What are the area and perimeter of rectangle MNOP

What Are The Area And Perimeter Of Rectangle MNOP

Answers

Answer 1

Answer :

Area of Rectangle = 48 sq. unitsPerimeter of rectangle = 28 units

Step-by-step explanation:

We are give with a rectangle MNOP.

As we can see from above graph,

Length of MN = 8 units

Length of MO = 6 units

MN = Length MO = Breadth

We know that

Area (rectangle) = length × breadth

area = 8 × 6

area = 48 sq. units

Now, Let's calculate the perimeter of the rectangle.

Perimeter (rectangle) = 2(l + b)

Substituting the values,

Perimeter= 2(8 + 6)

Perimeter = 2 × 14

Perimeter = 28 units


Related Questions

Select all names that apply to the number. 0

Answers

There is multiple names it has, like for example “Zero” and in British English it is “nought” which is often used as an archaic word for nothing, I hope this help’s.

The sum of the roots of the quadratic 5x^2 - 6x + 1 = 0 is

Answers

Answer:

here's your answer

hope this helped you

please mark as the brainliest (ㆁωㆁ)

The sum of the roots of the quadratic 5x^2 - 6x + 1 = 0 is

One-variable Statistics:Question 4
A survey of recent house sales shows that the mean and
median have the same value. Which of the following must
be true?
Select one:

1. The mode is the same value as the mean and median.

2. The data distribution is symmetric.

3. The data distribution is positively skewed.

4. The data distribution is negatively skewed.



Plsss help me

Answers

Answer:

2:The data distribution is symmetric.

Step-by-step explanation:

The value of mean and median is same, then the true statement will be that the data distribution is symmetric. Hence, option 2 is correct.

What is mean?

Along with the mode and median, the mean is the average of the central tendency. The average of the specified collection of numbers is what is referred to as the mean. It indicates a data set's values are distributed equally. The three most popular methods for determining maximum likelihood are the mean, median, and mode.

As per the given information in the question,

The survey report of recent house sales shows that the mean and the median have the same value, which means that the data distribution must be symmetric.

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help pls lol 31. What is the value of x?
(2x + 24)°
142°
(1 point)

help pls lol 31. What is the value of x?(2x + 24)142(1 point)

Answers

Answer:

59

Step-by-step explanation:

The angle measures (2x + 24) and 142 are equal to each other since we are looking at a line being cut by a "transversal" So, set them to equal each other like so:

2x + 24 = 142

Now solve:

2x + 24 = 142

2x = 118

x = 59

Answer:

a) x = 59

Step-by-step explanation:

Now we have to,

→ find the required value of x.

We know that,

→ opposite angles are always equal.

Then the value of x will be,

→ 2x + 24° = 142°

→ 2x = 142° - 24°

→ 2x = 118°

→ x = 118/2

→ [ x = 59 ]

Hence, the value of x is 59.

Which ordered pairs make the open sentence true?

3x+y<14

Select all the correct answers.


(3, 6)
left parenthesis 3 comma 6 right parenthesis

(7, −7)
left parenthesis 7 comma negative 7 right parenthesis

(6, 0)
left parenthesis 6 comma 0 right parenthesis

(−1, 6)
left parenthesis negative 1 comma 6 right parenthesis

(4, −1)

Answers

The ordered pairs which make the open sentence true are:

(-1, 6).(4, -1).

What is an inequality?

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an algebraic expression based on any of the following arguments:

Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).

For this exercise, you should evaluate each of the given expressions to determine which inequalities is true when the ordered pairs are substituted. This ultimately implies that, you would have to substitute the ordered pairs into each of the given algebraic expressions and then evaluate.

When ordered pairs = (3, 6), we have:

3x + y < 14

3(3) + 6 < 14

9 + 6 < 14

15 < 14 (False).

When ordered pairs = (7, -7), we have:

3x + y < 14

3(7) + (-7) < 14

21 - 7 < 14

14 < 14 (False).

When ordered pairs = (6, 0), we have:

3x + y < 14

3(6) + 0 < 14

18 - 0 < 14

18 < 14 (False).

When ordered pairs = (-1, 6), we have:

3x + y < 14

3(-1) + 6 < 14

-3 + 6 < 14

3 < 14 (True).

When ordered pairs = (4, -1), we have:

3x + y < 14

3(4) + (-1) < 14

12 - 1 < 14

11 < 14 (True).

