The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. if the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade? give the answer that is closest to the exact number.

Answers

Answer 1

The lowest score will be obtained as follows:
the z-score is given by:
z=(x-μ)/σ
where:
σ-standard deviation
μ- mean

we are required to evaluate for x, given that P(x<X)=0.05
The value of z that corresponds to 5% will be:
z=-1.65
thus plugging our values we obtain:
-1.65=(x-62)/11
solving for x we get:
-18.15=x-62
thus
x=-18.15+62
x=43.85
x~44
Thus the lowest score is 44

Answer 2

The lowest marks that a student can have and still be awarded a passing grade is 44.

Step-by-step explanation:

Given :

Mean, [tex]\mu = 62[/tex]

Standard Deviation, [tex]\sigma = 11[/tex]

Calculation :

z score is given by,

[tex]z = \dfrac{x-\mu }{\sigma}[/tex] ----- (1)

Value of z corresponds to 5% is,

[tex]z =-1.65[/tex]

from equation (1) we get,

[tex]-1.65=\dfrac{x-62}{11}[/tex]

[tex]x=43.85[/tex]

[tex]\rm x = 44 \;\;(Approx)[/tex]

The lowest marks that a student can have and still be awarded a passing grade is 44.

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Related Questions

Go to lesson page Problem If you flip three fair coins, what is the probability that you'll get a head on the first flip, a tail on the second flip, and another head on the third flip?

Answers

The probability of any particular sequence of N flips of a fair coin is 2^(-N).

Your probability of the given sequence of 3 coin flips is
2^-3 = 1/8

First if all, we know that the coin has two sides- head and tail

P(getting a head of the first flip):

1/2

P(getting a tail on the second flip):

1/2

P(getting a head on the third flip):

1/2

To find the final answer, take:

1/2×1/2×1/2=1/8

As a result, the probability that you'll get a head on the first flip, a tail on the second flip, and another head on the third flip is 1/8. Hope it help!

is 0.003km greater than, less than, or equal to 3 m

Answers

There are 1000 meters in a kilometer. 0.003 kilometers is equal to 3 meters

A copy machine makes 132 copies in 5 minutes and 30 seconds. How many copies does it make per minute?

Answers

24 copies per minute

please help with 23 and show how to work it out

Answers

For this problem, you best start with calculating how many miles they drive in 1 hour, by dividing 192 by 4.5, which equals 42.666. You then multiply this by 3 to get the distance after 3 hours.

To prevent rounding errors, you can put this all in one equation:

[tex]\frac{192}{4.5} \times {3} =128[/tex]

So answer C looks like the right one.

Which statements is true

A: all rectangles are squares
B: some trapezoids are parallelogram
C: all square are rhombues
D: no rhombuses are rectangles

Answers

All squares are rectangles
all squares are rhombuses

B and D are True Statements.

Hope this Helped!

;D
Brainliest??

Suppose u=⟨2,−2u=⟨2,−2⟩ and v=⟨6,2⟩v=⟨6,2⟩ are two vectors that form the sides of a parallelogram. then the lengths of the two diagonals of the parallelogram are

Answers

91.7
44.6
is the answer

Help with this math question please

Answers

51. The area of the rectangle is lw. The triangle's base and height are both w, so its area is 1/2 (w)^2. The total area will be lw + (1/2)w^2, which is choice A.
52. The best answer is G. This is a circle of diameter 10 in, so 10 in is the longest dimension, and you would not be able to cut a 2-in wide section that is 10 in long since the circle immediately gets smaller when you move away from the diameter.

Q #5 Solve the system by graphing

Answers

That first one is correct there is no solution since they are parallel.

We have the following system of equations:
(-1/3) x + y = -1
y = 4 + (1/3) x
Let's rewrite the system of equations:
y = (1/3) x - 1
y = (1/3) x + 4
We note that both lines have the same slope:
m = 1/3
Therefore, the lines are parallel.
The first line has a cut point with the y axis of:
(0, -1)
The second line has a cut point with the y axis of:
(0, 4)
Like the lines are parallel, the system has no solution.
Answer:
The system of equations has no solution.

