symbols, variables and coefficients, indeterminants. Expression shows relationship between variables. LCM is the smallest number that is divisible by both the numbers whose LCM has been taken. Coefficients are present in the beginning of variables. Symbols are arithmetic signs like addition, subtraction, multiplication and division, etc.

We have to take LCM of the expression and solve accordingly so that the expression can be solved =

[tex]p^{2} /(p-y)^{y} -2p/(p-y)^{y-1} +7/(p-y)^{y-2}[/tex]=  [tex][p^{2}(p-y)^{y-1} (p-y)^{y-2} -2p(p-y)^{y} (p-y)^{y-2} +7(p-y)^{y} (p-y)^{y-1}]/ (p-y)^{y} (p-y)^{y-1}(p-y)^{y-2}[/tex]

Hence the expression  [tex]p^{2} /(p-y)^{y} -2p/(p-y)^{y-1} +7/(p-y)^{y-2}[/tex] is equal to = [tex][p^{2}(p-y)^{y-1} (p-y)^{y-2} -2p(p-y)^{y} (p-y)^{y-2} +7(p-y)^{y} (p-y)^{y-1}]/ (p-y)^{y} (p-y)^{y-1}(p-y)^{y-2}[/tex]

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Answer:

     [tex]\frac{15*7^{x} }{7^{x} +9}[/tex]

Step-by-step explanation:

→ Substitute f(x) into g(x)

     [tex]\frac{15*7^{x} }{7^{x} +9}[/tex]

Answer:

A

Step-by-step explanation:

these two triangles are similar

therefore corresping sides are proportionate

12/8=9/x

12x=72

x=72/12=6

Answer:

the answer is 6

Step-by-step explanation:

i hope this is helpful

Answer:

90 liters

Step-by-step explanation:

please mark me as brainlest

Answer:

The slope is [tex]-\frac{1}{5}[/tex].

Step-by-step explanation:

Choose 2 points on the graph.

(7,3) and (2,2)

Use slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{2-3}{2-7}[/tex]=[tex]\frac{-1}{-5}[/tex]

The slope is [tex]-\frac{1}{5}[/tex].

Answer:

[tex]\frac{1}{5}[/tex] or [tex]0.2[/tex]

Step-by-step explanation:

The slope refers to the gradient of the line.

There is a formula to find the gradient of a line where m is the gradient:

[tex]m=\frac{y_{2}-y_{1} }{x_{2} - x_{1}}[/tex]

So, we will take two points on the line.

Let's take our first point as (-3, 1) and our second as (7, 3).

Let's work with the [tex]y[/tex] values.

The first [tex]y[/tex] value is 1 and the second [tex]y[/tex] value is 3.

So, in the numerator, they would look like [tex]3 - 1[/tex].

Let's work with the [tex]x[/tex] values.

The first [tex]x[/tex] value is -3 and the second [tex]x[/tex] value is 7.

So, in the denominator, this would look like [tex]7--3[/tex].

Let's use these in the fraction and work out our answer:
[tex]m = \frac{3-1}{7--3} = \frac{2}{10} = \frac{1}{5} = 0.2[/tex]

Therefore, our final answer is [tex]\frac{1}{5}[/tex] or [tex]0.2[/tex].

[tex]\large\sf{\sqrt{\frac{1+sin\theta}{1-sin\theta}}+\sqrt{\frac{1-sin\theta}{1+sin\theta}}}[/tex]

[tex]\\[/tex]

[tex]\large \sf{=\frac{\left(\sqrt{1+sin\theta}\right)^{2}+\left(\sqrt{1-sin\theta}\right)^{2}}{\sqrt{(1-sin\theta)(1+sin\theta)}}}[/tex]

[tex]\\[/tex]

[tex]\large\sf{=\frac{1-sin\theta+1+sin\theta}{\sqrt{1^{2}-sin^{2}\theta}}}[/tex]

[tex]\\[/tex]

[tex]\large \sf{=\frac{2}{\sqrt{cos^{2}\theta}}}[/tex]