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Problem. 6: Findinn equation of the set of all points equidistant from the points (2, 3,5) and B(5, 4, 1) Note: For plane equations, DO NOT check an individual coefficient. You MUST complete the entir

Answers

The equation of the set of all points equidistant from A(2, 3, 5) and B(5, 4, 1) is -3x - 3y - 4z

How to calculate the equation

Let's find the distance between M and B:

d₂ = √((x - x₂)² + (y - y₂)² + (z - z₂)²).

Substituting the coordinates of M and B, we have:

d₂ = √((x - 5)² + (y - 4)² + (z - 1)²)

Since we want to find the equation of the set of points equidistant from A and B, the distances d₁ and d₂ must be equal:

√((x - 7/2)² + (y - 7/2)² + (z - 3)²) = √((x - 5)² + (y - 4)² + (z - 1)²)

Squaring both sides of the equation, we get:

(x - 7/2)² + (y - 7/2)² + (z - 3)² = (x - 5)² + (y - 4)² + (z - 1)²

Expanding and simplifying, we have:

x² - 7x + 49/4 + y² - 7y + 49/4 + z² - 6z + 9 = x² - 10x + 25 + y² - 8y + 16 + z² - 2z + 1

Canceling out the common terms, we get:

-3x - 3y - 4z + 64/4 = 0

-3x - 3y - 4z + 16 = 0

Therefore, the equation of the set of all points equidistant from A(2, 3, 5) and B(5, 4, 1) is: -3x - 3y - 4z

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In which of the following cases is the construction of triangle ABC possible?

Answers

Triangle with sides AB = 8cm , CA = 5cm , BC = 7cm and AB = 7cm , BC = 10cm , CA = 8cm can construct a Triangle.

What are cases for construction of triangle?

Condition : For forming the triangle, the sum of two sides must be greater than the third side.

a.  AB = 4cm, CA = 3cm, BC = 10cm

   CA+BC=AB

   3+1=4

   4=4

Therefore, it cannot form a triangle because it is not satisfying the condition.

b.  AB = 8cm , CA = 5cm , BC = 7cm

    AB+CA>BC

    AB+BC>CA

    CA+BC>AB

    Therefore, it can form a triangle because it satisfies the condition.

c.  AB = 7cm, BC = 10cm, CA = 8cm

   AB+BC>CA

   AB+CA>BC

   BC+BC>AB

  Therefore, it can form triangle because it satisfies the condition.

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In the rectangle ABCD the area is 2x^2-4x-16 and the length is 2x+4, what is the breath of the rectangle

Answers

The width of the rectangle cannot be zero, this means that the given area and length do not correspond to a valid rectangle.

The area of a rectangle is given by the formula: area = length * width. We know that the area of the rectangle is 2x^2 - 4x - 16 and the length is 2x + 4.

So, we can set up an equation to find the width:

2x^2 - 4x - 16 = (2x + 4) * width

Expanding the right side of the equation:

2x^2 - 4x - 16 = 2x^2 + 8x + 16 - 16

Simplifying the equation:

0 = 8x - 32

Dividing both sides of the equation by 8:

0 = x - 4

Adding 4 to both sides:

x = 4

Now that we have the value of x, we can substitute it back into the expression for the length:

length = 2x + 4 = 2 * 4 + 4 = 12

And also into the expression for the width:

width = (2x^2 - 4x - 16) / (2x + 4) = (2 * 4^2 - 4 * 4 - 16) / (2 * 4 + 4) = (32 - 16 - 16) / 12 = 0

So, this means that the given area and length do not correspond to a valid rectangle. This could be due to an error in the calculation or an incorrect assumption.

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Students were asked to choose their favorite subject. If 3/10 of the students chose history and 5/10 chose biology, what fraction chose either history or biology?​

Answers

Answer: 8/10

Step-by-step explanation:

if you do 5/10 plus 3/10 it equals 8/10 and that is what the question is telling you to do.

What is the answer and solution steps I’ll give you brainlist and points

What is the answer and solution steps Ill give you brainlist and points

Answers

Answer:

the answer is b(-7/4)

Step-by-step explanation:

2(x+5)-3=(2x=1)+1

2x+10-3=-(2x+1)+1

2x+7=-(2x+1)+1

2x+7-2x-1+1

2x+7=2x

2x+7-7+2x-7

x=-7/4    

Answer:

Step-by-step explanation:

Use the equation F= (HG/S)+ G-A in my case is F=(1000/2)+0-15 please solve
F=father
HG=Hours on Genshin Impact
S=Showers
G= girls
A = age

Answers

The given equation and values, the value of F, which represents "father" in this context, is 485.