Use a net to find the surface area of the prism.

•213 m^2
•426 m^2
•336 m^2
•306 m^2

Answers

The surface area of the prism will be given by:
SA=2(L×W)+2(L×H)+2(H×W)
SA=2(12×5)+2(12×9)+2(5×9)
SA=120+216+90
SA=426m²

Answer: 426m²

There is a game at the carnival that costs $20 to play. There are two outcomes: either you win $100 , or you lose. To play you roll a die. If a six appears you win; all other rolls you lose. if 1000 people played this game during one afternoon what would you expect to be the outcome?

A. the game earns $3330

B. the game earns $1660

C. the game loses $3330

D. the game loses $1660

Answers

Outcome on winning = $100 - $20 = $80
Outcome on losing = $20

Probability of winning = 1/6
Probability of losing = 5/6

Expected Value = 1/6 (80) +5/6(-20) = -3.333

This shows on average from each game, the game earns $ 3.333.

So, if 1000 such games are played, the game will earn 1000 x 3.33 = $3330

So, the answer to this question is option A

Correct answer is Option(A) . The game earns $3330

Carnival Game Expected Outcome

To determine the expected outcome, we first need to calculate the expected value of playing this game once.

The cost to play is $20. If a six is rolled, the player wins $100; otherwise, they lose their $20.

Calculations:

Probability of rolling a six = 1/6Probability of not rolling a six (1, 2, 3, 4, or 5) = 5/6

Expected value (EV) for one game:

EV = (1/6 x ($100 - $20)) + (5/6 x (-$20))EV = (1/6 x $80) + (5/6 x -$20)EV = $80/6 - $100/6EV = -$20/6EV ≈ -$3.33

This means that on average, each player loses approximately $3.33 per game.

Outcome for 1000 Players

If 1000 people play the game, the total expected loss for the players will be:

Total Expected Loss = 1000 x EVTotal Expected Loss ≈ 1000 x (-$3.33) = -$3330

Therefore, the game earns approximately $3330.

The ratio of the length to the width of a map is 8 to 5. The map is exactly 32 inches in length. What is the width of the map? A. 13 inches B. 20 inches C. 24 inches D. 32 inches

Answers

Ratio of length to width of a map = 8:5

Length of the map = 32 inches
Let the width of the map = x inches

So,

Length : Width = 8 : 5
32 : x= 8: 5

x = 5/8 * 32

x = 20 inches

So, the width of the map is 20 inches

Answer:

B. 20 inches

Step-by-step explanation:

Remember that when dealing with ratios or unit rates you just have to do simple rules of three to calcuate what they are asking you, in this case you have that in the map for every 8 units in the length there will be 5 in the width, so how many will there be when the map is 32 inches in length?

[tex]\frac{8}{5}= \frac{32}{x}\\x=\frac{32*5}{8}\\ x=20[/tex]

So the width of a map with a length of 32 inches and a ratio of 8:5 will be 20 inches.

one day a store sold 12 sweatshirts white one cost $9.95 and yellow ones cost $12.50. In all 147.45 worth of sweatshirts were sold how many of each color were sold?

Answers

x= # of white sweatshirts
y= # of yellow sweatshirts

STEP 1:
set up quantity and cost equations

QUANTITY EQUATION
x + y= 12

COST EQUATION
$9.95x + $12.50y= $147.45

STEP 2:
solve for one variable in quantity equation

x + y= 12
subtract y from both sides

x= 12 - y

STEP 3:
substitute x value in step 2 in cost equation

$9.95x + $12.50y= $147.45
9.95(12 - y) + 12.50y= 147.45

multiply 9.95 by parentheses
(9.95*12) + (9.95*-y) + 12.50y= 147.45

119.40 - 9.95y + 12.50y= 147.45
combine like terms

119.40 + 2.55y= 147.45
subtract 119.40 from both sides

2.55y= 28.05
divide both sides by 2.55

y= 11 yellow

STEP 4:
substitute step 3 x value in either equation

x + y= 12
x + 11= 12
x= 1 white

CHECK:
$9.95x + $12.50y= $147.45
9.95(1) + 12.50(11)= 147.45
9.95 + 137.50= 147.45
147.45= 147.45

ANSWER: 1 white sweatshirt and 11 yellow sweatshirts were sold.

