in a test out of 40,the marks of 15 students were 31,18,6,26,36,24,23,14,28,28,32,9,11,22,21.
a.calculate the mean mark for the test
b.express the mean mark as a percentage

Answers

Answer 1

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.

Add all of the scores from each student. [tex]31+18+6+26+36+24+23+14+28+28+32+9+11+22+2=310[/tex]Divide the sum by the amount of students who took the test.[tex]310/15=20.667[/tex]Therefore, the mean mark for the test was 20.667.

b. Express the mean mark as a percentage.

Put mean mark and total possible marks in fraction form.[tex]\frac{20.667}{40}[/tex]Divide the numerator by the denominator (essentially changing the fraction into the decimal form). [tex]20.667/40=0.516[/tex]Multiply the quotient by 100. [tex]0.516*100=51.6[/tex]Therefore, the mean mark as a percentage is 51.6%

Related Questions

Line A and Line B are perpendicular. The slope of line A is -0.5. What is
the gradient of line B? Give reasons.

Answers

Answer:

Step-by-step explanation:

When 2 lines are perpendicular, their slopes are negative reciprocals of one another.  Here, if the slope of A is -1/2, the slope of B is +2/1, or just 2.

find the length of AD

Answers

The length of AD is 5 units. so, option A is the correct answer.

What is the Pythagoras theorem?

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

The length of DC is given as 13 units.

The length of AC is given as 12  units. We can see that angle D is a right angle, so the triangle will be a right-angle triangle.

by Pythagoras theorem;

[tex]DC ^2 = AD^2 + AC^2\\\\13^2 = AD^2 + 12^2\\\\AD^2 = 169 - 144\\\\AD^2 = 25\\\\AD = 5[/tex]

Hence, the length of AD is 5 units. so, option A is the correct answer.

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Which triangles in the diagram are congruent?
70°
triangle 1
70°
triangle 3
OA triangle 1 and triangle 2
OB. triangle 1, triangle 2, and triangle 3
OC. triangle 1 and triangle 3
OD. triangle 1, triangle 3, and triangle 4
70°
triangle 2
#
triangle 4
Submit Test
Rea

Answers

Answer:

its e

Step-by-step explanation:

because e is is referring to savvy

IMPORTANT, PLEASE HELP QUICKLY! 15 POINTS
Explain how to factor the expression q(x)=9x2−24x+16 to the expression q(x)=(3x−4)2 . You may show your work. Be sure to include a detailed explanation of your steps.

Answers

Answer:

Given function:

[tex]q(x)=9x^2-24x+16[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex],  find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:

[tex]ac=9 \cdot 16=144[/tex]

Two numbers that multiply to 144 and sum to -24 are: -12 and -12

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies q(x)=9x^2-12x-12x+16[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies q(x)=3x(3x-4)-4(3x-4)[/tex]

Factor out the common term [tex](3x-4)[/tex]:

[tex]\implies q(x)=(3x-4)(3x-4)[/tex]

Therefore:

[tex]\implies q(x)=(3x-4)^2[/tex]


3. (3, 5) and (k, 9), slope = 1/2
Linear relationships unit 3 lesson 10 grade 8 openuprespurces

Answers

Answer:

k = 11, if I understand the question.

Step-by-step explanation:

Please rephrase the question if my interpretation is incorrect.  (BTW, isn't (k,9) a dog?)

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

I'll assume that we want to find the value of k as given by the equation of a line that has a slope of (1/2).  

Let's determine if we can establish an equation with what we know:

1.  It goes through point (3,5), and

2.  It has a slope of (1/2)

We'll look for a line with the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).

From (2) we know y = (1/2)x + b.

We can find b by using the one known point that lies on the line (3,5).  Use y = (1/2)x + b, insert the point (3,5), and solve for b:

y = (1/2)x + b

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

5 = 1.5 + b

b = 3.5

The line is y = (1/2)x + 3.5.

Now use the point (k,9):

y = (1/2)x + 3.5

9 = (1/2)k + 3.5

(1/2)k = 5.5

k = 11

The point is (11,9) so k = 9

See the attached graph.

20 POINTS TO THE FIRST RIGHT ANSWER!!!! PLS HELP

A sculptor is planning to order a rectangular block of composite stone to sculpt a lion. The sculptor anticipates that the lion will be 5 feet long, about 2 feet wide and at the tallest part of the lion's body, have a height of 3.5 feet. The composite stone weighs 40 pounds per cubic foot. To the nearest cubic foot, estimate the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue.