Using the equation F=(HG/S)+G-A, and substituting the given values, we get:

F = (1000/2) + 0 - 15

F = 500 + 0 - 15

F = 485

Therefore, based on the given equation and values, the value of F, which represents "father" in this context, is 485.

It's important to note that this equation is not a scientifically valid or meaningful equation, and is not intended for serious use in any context.

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Please help ASAP! Will give 20 points!!! German Silver is an alloy composed of nickel, zinc, and copper in a 3:4:13 ratio. How many kilograms of each metal are needed to make 4 kg of this alloy?

Answers

Answer:

Step-by-step explanation:

first lets find the total # of portions:

3+4+13=16+4=20

To make 4kg of this alloy you have to use:

nickel: (4/20)*3=12/20=6/10=0.6 kg

zinc: (4/20)*4=16/20=8/10=0.8 kg

copper: (4/20)*13=52/20=26/10=2.6 kg

Simplify.40x8y5
2
O 4x¹y²√10y
○ 4x¹y² √10
O 2x¹y²√10
O 2x¹y²√10y

Answers

Answer:

\( \sqrt{40 {x}^{8} {y}^{5} } \)

\( \sqrt{40} \sqrt{ {x}^{8} } \sqrt{ {y}^{5} } \)

\((2 \sqrt{10} )( {x}^{4} )( {y}^{2} \sqrt{y} )\)

\(2 {x}^{4} {y}^{2} \sqrt{10y} \)

ASAPPPP!!! CAN U START FROM SECTION A TO SECTION B!!!!????
LISTEN HERE I NEED SOMEONE TO WORKOUT ALL OF THESE CUZ IF I DONT FINISH IT BY TOMZ I GET A DETENTION !!

ASAPPPP!!! CAN U START FROM SECTION A TO SECTION B!!!!????LISTEN HERE I NEED SOMEONE TO WORKOUT ALL OF

Answers

Answer: I just did the ones that did not already have an answer

Section A:

7. 1.5 hours

9. 480 meters

10. 10 km

Section B:

1. 40 mph

2. 160 miles

3. 168 miles

4. 5.2 mph

5. 26.25 km/h

Here is a system of three linear equations:
−3x+3z=−1
2y+4z=−3
−9x−4y+z=5

a. Write down the augmented matrix: Put the augmented matrix into row echelon form: Find one point that is a solution to this system of equations.




x
y
z





=

Answers

The augmented matrix, we take the coefficients of the variables and the constant terms from each equation and arrange them in a matrix format. Therefore, the point (x, y, z) = (3/8, -7/4, 1/8) is a solution to the system of equations.

To write down the augmented matrix, we take the coefficients of the variables and the constant terms from each equation and arrange them in a matrix format. The augmented matrix for this system of equations is: \(\[ \begin{bmatrix} -3 & 0 & 3 & -1 \\ 0 & 2 & 4 & -3 \\ -9 & -4 & 1 & 5 \\ \end{bmatrix} \]\)

To put the augmented matrix into row echelon form, we perform row operations to transform it. The goal is to create zeros below the main diagonal.

We start by dividing the first row by -3 to make the leading coefficient 1: \(\[ \begin{bmatrix} 1 & 0 & -1 & \frac{1}{3} \\ 0 & 2 & 4 & -3 \\ -9 & -4 & 1 & 5 \\ \end{bmatrix} \]\)

Next, we perform row operations to eliminate the -9 in the third row. We replace the third row with the sum of the third row and 9 times the first row:

\(\[ \begin{bmatrix} 1 & 0 & -1 & \frac{1}{3} \\ 0 & 2 & 4 & -3 \\ 0 & -4 & 8 & 8 \\ \end{bmatrix} \]\)

Now, we eliminate the -4 in the third row by replacing the third row with the sum of the third row and 2 times the second row:

\(\[ \begin{bmatrix} 1 & 0 & -1 & \frac{1}{3} \\ 0 & 2 & 4 & -3 \\ 0 & 0 & 16 & 2 \\ \end{bmatrix} \]\)

Finally, we divide the third row by 16 to make the leading coefficient 1:

\(\[ \begin{bmatrix} 1 & 0 & -1 & \frac{1}{3} \\ 0 & 2 & 4 & -3 \\ 0 & 0 & 1 & \frac{1}{8} \\ \end{bmatrix} \]\)

This is the row echelon form of the augmented matrix. To find one point that is a solution to the system of equations, we can back-substitute. Starting from the bottom row, we substitute the values of z and continue substituting the values of y and x into the equations above. The solution to this system of equations is:

\(\[ \begin{aligned} x &= \frac{3}{8} \\ y &= -\frac{7}{4} \\ z &= \frac{1}{8} \end{aligned} \]\)

Therefore, the point (x, y, z) = (3/8, -7/4, 1/8) is a solution to the system of equations.