Hope this helps! :)

Test the claim that mean gpa of a night student is significantly different than 2.1 at the 0.02 significance level

Answers

0.60. Is your answer have a nice day

Can someone please help me with this problem. I need help solving a and b

Answers

(a) A generic quadratic expression is often written
ax² +bx +c
Then the "a" and "b" in the expression -b/(2a) represent the coefficients of the squared term and the linear term, respectively. In your quadratic expression, the variable is "t", not "x", but that makes no difference. You have
a = -16
b = 96
Then the time (t) at the maximum height is
t = -b/(2a)
t = -96/(2(-16)) = 96/32 = 3

The ball is highest 3 seconds after being fired.

(b) Evaluating h for t=3, we get
h = -16*3² +96*3 +11
h = -144 +288 +11
h = 155

The maximum height of the ball is 155 ft.

What is the y-intercept of the quadratic function fx) (x- 6)(x-2)?

Answers

Option 1
To find the y-intercept of a quadratic that is in factor formed follow the steps below:

First take the factor form and put it into standard quadratic form
Standard quadratic form:
[tex]ax^2 + bx + c[/tex]

To put the the factor form of a qudratic into standard form, we use the foil method

(x-6)(x-2) = [tex]x^2 - 8x +12[/tex]

Now to find the y-intercept, input 0 where the x is located:

[tex]f(x) = x^2 - 8x +12[/tex]
[tex]f(0) = 0^2 - 8(0) +12[/tex]
[tex]f(0) = 12[/tex]
y-intercept = (0,12)

Why did I use 0? Remember the y-intercept is where the line crosses the y axis so this means the x value of the y intercept is always = 0. Also, not, to find the y-intercept, you could of just multiplied the 6 and 2 in the factored form to get the 12 and since you know that the x is always 0 at the y-intercept, you know that the y-intercept is at (0,12)

Option 2
Input 0 for x in f(x) = (x-6)(x-2)
f(x) = (x-6)(x-2)
f(0) = (0 - 6)(0 - 2)
f(0) = (6)(2) = 12
x = 0
f(0) = y = 12
y-intercept = (0,12)

Answer:

The answer is B just took the test

Step-by-step explanation:

hey can you please help me posted picture of question

Answers

The correct answer is option A

( 2 - 8i ) + ( 5 - i )

Real part is added in real part and the complex part is added in complex part

= 2 +5 - 8i - i

= 7 - 9i

So, the answer is 7 - 9i

What is the interquartile range for the data set?

Could you please double check my answer for me?

Answers

To solve this problem you must apply the proccedure shown below:

1- By definition, the formula for calculate the interquartile range is

Interquartile range=Q3-Q1

Where Q1 is the lower quartile and Q3 is the upper quartile.

2-Keeping this on mind, you have:

Interquartile range=Q3-Q1

Q3=245
Q1=201

Interquartile range=245-201
Interquartile range=44

Therefore, the answer is: 44

Two trains leave stations 532 miles apart at the same time and travel toward each other. One train travels at 90 miles per hour while the other travels at 100 miles per hours. How long will it take for the two trains to meet?

Answers

The two trains will meet in 2.4 hours.

What is the distance?

Distance is defined as the product of speed and time.

We have been given that two trains depart from stations 532 miles apart at the same time and head in the opposite direction. The first train runs at 90 miles per hour, while the second at 100 miles per hour.

Let's assume x distance 90 mph train traveled

Then (532 - x) is the distance 100 mph train traveled

Travel time = distance/speed (equal in both directions)

⇒ x/90 = (532 -x)/100

⇒ 100x = 90× 532 - 90x

⇒ 100x + 90x = 47880

⇒ 190x = 47880

⇒ x = 47880/190

⇒ x = 252

So travel time = 252/90 = 2.4 hrs

Therefore, the two trains will meet in 2.4 hours.