The weight of the smallest rectangular block is ____
pounds.

Answers

The weight of the smallest rectangular block is 1400 pounds.

What is density?

The density refers to the heaviness of an object. It is the ratio of mass to volume.

Then we have

Density = Mass / Volume

A sculptor is planning to order a rectangular block of composite stone to sculpt a lion.

The sculptor anticipates that the lion will be 5 feet long, about 2 feet wide and at the tallest part of the lion's body, have a height of 3.5 feet.

The composite stone weighs 40 pounds per cubic foot.

To the nearest cubic foot, estimate the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue.

Then the weight of the smallest rectangular block will be

Mass = density x volume

The volume will be

V = 5 x 2 x 3.5

V = 35 cubic feet

Then the weight will be

Mass = 40 x 35

Mass = 1400 pounds

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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Using the properties of integer exponents, match each expression with its equivalent expression.

Answers

From the power rules, the matching of  each expression with its equivalent expression is:

[tex]5^{-3}=\frac{1}{125}[/tex]

[tex]-5^{-3}=-\frac{1}{125}[/tex]

[tex](-5^{-3})^{-1}=-125[/tex]

[tex](-5^{-3})^{0}=1[/tex]

Power Rules

There are different power rules, see some them:

1. Negative exponent. For this rule when you have a negative exponent, you need to invert the number, i.e, the power base is converted to the denominator. After that, you should solve the power with a positive exponent.  See the  examples:

[tex]4^{-3}=\frac{1}{4^3} =\frac{1}{64} \\ \\ {\frac{4}{6} }^{-2}=( {\frac{6}{4} })^{2}=\frac{36}{16}[/tex]

2. Power. For this rule, you should repeat the base and multiply the exponents. See the  example, [tex](2^{2})^3=2^6=64[/tex].

3. Zero Exponent. When you have an exponent equals to zero, the result must be 1.  See the  example, [tex]2^0=1[/tex].

From this for your question, you have:

[tex]5^{-3}=\frac{1}{5^3}=\frac{1}{125}[/tex]

[tex]-5^{-3}=-\frac{1}{5^3}=-\frac{1}{125}[/tex]

[tex](-5^{-3})^{-1}=(-5)^{3}=-125[/tex]

[tex](-5^{-3})^{0}=(-5)^{0}=1[/tex]

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please help me with these or just the first one even ty

Answers

Answer:

-3+15-75+375

=12-75+375

=-63+375

=302

n=8

302÷8 = 37

Which equation represents the line that passes through the point (-2.4, -7.1) and has a slope of -5.3

Answers

Y= -5.3x + c

-7.1= -5.3(-2.4) + c

C= -12.72-7.1 = −19.82

Y= —5.3x-19.82

A plant grows at a constant rate . daniel records the height of the plant each week . the unit reat is meausred in inches per week . what is the constant of proportionality ?

Answers

By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.

How to find a constant of proportionality in direct proportional equation

Let x and y the number of weeks and the height of the plant, respectively. Given the consideration of direct proportionality, the height of the plant inasmuch as the number of weeks increases. Then, the constant of proportionality (in inches per week) is found by dividing the height of the plant by the number of the respective week:

k = 18 inches /6 weeks = 15 inches /5 weeks = 12 inches/4 weeks = 3 inches/week

By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.

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The sum of the reciprocals of the first four consecutive positive integers is greater than two. What is the least number of consecutive positive integers necessary to make the sum of the reciprocals greater than three?

Answers

The least number of consecutive positive integer that is required to make the sum of the reciprocals greater than three is 7.

What is an integer?

An integer is simply a number that is not  a  fraction.

The first four consecutive positive integers are:

1, 2, 3 , 4.

Their reciprocals are:

1/1, 1/2, 1/3, 1/4; and

The sum of them are greater than 2; that is

1/1 + 1/2 + 1/3 + 1/4 = 2.08333333333 > 2

to make the expression >3

We would require the following integers

1/1 + 1/2 + 1/3 + 1/4+ (1/5) + (1/6) + (1/7) + (1/8)+ (1/9) + (1/10) + (1/11) = 3.01987734488


Thus, the additional consecutive reciprocal integers that is required to make the sum of the reciprocal of the fist four greater than 3 is 7.