[tex]\\[/tex]

[tex]\large\sf{= \frac{2}{cos\theta}}[/tex]

[tex]\\[/tex]

[tex]\large\sf{= 2sec\theta}[/tex]

[tex]\\[/tex]

[tex]\large\sf{=RHS}[/tex]

Therefore,

[tex]\large\sf\red{\sqrt{\frac{1+sin\theta}{1-sin\theta}}+\sqrt{\frac{1-sin\theta}{1+sin\theta}}=2sec\theta}[/tex]

Answer:

  (-1, -5)

Step-by-step explanation:

Each point on a graph is the ordered pair (x, f(x)). Then the point M(-1 -3) is the ordered pair (-1, f(-1)) where f(-1) = -3.

A point on the shifted graph will be ...

  (x, f(x) -2)

Then for x = -1, the point is ...

  (-1, f(-1) -2) = (-1, -3 -2) = (-1, -5)

The minimum on the shifted curve is M'(-1, -5).

_____

Additional comment

f(x) is the y-coordinate of a point on a graph. Then f(x) -2 is the y-coordinate shifted down 2 units.

Answer:

This answer assumes that the first equation is meant to read:

2x + y +3z = 12, and not

1.22x+y+3:= 12

Spoiler Alert:  x = 1, y=4, and z=2

Step-by-step explanation:

1.    2x + y +3z = 12

2.     x - 2y + z = -5

3.    5x - y+ 2z = 5

==============

Use equations 2 and 3 to eliminate z:

2.  x - 2y + z= -5

3.  5x - y+ 2z = 5

-2(x - 2y + z) = -2(-5)   [Multiply equation 2 by -2]

             5x -   y+  2z =  5

Now subtract this new equation from equation 3:

-2x + 4y - 2z = 10  (Eq 3)

 5x -   y+  2z =  5   [

 3x +3y = 15   [Equation A]

=================

Use equations 1 and 2 to eliminate z:

   2x +  y +3z = 12   (Eq. 1)

      x - 2y +  z = -5   (Eq. 2)

   2x +  y +3z = 12

(-3)(x - 2y +  z = -5)  [Multiply Eq. 2 by (-3)]

    -3x + 6y -3z = 15

Now add the resulting two equations.

   2x +   y + 3z = 12     (Eq. 1)

  -3x + 6y -3z =  15       (Eq,2 times -3)

   -x   +7y         = 27    [Equation B]

=============

  Eliminate x with the 2 resulting equations (from above)

  3x +3y = 15  [Equation A]

   -x +7y = 27  [Equation B]

----

   3x +3y = 15

   3*(-x +7y = 27)  [Multiply the Equation B by 3]

  -3x +21y = 81     [Aha - this equation has a -3x term, exactly what we need to eliminate the x term in Equation A]

---

Now add the two resulting equations:

    3x +3y = 15

   -3x +21y = 81

            24y = 96  [The x term disappears.  But we'll "find x" later]

                 y = 4   [Divide both sides by 24]

Find y and z:

Since y = 4,

-x  +7y   = 27 (From above, Equation B]

-x = -7y + 27

 x = 7y - 27

x = 7(4)-27

 x = 1                  [Looking good]

=====

Find z:  (Use y = 4 and x = 1)

x - 2y + z = -5  [Equation 2]

(1) -2*(4) + z = -5

1 - 8 + z = -5

z = 2

Check:

Do the original equations work when x = 1, y = 4, and z = 2?

Results:  

1.    2x + y +3z = 12      

     (1) + (4) +3(2)    YES, this equals 12

2.     x - 2y + z = -5  

       (1)  -2*(4) + (2)   YES, this equals -5

3.    5x - y+ 2z = 5

       5(1) - (4) + 2(2)   YES, this equals 5

x = 1, y=4, and z=2

Answer:

The place value of 3 is tens

the 3 is in the value of tens

Answer:

A and B are correct

Step-by-step explanation:

The middle letter represents the vertex of an angle. For instance, angle ABC has a vertex at B. Because the letter "e" is in the middle of angle FED and angle DEF, it represents the vertex of those angles. Hope this helps

The points  (2,6) (-4,-7) have a slope of 13/6 which satisfies the perpendicular condition option (B) is correct.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The question is incomplete.

