There are 10 girls and 20 boys in a class.
The class has a test.

The mean mark for all the class is 70
The mean mark for all the boys is 62

Work out the mean mark for the girls.

There Are 10 Girls And 20 Boys In A Class.The Class Has A Test.The Mean Mark For All The Class Is 70The

Answers

Answer 1

Answer:

86

Step-by-step explanation:

mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

given mean mark for class of 30 is 70 , then

[tex]\frac{sum}{30}[/tex] = 70 ( multiply both sides by 30 )

sum = 2100

given the mean mark for 20 boys is 62, then

[tex]\frac{sum}{20}[/tex] = 62 ( multiply both sides by 20 )

sum = 1240

the sum for the 10 girls is then 2100 - 1240 = 860

then mean score for the 10 girls is

mean = [tex]\frac{860}{10}[/tex] = 86


Related Questions

suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. we find the heights of 60 people. (you may need to use the standard normal distribution table. round your answers to the nearest whole number.) (a) how many would you expect to be between 165 and 175 cm tall? people (b) how many would you expect to be taller than 167 cm?

Answers

The expected number of people between 165 and 175 is 41.

The expected number of people taller than 168 is 39.

Given that the mean and standard deviation of people's heights (measured in centimeters) are 170 and 5 respectively. The heights of 60 people are revealed.

μ = 170

σ = 5

n = 60

(a) The probability would you expect to be between 165 and 175 cm tall;

P( 165 < x < 175 ) = P( (165 - 170)/5 < z < (175 - 170)/5 )

                            = P( -1 < z < 1 )

                            = P( z < 1) - P( z < -1 )

                            = 0.8413 - 0.1587

                            = 0.6826

Expected number of people between 165 and 175 = n * p

                                                                                    = 60 * 0.6826

                                                                                    = 40.956

                                                                                    ≅ 41

(b) The probability would you expect to be taller than 167 cm;

P( x >  167 ) = P( z > (167 - 170)/5 )

                   = P( z > -0.6 )

                   = 0.7257

Expected number of people taller than 168 = n * p

                                                                        = 60 * 0.7257

                                                                        = 43.542

                                                                        ≅ 39

Hence,

The expected number of people between 165 and 175 is 41.

The expected number of people taller than 168 is 39.

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A 145-ft tower is located on the side of a mountain that is inclined 32° to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 55 ft downhill from the base of the tower. Find the shortest length of wire needed. (Round your answer to the nearest foot.)

Answers

By apply the law of cosine, the shortest length of wire needed is 180 feet.

How to determine the shortest length of wire needed?

In order to determine the shortest length of wire needed, we would apply the law of cosine because a mental image of the scenario described produces a right-angled triangle.

In Trigonometry, law of cosine (cos) is given by this mathematical expression:

C² = A² + D² - 2(A)(D)cosD

Note: Angle D = 90° + 32° = 122°

Substituting the given parameters into the formula, we have;

C² = 55² + 145² - 2(55)(145)cos122°

C² = 3,025 + 21,025 - 2(7,975)(-0.5299)

C² = 24,050 - (-8,451.905)

C² = 24,050 + 8,451.905

C² = 32,501.905

C = √32,501.905

C = 180.28 ≈ 180 feet.

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Four different linear functions are shown below. Drag the representation of each function in order from greatest y intercept ti least y intercept

Answers

Order of greatest y intercept to least y intercept,

1). A linear function has been given as,

   y = [tex]\frac{1}{2}[/tex]x + 4

   Y intercept = 4

2). The graph,

    Y intercept = (2)

3). Graph represented by table

    Y intercept = 1

4). A line passes through two points (-2, -3) and (4, 0)

    Y intercept = -2

What is Y- intercept?

It is the total distance from the origin and the intersection of y axis and the formed line. It may be positive, negative or zero.