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the back of dante's property is a creek. dante would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a corral. if there is 200 feet of fencing available, what is the maximum possible area of the corral?

Answers

If there is 200 feet of fencing available, the maximum possible area of the corral is 5000 Feet.

In the question, if there is 200 feet of fencing available, then we have to find the maximum possible area of the corral.

The formula of area of rectangle is:

A = L × B, where L is the length of the rectangle and B is the breadth of the rectangle.

The A = 200 feet and rectangular area is enclosed using the creek as one side and fencing for the other three sides, to create a corral.

So, L + 2B = 200

Subtract L on both side, we get

2B = 200 - L

Divide by 2 on both side, we get

B = 100 - L/2

A = f(L)

A = L·(100 - L/2)

A = 100L - \(L^2\)/2

Now finding the derivative.

A' = \(\frac{df(L)}{dL}\)

A' = -L + 100

Let A' = 0

-L + 100 = 0

Subtract 100 on both side, we get

-L = -100

L = 100 feet

Now putting the value of L in B = 100 - L/2.

B = 100 - 100/2

B = 100 - 50

B = 50 feet

The maximum possible area of the corral = 100 × 50

The maximum possible area of the corral = 5000 Feet

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high-low or least squares regression analysis should only be done it a(n) ____ plot depicts linear cost behavior.

Answers

High-low or least squares regression analysis should only be done if a scatter plot depicts linear cost behavior.

A scatter plot is a graphical representation of data points, with the x-axis representing the independent variable (such as the level of production) and the y-axis representing the dependent variable (such as the cost). Linear cost behavior means that the relationship between the independent and dependent variables can be approximated by a straight line. In other words, as the independent variable increases or decreases, the dependent variable changes proportionally.

To determine if a scatter plot depicts linear cost behavior, you need to visually examine the data points. If the points appear to align closely along a straight line, it indicates a linear relationship. However, if the points are scattered and do not follow a clear pattern, it suggests non-linear cost behavior.

High-low or least squares regression analysis are statistical techniques used to estimate and quantify the linear relationship between variables. These methods help determine the equation of the line that best fits the data points and can be used to predict future values. Therefore, performing these analyses is only meaningful when the scatter plot indicates linear cost behavior.

In summary, high-low or least squares regression analysis should only be done if a scatter plot depicts linear cost behavior.

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Find the Domain:
And Range:

Find the Domain: And Range:

Answers

Answer:

Find the domain by finding where the expression is defined.

Interval Notation: ( −∞, −4) ∪ (−4,∞)

range is

y ∈ R, y ≠ 1  or

(−∞,1)∪(1,∞)

sorry if this is wrong I tried!

The domain and range of the function are:

Domain: (-∞, -4) U (-4, ∞)

Range: (0. 1)

We have,

Domain:

The domain represents the set of all possible input values for the function.

Since the expression (x + 4) appears in the denominator, we must exclude any values of x that would make the denominator equal to zero.

The domain of the function is all real numbers except for x = -4.

So,

Domain: (-∞, -4) U (-4, ∞)

Range:

The range represents the set of all possible output values of the function.

As x approaches negative infinity (x → -∞):

Since both the numerator and denominator approach negative infinity,

lim(x → -∞) 2x/(x + 4) = 2(-∞)/(-∞ + 4) = -∞/(-∞) = 1

As x approaches positive infinity (x → +∞):

lim(x → +∞) (2x/(x + 4))² = (lim(x → +∞) 2x/(x + 4))²

lim(x → +∞) 2x/(x + 4) = 2(+∞)/(+∞ + 4) = +∞/(+∞) = 1

So,

Range: (0, 1)

Thus,

The domain and range of the function are:

Domain: (-∞, -4) U (-4, ∞)

Range: (0. 1)

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Which of the following taxpayers would be most likely to benefit from an installment sale?
Allan - He sold a business use car at a net gain that was less than the amount of depreciation
Kayla She sold business ue land for a gain
Marie She sold property she had held in inventory in her business at a net gain
Robert - He sold a fishig boat at a net loss

Answers

The taxpayer who would most likely benefit from an installment sale is Allan, who sold a business use car at a net gain that was less than the amount of depreciation.