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could someone please help me with this ​

Answers

Answer:

  ia) center: (0, 0), the origin

  ib) angle: 90°

  ic) direction: CCW

  ii) LM ≅ L'M', ∠L ≅ ∠L'

  iii) (2, 1)

Step-by-step explanation:

A rigid transformation preserves size and shape of a figure, so the image is congruent to the original. The rigid transformations are rotation, reflection, and translation. Each has characteristics that allow one to determine the nature of the transformation(s) involved.

__

rotation

angle and direction

One way to determine the angle and direction of rotation of a figure is to compare a horizontal segment on the original with the corresponding segment on the image. Here, a convenient segment is NM, which is horizontal and points to the right. Its angle relative to the direction of the +x axis is 0°.

The transformed segment N'M' points upward, at an angle relative to the +x axis of 90°. This tells you the figure was rotated 90° in the CCW direction. (This is fully equivalent to a rotation of 270° in the CW direction.)

center

Points in a rotated image always remain at the same distance from the center of rotation as the original points. In most cases, the center of rotation is the origin. We can check to see if that is the case by looking at the distances of a couple of points from the origin.

  N is at coordinates (1, 1), so is √(1² +1²) = √2 from the origin

  N' is at coordinates (-1, 1), so is √((-1)² +1²) = √2 from the origin

  L is at coordinates (1, 3), so is √(1² +3²) = √10 from the origin

  L' is at coordinates (-3, 1) so is √((-3)² +1²) = √10 from the origin

This confirms that the origin is the center of rotation.

__

Since each point and its image are on a circle centered at the center of rotation, the line between them is a chord of that circle. The perpendicular bisector of that chord goes through the center of rotation. Here, we observe that the perpendicular bisector of NN' is the y-axis. The perpendicular bisector of LL' is a line with slope -2 through (-1, 2). It will intersect the y-axis at the origin, confirming the origin as the center of rotation.

__

geometric relationships

A rigid transformation preserves lengths and angles, so any length or angle on the rotated figure is congruent to the original:

 LM ≅ L'M', MN ≅ M'N', NL ≅ N'L'

  ∠L ≡ ∠L', ∠M ≡ ∠M', ∠N ≡ ∠N'

__

translation

The components of a translation vector add to the corresponding coordinates of a point.

  L +v = L'

  (1, 3) +(1, -2) = (2, 1) . . . image of point L

please solve this question​

Answers

Step-by-step explanation:

please give this answer brainlist answer

There are two approaches to solving the equation -3x + 10 = 4x - 20

Subtract 4x from both sides. OR Add 3x to both sides.

–7x + 10 = –20 OR 10 = 7x – 20

Solve the equation using both approaches.

Answers

this is the answer using both approaches

Is LMN OPQ If so name the congruence postulate that applies

Answers

The triangle is congruent by SSS congruency because the corresponding two sides of two triangles are of the same measurement Hence, Option D is correct.

What is SSS congruency?

If the corresponding two sides of two triangles are of the same measurement, then the considered pair of triangles are congruent.

We have given two triangles that are congruent to each other;

LMN is congruent to OPQ

Given;

LM = OP

MN = PQ

LN = OQ

Thus, the triangle is congruent by SSS congruency because the corresponding two sides of two triangles are of the same measurement

Hence, Option D is correct.

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Solve for x. Round to the nearest hundredth sin x ≈ 0.965926
how do u do a problem like this?

Answers

In the given equation, the value of x is approximately 75°

Trigonometry

From the question, we are to determine the value of x

The given equation is

sin x ≈ 0.965926

If sin x ≈ 0.965926

Then,

x ≈ sin⁻¹(0.965926)

∴ x ≈ 75.0°

Hence, the value of x is approximately 75°

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Multiplying Monomials and Binomials:16x(x+24)

Answers

Answer
16x^2+384x
x equals -24

Please help me with this question
I tried to use the law of cosine but the numbers I get are in decimal places and are too small for the angles.