  From the graph,

    y-intercept = (2)

A line passes through two points (-2, -3) and (4, 0),

Slope of the line = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

                           = [tex]\frac{0-(-3)}{4-(-2)}[/tex]

                           = 1/2

Equation of a line passing through a point (x', y') and slope = m

y - y' = m(x - x')

If the point is (4, 0) and slope = 1/2

y - 0 = 1/2 ( x - 4 )

y = 1/2x - 2

y-intercept of this line = (-2)

A linear function has been given as,

y = [tex]\frac{1}{2}[/tex]x + 4

Comparing it with the slope intercept equation,

y = mx + b

b = y-intercept = 4

From the given table,

For x = 0, f(x) = 1

Therefore, y-intercept = 1

Order of greatest y intercept to least y intercept,

1). A linear function has been given as,

   y = [tex]\frac{1}{2}[/tex]x + 4

Y intercept = 4

2). The graph,

Y intercept = (2)

3). Graph represented by table

Y intercept = 1

4). A line passes through two points (-2, -3) and (4, 0)

Y intercept = -2

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Y+2=1/4 x in standard form

Answers

Answer:

-[tex]\frac{1}{4}x[/tex] + y = -2

Step-by-step explanation:

Standard form: Ax + By = C

y + 2 = [tex]\frac{1}{4} x[/tex]

Rearrange terms:

1. Subtract 2 from both sides

y =  [tex]\frac{1}{4} x[/tex] - 2

2. Subtract  [tex]\frac{1}{4} x[/tex] from both sides

-[tex]\frac{1}{4}x[/tex] + y = -2

a statistical quality control process for cereal production measures the weight of a cereal box. the population standard deviation is known to be .06 ounces. in order to achieve a 97% confidence with a margin of error of .02 ounces, how large a sample should be used?

Answers

The sample size that should be used is 43.

Given that;

The weight of a cereal box is measured as part of a statistical quality control process for the manufacture of cereal. It is understood that the population standard deviation is 0.06 ounces. To attain a margin of error of and a confidence level of 97% 0.02 ounces.

By considering the confidence level scenario, we get to solve how large a sample should be utilized.

The significance level is (α) = 0.03 ( 97% confidence level )

The critical value is (z*) = 2.17 ( From z-table )

The population standard deviation (σ) = 0.06

The margin of error (E) = 0.02

Therefore, the required sample size is;

n = [(z* × σ)/E ]²

n = 42.383

n ≅ 43

Finally, the sample size that should be used is 43.

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which of the following quantitative research methods uses a relatively small group of people for testing and is most helpful in obtaining data that are representative of the whole population? a.) in-depth interviews b.) secondary data analysis c.) natural experiments d.) random sampling

Answers

In-depth interviews are a quantitative research method that uses a relatively small group of people for testing and is most helpful in obtaining data representative of the whole population. The correct option to this question is A.

Although you can use all of these techniques in your comprehensive customer experience management strategy, in-depth interviews can help you gather the information that can give you rich insights into the experiences and preferences of a large sample of your target audience.

An extensive amount of data can be gathered on the behavior, attitude, and perspective of the interviewers through in-depth interviews, a qualitative data collection technique.

Researchers and subjects are free to explore additional topics and alter the course of the interview when necessary during in-depth interviews. It is an independent research methodology that can use a variety of approaches depending on the needs of the study.

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on average, the number of students that choose to study application development subjects at brock university is 18 each year. (hint: use poisson distribution formula). what is the probability that exactly 13 students will take up application development in the coming year? a. 0.06585 b. 0.05093 c. 0.14260 d. 0.08795

Answers

0.05093 is the probability that exactly 13 students will take up application development in the coming year .

Describe probability using an example?

It is based on the probabilities that something could happen. The theory of probability primarily relies on the justification for probability. A coin is tossed, for instance, and the theoretical likelihood of receiving a head is 1 in 2.

Average rate (number) of students who chose to study Application Development (λ)= 18

Poisson random variable(number of students taking up Application Development in the coming year)(x)=13

Poisson distribution = P(X = x) = e^−λ (λ)^x/ x!

Here, probability of 13 students choosing application development next year= P(X=13)

               =   ^(−18 ) 18^13/  13!