What is an installment sale?

An installment sale is a transaction in which the sales price is received over a period of time that spans more than one tax year. Installment sales may have tax advantages, which is why taxpayers should consider them.

The taxable profit in an installment sale is not calculated using the entire sales price. Instead, it is calculated by applying the gross profit percentage to each installment's payments received during the year. In general, if an installment sale meets the definition, the taxpayer reports income from the sale as the payments are received, rather than in the year of sale.

However, in some situations, taxpayers might choose to report the entire profit from an installment sale in the year of sale. In such instances, an election to do so must be made.

What is net gain?

The difference between the sales price and the adjusted cost basis of the asset is known as the gain. The gain is reduced by selling expenditures to arrive at the net gain. Net gain occurs when the sales price of a commodity is higher than its cost of acquisition and other fees or expenses related to its purchase and sale.

What is depreciation?

Depreciation is a term used in accounting and finance to describe the systematic decrease in the value of an asset over time due to wear and tear. It is an expense that lowers a company's net income and lowers the value of an asset on the balance sheet.

Hence, Allan, who sold a business use car at a net gain that was less than the amount of depreciation, will most likely benefit from an installment sale.

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Carlos is playing a dice game with Elena. Carlos will roll 222 six-sided dice, and if the sum is greater than 777, he will win \$5$5dollar sign, 5. If the sum is 777, they will tie and he will break even. If the sum is less than 777, he will lose \$4$4dollar sign, 4. What is Carlos's expected value of playing this game? Round your answer to the nearest cent.

Answers

Answer:

Step-by-step explanation:

The expected value of one six-sided dice is (1 + 2 + 3 + 4 + 5 + 6)/6 = 3.5.

So, the expected value of the sum of 222 dice is 3.5 * 222 = 777.

This means that the expected value of playing this game is 0, since the expected outcome is to break even.

Thus, Carlos's expected value of playing this game is 0, rounded to the nearest cent.

Answer:

Step-by-step explanation:

The expected value of Carlos playing this dice game is

$0.42

The length of a rectangle is 19 centimeters less than its width. Its area is 20 square centimeters. Find the dimensions of the rectangle.

Answers

The dimensions of the rectangle are width = 20 centimeters and length = 1 centimeter.

Let's denote the width of the rectangle as "w" centimeters. According to the problem, the length of the rectangle is 19 centimeters less than its width, so the length can be expressed as "w - 19" centimeters.

The formula for the area of a rectangle is length multiplied by width. In this case, the area is given as 20 square centimeter

Area = Length × Width

20 = (w - 19) × w

To solve this equation, we can expand it:

20 = \(w^2\) - 19w

Rearranging the equation to bring everything to one side:

\(w^2\) - 19w - 20 = 0

Now, we can factor the quadratic equation:

(w - 20)(w + 1) = 0

Setting each factor equal to zero and solving for "w":

w - 20 = 0 --> w = 20

w + 1 = 0 --> w = -1

Since a negative width doesn't make sense in this context, we discard w = -1.

Therefore, the width of the rectangle is 20 centimeters (w = 20).

To find the length, we substitute this value back into the expression for length:

Length = w - 19

Length = 20 - 19

Length = 1 centimeter

So, the dimensions of the rectangle are width = 20 centimeters and length = 1 centimeter.

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How can you find the common ratio of an exponential function set from a table of values?
Help<3 I'll give brainlist <3

Answers

Answer:

omg stop taking the poimts away from me it eas right nesus

For the table that represents an exponential function, the common ratio of the associated geometric sequence is 6.

Used the concept of a geometric sequence,

A sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

And, The common ratio refers to the rate of change in an exponential function.

Given that,

The table represents an exponential function.

Let us assume that, the standard form of an exponential function,

\(y = a (b)^x\)

Where 'a' and 'b' are constants.