Answers

Answer:

y = √119 ≈ 10.909θ ≈ 65.376°α ≈ 24.624°sin(θ) = (√119)/12 ≈ 0.909059cos(θ) = 5/12 ≈ 0.416667tan(θ) = (√119)/5 ≈ 2.181742csc(θ) = (12√119)/119 ≈ 1.100038sec(θ) = 2.4cot(θ) = (5√119)/119 ≈ 0.458349

Step-by-step explanation:

You can use the Law of Cosines after you find y or θ. Using the given information, you can apply the Pythagorean theorem, the Law of Sines, or the definition of the cosine trig function.

The mnemonic SOH CAH TOA is intended to remind you of the relations between sides and angles in a right triangle. It tells you ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

Find y

The Pythagorean theorem relates the measures of the sides. It tells you ...

  y² +5² = 12²

  y = √(144 -25) = √119

Find angles

The trig relations above tell you ...

  sin(α) = 5/12   ⇒   α = arcsin(5/12) ≈ 24.624°

 cos(θ) = 5/12   ⇒   θ = arccos(5/12) ≈ 65.376°

Of course, once you find one of the angles, you can find the other. The sum of the two acute angles in a right triangle is 90°.

Find trig functions

Using the definitions above for the trig functions, you have ...

  sin(θ) = y/12 = (√119)/12

  cos(θ) = 5/12

  tan(θ) = y/5 = (√119)/5

Using trig identities, you have ...

  csc(θ) = 1/sin(θ) = 12/√119 = (12√119)/119

  sec(θ) = 1/cos(θ) = 12/5 = 2.4

  cot(θ) = 1/tan(θ) = 5/√119 = (5√119)/119

_____

Additional comment

The attached calculator screen shot shows you the angle θ on the first line, and the value of y on the second line. The csc, sec, and cot are shown on the third line. You will notice the angle mode (DEG) is seen in the lower left corner. If the calculator angle mode is set to radians, you will see the angles as relatively small radian values: θ ≈ 1.141, α ≈ 0.4298.

We have shown both exact values and decimal values you can round to the desired precision.

Find the vertex and focus of the
parabola:
y²-10y + 4x + 21 = 0
Vertex = ([?],
[]
Focus=([], [])

Answers

Answer:

Vertex: (1, 5)

Focus: (0, 5)

Step-by-step explanation:

Given that the parabola's equation is y² - 10y + 4x + 21 = 0, solve for the vertex and the focus.

Vertex:

Step 1: Isolate x to the left side of the equation; we get x = - (y² / 4) + (5y / 2) - (21 / 4).

Step 2: Complete the square of the previous equation; here we get - (1 / 4) * (y - 5)² + 1. x is squal to this.

Step 3: Use the vertex form, x = a(y - k)² + 1. a is - 1 / 4, h is 1, and k is 5.

Step 4: Fill in (h, k). We get the answer (1, 5) as the vertex.

Focus:

Step 1: Find p, and distance from the vertex to the focus. We can find p by using 1 / (4a).

Step 2: Simplify. This gives us -1 as p.

Step 3: We plug in the values we just got earlier to get the vertex. The focus of a parabola can be found by using: (h + p, k).

Step 4: Substitude the values. We have (1 + -1, 5).

Step 5: Simplify. Therefore, the answer is (0, 5).

This took me a long time to calculate. Please mark me as Brainliest!!!

This uservabove me did it all for you. I don't have much to say...

Identify the geometric mean of 9 and 9/4.

Answers

The geometric mean of 9 and 9/4 will be 9/2 or 4 1/2.

How to calculate the mean?

It should be noted that in order to find the geometric mean of the numbers given, give to find the square root and then multiply.

This will be:

= ✓9 × ✓9/4

= 3 × 3/2

= 9/2 = 4 1/2

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Hey, any help would be very needed thanks so much!!

Answers

Let's take this problem step by step:

To find the ordered pair of the system:

⇒ must set both equations equal to each other

    ⇒ must solve for 'x'

Let's solve:

 [tex]x^2-2x+3=-2x+28\\x^2-2x+3+2x-28=0\\x^2-25=0\\(x-5)(x+5)=0[/tex]

Let's find the x-values:

 [tex](x-5)=0\\x=5\\\\(x+5)=0\\x=-5[/tex]

Let's find f(x)'s value for each of the 'x':

[tex]x=5\\f(5)=-2(5)+28=18\\\\x=-5\\f(-5)=-2(-5)+28=38[/tex]

Answer: (5, 18), (-5,38)

Hope that helps!