     

P(X=13) = 0.0509286= 0.05093

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f(x) = x +4
g(x) = 3x
What is the value of fg(7)?

Answers

Answer: 105 (altough im not entirely sure sry...)

Step-by-step explanation:

I believe since it is "fg" then only the g gets the 7 (g(7)) and the f is just f(1)

This is quite difficult so you this may not be correct

I hope

Can anyone write the equation of the graph?

Answers

the answer is (3,5) since that’s where the point is

a subset of the whole population selected to be questioned for the purposes of prediction or gauging opinion is called

Answers

The sample is a subset of the whole population selected to be questioned for the purposes of prediction or gauging opinion .

A sample is a collection of people, things, or things used in research that is taken for analysis from a larger population. To enable us to extrapolate the research sample's findings to the entire population, the sample must be representative of the population.

We must utilize inferential statistics to discover a population's characteristics by directly observing only a subset (or sample of the population) in order to derive conclusions about populations from samples.

Since it is frequently impractical and hardly ever possible, we acquire a sample of the population.

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how do i work this out please?

Answers

By evaluating the linear equation we will see that:

A = -3

B = 4

And the correct line is the purple one.

How to get the values of A and B?

We know that the points (0, A) and (B, 0) lie on the line 3x - 4y = 12

To find the value of A, we can replace the values of the point on the line, so we get:

3*0 - 4*A = 12

-4*A = 12

A = 12/-4 = -3

A = -3

To get the value of B we do the same thing.

3*B - 4*0 = 12

B = 12/3

B = 4

So the points are (0, -3) and (4, 0).

Then the correct line is the purple one.

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What is the constant of variation, k of the direct variation, y=kx,through (5,8)

Answers

Constant of variation, k of the direct variation is 8/5.

Equation -> y = kx

Point (x,y) = (5,8)

Putting the value in the equation,

8 = 5k

k = 8/5

Hence, k = 8/5.

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Help Please!

Solve the inequality and graph it’s solution.

Answers

The correct answer would be r < 2

when two pipes fill a pool together, they can finish in 4 hours. if one pipe fills half of the pool and then the other takes over and finishes filling the pool, the pool will fill in 9 hours. how long would it take each pipe to fill the pool if it were working alone?

Answers

Time taken by pipe 1 to fill the pool is 6 and by pipe 2 is 12.

Here we have to find the time taken by each pipe to fill the pool.

Formula to find the work:

w = r × t

where

w =  is the work done

r = is the rate of work done

t =  is the time taken to do the work

For pipe 1 working alone to fill 1 pool, the work done is 1

w1 = r1 t1

1 = r1 × t1

t1 = 1/r1

For pipe 2 working alone to fill 1 pool, the work done is 1;

w2 = r2 t2

1 = r2 × t2

t2 = 1/r2

From the question, it would take 9 hours if each pipe took turns filling half the pool. That is;

t1/2 + t2/2 = 9

t1 + t2 = 18

However, if both pipes worked together, it would take 4 hours for each pipe. That is;

w1 + w2 = w

r1t1 + r2t2 = 1

4r1 + 4r2 = 1

r1 + r2 = 1/4

As we know from the above:

r1 = 1/t1 and r2 = 1/t2

So;

1/t1 + 1/t2 = 1/4

(t2 + t1)/ t1 t2 = 1/4

t1 + t2 = 18

So

t1 t2 = 72

The only factors of 72 that satisfy the conditions

t1 + t2 = 18

t1 . t2 = 72

are 6 and 12.

Therefore, pipe 1 will take 6 hours, and pipe 2 will take 12 hours.

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Expand and simplify (3x + 4)(2x + 3)

Answers

Answer:

6x^2+17x+12

Step-by-step explanation:

(3x+4) * (2x+3)

3x * 2x = 6x^2

3x * 3 = 9x

+4 * 2x = +8x

+4 * +3 = +12

6x^2+ 9x+8x +12

Simplify:
6x^2+17x+12

a fence is to be built to enclose a rectangular area of 310 square feet. the fence along three sides is to be made of material that costs 4 dollars per foot, and the material for the fourth side costs 14 dollars per foot. find the dimensions of the enclosure that is most economical to construct.