From the table substitute x = 1 and y = 6 in above function,

\(6 = a (b)^1\)

\(6 = ab\\\)  

\(a = \dfrac{6}{b}\) ... (i)

And, substitute x = 2 and y = 36 in above function,

\(36 = a (b)^2\)

Substitute the value of 'a' from (i) into the above equation,

\(36 = \dfrac{6}{b} \times b^2\)

\(36 = 6 \times b\)

Divide 6 on both sides,

\(b = 6\)

So, From (i),

\(a = \dfrac{6}{b}\)

Substitute b = 6;

\(a = \dfrac{6}{6}\)

\(a = 1\)

Therefore, the equation of an exponential function,

\(y = a (b)^x\)

Substitute a = 1, b = 6;

\(y = 1 (6)^x\)

\(y = 6^x\)

Since the common ratio refers to the rate of change in an exponential function.

Hence, the common ratio of an exponential function

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The complete question is shown in the attached image.

How can you find the common ratio of an exponential function set from a table of values?Help&lt;3 I'll

Spin a spinner with three equal sections colored red, white, and blue. What is P(yellow)?
a.100%
b.66%
c.33%
d.0%

Answers

The probability of getting the color yellow when spinning a spinner with three equal sections colored red, white, and blue is 0%. Therefore, the correct answer is d) 0%.

Since the spinner has three equal sections colored red, white, and blue, and there is no section labeled yellow, it is not possible to obtain the color yellow when spinning the spinner. Each section has an equal chance of being landed on, but none of them represent the color yellow. Therefore, the probability of getting the color yellow is 0%. It's important to note that probability represents the likelihood of an event occurring, and in this case, the event of landing on the color yellow is not possible given the given information about the spinner. Therefore, the probability is 0%.

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The weather forecast for the weekend is a 35% chance of rain on Saturday and a 65% chance of rain on Sunday. Your friend says that means there is a 100% chance of rain this weekend. What error did your friend make?

Answers

Answer:

Because these probabilities are independent, the friend was supposed to multiply them, not add them. So the probability of rain this weekend is

.35 × .65, or .2275, meaning that the probability of rain this weekend is 22.75%

Gavin has 16 blue marbles and 8 white ones. If he wants to place them in identical groups
without any marbles left over, what is the greatest number of groups Gavin can make?

Gavin has 16 blue marbles and 8 white ones. If he wants to place them in identical groupswithout any

Answers

Answer:

6

Step-by-step explanation:

Equation 4x - 12 = 12 - 4x

Answers

Answer:

this is infinite solutions

1. The sum of three times k and eight is eleven

Answers

Answer:

k=1

Step-by-step explanation:

\(3k + 8 = 11\\\)

Subtract 8 from both sides

\(3k = 3\)

Divide

\(\frac{3k}{3} = \frac{3}{3}\)

Simplify

\(k =1\)

Answer:

k=1

Step-by-step explanation:

   

The sum of two consecutive even integers is 150. What are the two integers?

Answers

Answer:

74 + 76 = 150

Step-by-step explanation:

Given it's Even integers,  150/2 =75. Take the preceding and following even numbers. They are consecutive even numbers.

What is the Greatest Common Factor of 48r^2-52r ?

Answers

Step-by-step explanation:

4r is the greatest common factor

An exam consists of 50 multiple choice questions. Based on how much you studied, for any given question, you think you have a probability of 0.64 of getting the correct answer. Consider the sampling distribution of the sample proportion of correct questions out of 50. (a) Find the mean and standard error of the sampling distribution of this proportion; (b) What do you expect for the shape of this sampling distribution? - approximately normal because n is large; - cannot be determined because p is greater than 0.5; - cannot be determined because n is large; - approximately normal because the population is normal.

Answers

(a) The mean is 32, and the standard error is 0.068 (b) The expected shape will be approximately normal (c) The probability of scoring less than 60% is 0.278

As the number of questions (n) is 50 and the probability of getting the correct answer (p) is 0.64, the mean can be calculated as follows;

E(x) = np

E(x) = 50 × 0.64

E(x) = 32

The standard error is calculated as follows;

SE = √p×(1-p) ÷ n

SE = √0.64 × (1-0.64) ÷ 50

SE = √0.004608

SE = 0.068

Therefore, the mean is calculated to be 32, and the standard error is 0.068

As the sample size is large therefore the expected shape will be approximately normal

To calculate the probability of scoring less than 60%, we first calculate the z-score using:

z = (x – μ) / σ

z = (0.60 - 0.64) / 0.068

z = -0.588

So we have;

P (x < 60%) = P (z < -0.588)

P (x < 60%) = 0.278

Therefore the probability of scoring less than 60% is 0.278

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