#LearnwithBrainly

Two linear equations are shown.
C
654321₁
4
66
y=1/3x+2
y=4/3x-5
What is the solution to the system of equations?
O (7.4)
0 (7.33)
O
0 (8)
O
O (9.7)

Answers

Answer: Option (2)

Step-by-step explanation:

Setting the equations equal to each other,

[tex]\frac{1}{3}x+2=\frac{4}{3}x-5\\\\7=x[/tex]

If x=7, then [tex]y=\frac{7}{3}+2=\frac{13}{3}[/tex]

How do you solve this?

Answers

Step-by-step explanation:

to "solve" this I need an equation.

this whole expression must be equal to something.

without that I can only try to simplify the expression.

remember that

a/b / c/d = ad / bc

so, here we have

3a/(((a²/x) - 1)(a/x - 1)) = 3a/(a³/x² - a²/x - a/x + 1) =

= 3a/(a³/x² - a²/x - a/x - a/a) =

= 3a/((a²/x² - a/x - 1/x - 1/a)×a) = 3/(a²/x² - a/x - 1/x - 1/a)

??????????????????????????????????????????????????

Answers

Answer:

x=20

Step-by-step explanation:

The angles are 'Co-interior Angles', they make a C shape and add up to 180 degrees

so 4x +5x =9x

9x=180

x=20

4x=80

5x=100

Does this graph represent a function? Why or why not?

Answers

Answer:

the answer is D

Step-by-step explanation:

I'm not good at explaining but, it is because the line is not touching more than 1 point on the graph. Basically making it pass the vertical line test, therefore making the answer D.

Good luck, hope this helps !!!

Select all the functions that show an inverse variation...
a) y=6x
b) y=3/x
c) y=1/3x
d) y= -.07x
e) y= 2/x+4
f) xy=-3
PLEASE HELP ILL MARK BRAINLEST

Answers

A and d would be the answers for this question

pe-intercept Equatic
Question 4 of 10
If f(x) = 5x - 12, what is f(2)?

Answers

f(2) = 5(2) - 12
That show f(2) = -2

Answer:

f(2) = 2

Step-by-step explanation:

Given function:

f(x) = 5x - 12

To Find:

f(2)

Solution:

Well,it is absolutely clear from the problem,that x = 2.So just substitute 2 in x's place on the function,then simplify using PEMDAS.

[tex]f(x) = 5x - 12[/tex]

[tex]f(2) = 5(2)- 12[/tex]

[tex]f(2) = 10 - 12[/tex]

[tex]\boxed{f(2) = - 2}[/tex]

Hence,f(2) is equal to -2.

A proportional relationship between the number of pounds of cabbage (x) and the price in dollars (y) is graphed, and the ordered pair (5, 2) is on the graphed line.

Part A: What is the price of 1 pound of cabbage? Show your work.
Part B: What does the ordered pair (10, 4) on the graph represent? Explain in words.

Answers

Answer:

Part A -  2/5 of a dollar

Part B - It shows that 10 pounds of cabbage cost $4

Step-by-step explanation:

If 5 pounds cost $2 then 1 pound costs 2/5 of a dollar.

(10,4) - 10 is the x-axis which is pounds and 4 is the y-axis which is $. So 10 pounds cost $4.

what is the factored form of x^3 - 729

Answers

Answer:

(x - 9)(x^2 + 18x + 81).

Step-by-step explanation:

Use the difference of cubes factorization, which claims that a^3 - b^3 = (a - b)(a^2 + ab + b^2)

x^3 - 729 = (x - 9)(x^2 + 18x + 81)

Answer:[tex](x-9) (x^{2} +9x + 81)[/tex]

Step-by-step explanation:

If f(x) = 2x² - 5 and g(x) = 3x + 3, find (f- g)(x).
OA. 3x-2x2 - 2
OB. 2x²-3x-8
OC.-²2²-8
OD. 2x²-3x-2

Answers

(f- g)(x) = 2x²-3x -8 , Option B is the correct answer.

What is a Function ?

A function is a mathematical statement that derives relation between two variables.

Two functions are given in the question

f(x) = 2x² - 5

g(x) = 3x + 3

(f- g)(x) = ?

(f- g)(x) = (2x² - 5 - (3x + 3))

(f- g)(x) = 2x²-3x -8

Therefore Option B is the correct answer.

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