Answers

The dimension for the enclosure that is most economical to construct will be length=11.13 feet and width=27.85 feet.

What is area?

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

A=l*b

=310

b=310/l

total cost=(8b+4l+16l)

=8b+20l

=8*310/l+20l

t=2480/l+20l

t'=20-2480/l²

t'=0

20l²=2480

l²=124

l=11.13 feet

b=310/11.13

b=27.85 feet

The enclosure's length and width, which add up to 11.13 feet and 27.85 feet respectively, will be the most cost-effective dimensions to build.

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What is the length of the hypotenuse in 2 decimal places

Answers

For this triangle you would use sine. The equation would be sin 32 = (21/x).

1) What is the slope of the following graph?

Answers

Answer:[tex]\frac{3}{-2}[/tex]

Step-by-step explanation:

slope= [tex]\frac{rise}{run}[/tex]

start at (0,1)

go up 3 units

then go left 2 units

slope= [tex]\frac{3}{-2}[/tex]

How many dogs could Roscoe groom if he worked for 40 hours?

90

120

220

200

Answers

There are 200 dogs Roscoe groom if he worked for 40 hours.

What is working time?

A person's working time is the time they are engaged in paid work. Personal housework, childcare, and pet care are examples of unpaid work that is not included in the definition of the working week.

In most cases, when someone inquires about your working hours, you should first provide the start time before providing the time you leave for home.

From the given graph we can see that for each three hours the number of dogs are increased by 15.

So, for each one hour the number of dogs increased by 5.

For 18 hours the the number of dogs are 90.

After 18 hours to complete 40 hours we need 22 hours.

So, for 22 hours the number of dogs are

22 x 5 = 110.

Therefore, the total number of dogs worked for 40 hours are,

90 + 110 = 220.

Hence, there are 200 dogs Roscoe groom if he worked for 40 hours.

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The temperature on a summer afternoon is 85°F. Define a variable and write an expression to find the temperature after it changes. Then evaluate your expression for a decrease of 11 degrees Fahrenheit.

Answers

The expression that can be used to find the temperature after it changes is 85°F + C

How to find a change in temperature?

Temperature refers to the degree of hotness or coldness of a body at a particular time. It is measured in degree Celsius, degree Fahrenheit an Kelvin.

The instrument used to measure temperature is a thermometer.

Temperature on a summer afternoon = 85°FDecrease in temperature = -11°F

let

C = change in temperature

The change in temperature = 85°F + C

= 85°F + (-11°F)

= 85 - 11

= 74°F

Therefore, the new temperature after a decrease in 11°F is 74°F

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If y is directly proportional with x and y = 91 when x = 7 what is the value of y when x = 15
What is the constant of variation (k)?
What is the value of Y when X = 15?

pls help 30 points :)

Answers

The constant of variation is 13.

The value of y when x is 15 is 195.

What is direct variation?

Direct variation is when two values move in the same direction. If one variable increases, the other variable increases.

The equation that represents direct variation is:

y = kx

Where:

y = dependent variable k = constant of variationx = independent variable

91 = 7k

k = 91 / 7

k = 13

The value of y when x = 15

y = 13 x 15

y = 195

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What is the range of the following function

Answers

The range of the given function is y ≥ 0 which is option B.

From the graph:

Some points (-1,1),(-2,2),(0,0),(1,1),(2,2)

Range is defined as the set of y values or outputs.

range = 0,1,2,3 ......

Means range starts from zero to infinite(0 to all positive values.

so range = y ≥ 0

Therefore  range of the given function is y ≥ 0 which is option B.

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Can someone please help !

Answers

[tex]\huge\begin{array}{ccc}BT=21\\DC=10.2\end{array}[/tex]

If BT is the midsegment of ΔMAH and DC is the midsegment of ΔBTH, then MA, BT and DC are parallel.