The complete question is:

Line L has a slope of -6/13. The line through which of the following pair of points is perpendicular to L?

A) (6,-4) (-7,2)

B) (2,6) (-4,-7)

C) (6,9) (-4,-4)

D) (13,-4) (-7,2)

Line L slope m = -6/13

If two lines are perpendicular:

(m)(m') = -1

(-6/13)(m') = -1

m' = 13/6

From the points given finding the slope of every point:

A) (6,-4) (-7,2)

[tex]\rm m' =\dfrac{2+4}{-7-6}[/tex]

m' = -6/13

B) (2,6) (-4,-7)

[tex]\rm m' =\dfrac{-7-6}{-4-2}[/tex]

m' = 13/6

Thus, the points  (2,6) (-4,-7) have a slope of 13/6 which satisfy the perpendicular condition option (B) is correct.

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The answer choice which explains whether the function is a direct variation or not is; This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.

It follows from the task content that the function passes through the origin and hence, if the function was represents as a linear function, it's y-intercept would be zero.

Furthermore, the slope, otherwise termed it's rate of chage is constant and is evaluated as; $5 per hour. Hence, the aforementioned form the basis for the classification of the function as a direct variation.

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The system of equation has an infinitely many solutions

The equations are given as:

2x + y = -3

-2y = 6 + 4x

Express 2x + y = -3 in slope-intercept form

y = - 3 -2x

Divide through by -2 in -2y = 6 + 4x

y = -3 - 2x

So, we have:

y = - 3 -2x  and y = -3 - 2x

Both equations are the same.

This means that the system of equation has an infinitely many solutions

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Answer:

C. Line PQ

Step-by-step explanation:

Tangent means touching, not crossing.

The expression 6000 + 50 + 5 in standard form is 6.055 * 10^3

The expression is given as:

6000 + 50 + 5

Evaluate the sum

6055

A number in standard form is represented as

a * 10^b

Where:

0 < a < 1

b is an integer

So, we have:

6055

Multiply by 1

6055 * 1

Express 1 as 1000/1000

6055 * 1000/1000

This gives

6.055 * 1000

Express 1000 as 10^3

6.055 * 10^3

Hence, 6000 + 50 + 5 in standard form is 6.055 * 10^3

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Using translation concepts, the method that Howard could have used to determine the coordinates of the vertices of the image is:

(x,y) -> (-x,y).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

A reflection over the y-axis can be described according to the following rule:

(x,y) -> (-x,y).

Hence this rule can be applied to find the vertices.

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[tex]\huge\textbf{Hey there!}[/tex]

[tex]\mathsf{ASSUMING: }\\\mathsf{22\times90}\\\mathsf{= 90 \times 22}\\\mathsf{= 1,980}[/tex]

[tex]\mathsf{ASSUMING: }\\\mathsf{2 + 2 + 3 + 3 + 3 + 3}\\\mathsf{= 2\times 2 + 3\times4}\\\mathsf{= 4 + 12}\\\mathsf{= 16}[/tex]

[tex]\huge\textsf{Answer \#1. 1,980 }\huge\checkmark\\\\\\\huge\textsf{Answer \#2. 16 }\huge\checkmark[/tex]

[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Laurel has to cover this area with 2.64 ounces of seeds.

Step-by-step explanation:

Given

Base of Parallelogram = 30ft

Height of Parallelogram = 22ft

Area of Parallelogram = 1/2*base*height

Therefore, Area of Parallelogram =  1/2*30*22

                                                        = 330sq. ft

Given

One ounce of seed covers 125 sq. ft

Hence, No. of ounces needed to cover 330 sq. ft= 330/125

                                                                                  = 2.64

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