Therefore the segments form the proportion:

[tex]\dfrac{HM}{MA}=\dfrac{HB}{BT}=\dfrac{HD}{DC}[/tex]

BT is the midsegment of ΔMAH, therefore

[tex]HB=\dfrac{1}{2}HM[/tex]

DC is the midsegment of ΔBTH, therefore

[tex]HD=\dfrac{1}{2}HB=\dfrac{1}{2}\cdot\dfrac{1}{2}HM=\dfrac{1}{4}HM[/tex]

Substitute:

[tex]\dfrac{HM}{42}=\dfrac{\frac{1}{2}HM}{BT}[/tex]

cross multiply

[tex]HM\cdot BT=42\cdot\dfrac{1}{2}HM[/tex]

divide both sides by HM

[tex]\boxed{BT=21}[/tex]

[tex]\dfrac{HM}{42}=\dfrac{\frac{1}{4}HM}{DC}[/tex]

cross multiply

[tex]HM\cdot DC=42\cdot\dfrac{1}{4}HM[/tex]

divide both sides by HM

[tex]\boxed{DC=10.5}[/tex]

Find the measure of the exterior angle.

Answers

The measure of the exterior angle as shown in the triangle is 140°.

What is exterior angle?

Exterior angle is the angle between a side of a polygon and an extended adjacent side.

Exterior angle theorem: The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

From the diagram below, applying the theorem above,

k = 64+76k = 140°

Hence, the exterior angle is 140°.

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you can answer any 17 questions from a total of 20 questions on an exam. in how many different ways can you select the questions?

Answers

With the help of probability we can say that there are 1140 ways.

What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .

acc to our question-

permutation= 20!/ (20-17)!ncr= 20!/ 17!(20-17)!=1140

Hence,we can say that there are 1140 ways.

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There are 5 consecutive even integers with a sum of –80. What is the greatest of these integers?

Answers

The greatest even integers that the 5 consecutive number has a sum of - 80 is - 12.

How to find the greatest even integers?

Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2.

Therefore, even integers are integers that are even.

There are 5 consecutive even integers with a sum of –80.

let

x = first integers

Therefore,

x + x + 2 + x + 4 + x + 6 + x + 8 = - 80

5x + 20 = - 80

5x = -80 - 20

5x = - 100

divide both sides by 5

x = - 100 / 5

x = -20

Therefore,

greatest integer = - 20 + 8 = - 12

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What is the image point of (-8, 1) after the transformation 7x-axis R180°?

Answers

The image point of (-8, 1) after the transformation D₂ о R180° is equal to (16, -1).

What is a rotation?

A rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).

For a dilation with a scale factor of 2, we have:

Point A (-8, 1)   →   (-8 × 2, 1 × 2)  = Point A' = (-16, 2)

By applying a rotation of 180° to the given point, the coordinates of its image is given by:

(x, y)                           →               (-x, -y)

Points A' = (-16, 2)   →  Points A' = (-(-16), -(1)) = (16, -1).

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Complete Question:

What is the image point of (-8, 1) after the transformation D₂ о R180°?

Compute the the directional derivative Da(f) of f(x, y) = xy + x³ at the point (1, 2) and
in the direction of (1,-1).

Answers

Refer to the photo taken.
Answer is at the bottom circled.

ASAP!! Brainliest to first answer
3x - 2/3x = 14

Answers

The appropriate answer is
Firstly we go with BODMAS

2/3=0.6

3x-0.6x=2.4x

x=9/2.4=5.83 approximately 5.8

Please rate as the brainliest

Answer:

x = 6

Step-by-step explanation:

Given equation,

→ 3x - (2/3)x = 14

Now the value of x will be,

→ 3x - (2/3)x = 14

→ (9/3)x - (2/3)x = 14

→ ((9 - 2)/3)x = 14

→ (7/3)x = 14

→ 7x = 14 × 3

→ x = 42/7

→ [ x = 6 ]

Hence, the value of x is 6.

HELP ME PLEASE.

f(x) = √2x
g(x) = √50x

Find (f g)(x). Assume x ≥ 0.

A. (f.g)(x) = 10√
B. (f.g)(x) = √52x
C. (f.g)(x) = 10x
D. (f g)(x) = 50x

Answers

The representation of the composite function (fg)(x) is (fg)(x) = 10x

How to determine the possible value of the composite function?

From the question, we have the following function definitions

f(x) = √2x

g(x) = √50x

The function to calculate is given as (fg)x

This can be calculated using

(fg)(x) = f(x) * g(x)

Substitute √2x for f(x) and √50x for g(x) in the above equation

So, we have

(fg)(x) = √2x  * √50x

Evaluate the products

(fg)(x) = √100x²

Evaluate the exponents

(fg)(x) = 10x

Hence, the possible equation is (fg)(x) = 10x

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what are the roots of the following function? f(x) (4x-1)(x+9) please answer due today. In rain myths,in Madagascans myth what is one effect of Ndriananahary sending his son, atakoloina , to earth Marie mixed 5 g of carbon with 5 g of lead oxide. She heated the mixture strongly for 15 minutes in a fume cupboard. After 15 minutes, Marie found some shiny beads in the mixture. a. i) Marie collected all the shiny beads from this experiment. How could she test them to show they were metal? _________________________________________________________ _________________________________________________________ ii) Maries test showed that the tiny beads were metal. What metal were the beads likely to be? ________________________________________________________ b. Marie also expected carbon dioxide to be formed in this experiment. i) In carbon dioxide, what element is combined with carbon? __________________ ii) Where, apart from the air, did this element come from in this experiment? __________________c. Give one safety precaution Marie should take during this experiment. Which statement describes the process of cellular respiration?ResponsesA. It takes place in plant cells and involves chemical reactions with carbon dioxide, water, and energy from the sun to produce sugars.B. It takes place only in animal cells and involves chemical reactions with oxygen and releases stored energy.C. It takes place in plant and animal cells and involves the division of cells.D. It takes place in plant and animal cells and involves chemical reactions with oxygen to release stored energy. Find the vertex of the parabola y=2(x-1)2+4. Which of the following qualifies the consumer to be transferred to a licensed Medicare Agent?A) 65 or older & MedicaidB) SSIC) SSDI for more than 2 yearsD) Medicare Part A or BE) Medicare Parts A & B to get more detailed information about the current and predicted effects of the hurricane for your local area, you should? a. read the latest tropical cyclone public advisory b. talk with the hurricane liaison team at the national hurricane center c. read the latest hurricane local statement d. read the latest tropical cyclone forecast discussions 3409.1 in exponential form After energy conversions, you end up with the same total amount of energy as the original amount energy. Which law explains this rule?. Mrs. Ferrell spent 40 minutes grading tests. That was 80% of the total number of minutes shespent grading.How many minutes did she spend grading? four resistors having a value of 100 ohms each are connected in parallel. what is the total resistance of the circuit? 2. Pretend that the temperature today is 5 C (9 F) higher than yesterday. Now consider an increase of 5 C (9 F) in average global temperature. How are these two scenarios different? Major activity injuries includeBone breaksConcussionsJoint DislocationsAll of the above el profesorunos profesorslos profesorslos profesoresunos profesores please help me with this problem!! which category of joint provides a very slight degree of movement, but isn't designed to be highly mobile? jenna is seeking to raise money to develop a new app where individuals can buy and sell used clothing. she is looking for long-term investors in her product, and she wants to protect her personal assets from any liabilities associated with borrowing capital. which form of business structure would clearly meet jenna's needs? a.) partnership b.) limited liability partnership c.) sole proprietorship d.) corporation which of the choices is/are secretions produced by the pancreas? select all that apply. bicarbonate ions to neutralize stomach acid methane from fermentation gastrin to stimulate hcl production trypsin for further protein digestion lipase for fat digestion Who is the original artist of this image? when butane, c4h10, undergoes combustion, it reacts with o2 to form co2 and h2o. how many moles of o2 are required to react completely with 10.6 moles of butane?