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A 12-foot ladder is leaning against a wall. The distance from the base of the wall to the base of the ladder is feet. Given this information, what can be determined about the triangle formed by the ground, wall, and ladder? Check all that apply.

Answers

Putting into diagram the information provided. The triangle formed is a right triangle. (Find Attached).

We are given the length of the ladder and the distance of the base of the ladder from the wall. With that we can solve for the height of the triangle as well as the angle of inclination wrt to the floor and foot of the ladder or the wall to the tip of the ladder.

Pythagorean's theorem provides for the following formula

Square of hypotenuse (longest side of the triangle) equals the sum of the squares of the two other sides for right triangles.

Thus
Length of ladder being the hypotenuse we have below equation
Hypotenuse = 12
Distance from the base to the foot of ladder = 1 foot/feet
height = ?

12² = 1² + h²
h = √144-1
h=√143

Solving for inclination with respect to wall to tip of the ladder we can use rule of sine for right triangle

sineФ = opposite side / hypotenuse
sineФ = 1/12 = 0.083333
Ф = sin^-1 or inverse sine of 0.083333
Ф = 4.78017268 degrees

Note : If the distance between the base is not interpreted correctly, just change the value and plugin to the equation to get the result.

Answer:

A,B,D,E

Step-by-step explanation:

did it on edge

*Please help, will mark correct answer as brainliest*
What is the formula for finding a break-even point?

Answers

The break-even point formula is calculated by dividing the total fixed costs of production by the price per unit less the variable costs to produce the product.

Break-even point in units =
Fixed costs/( Sales price per unit - Variable cost per unit )

Break-even point in Dollars = Break-even point in units * Sales price per unit

Answer:

break even point=(0.01)(# of points)(P)/monthly savings

Step-by-step explanation:

ap3x

Refer to narrative 14-1. a house is selling for $150,000. a deposit of $20,000 was made when the sales contract was signed. the down payment is 30% and the balance will be financed with a 25-year mortgage at 11% and 4 discount points. if the sellers are responsible for the broker's commission (6% of the purchase price); $1,300 in other closing costs; and the existing mortgage, with a balance of $40,000; what proceeds will they receive on the sale of the property?

Answers

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

-4 log8 x - 2 = 6
Round to the nearest ten - thousandth

Answers

-4 log8 x - 2 = 6

log8 x - 2 = 6/-4 = -3/2

log(x-2)/log8 = -3/2 ; log8 = 0.903089987
log(x-2)/0.903089987= -3/2
log(x-2) = -1.35463498

10 ^ -1.35463498 = x-2

x = 2.044194174

Logarithmic form x^19 = y

Answers

To solve the problem given in the figure attached, you must apply the proccedure shown below:

1. You have the following expression given in the problem:

x^19 = y

2. By definition, you have:

logb(x)=y
b^y=x

3. Therefore, you have:

x^19 = y
logx(y)=19

4. Then, as you can see, the answer is: logx(y)=19

log properties or log transformation is;

b ^ x = a , then to solve for the exponent x, log b a = x or read as log a base b = x.

x^19 = y

x = b
a = y
x = 19

log x y = 19 or log y base x = 19

your drawer contains 6 black socks and 8 white socks. what is the probability that both socks are black

Answers

[tex] \displaystyle
|\Omega|=\binom{14}{2}=\dfrac{14!}{2!12!}=\dfrac{13\cdot14}{2}=91\\
|A|=\binom{6}{2}=\dfrac{6!}{2!4!}=\dfrac{5\cdot6}{2}=15\\\\
P(A)=\dfrac{15}{91}\approx16\% [/tex]

The diameter of a circle is 8 inches.What is the area?
A.8 inches
B.16 inches
C.32 inches
D.64 inches

Answers

The required correct answer is not listed among the given options. The area of the circle is approximately 50.24 square inches.

The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius of the circle. Since the given information provides the diameter (twice the radius), we need to first find the radius by dividing the diameter by 2.

Given: Diameter = 8 inches

Radius = Diameter / 2 = 8 inches / 2 = 4 inches

Now we can calculate the area using the formula:

= πr² = π * (4 inches)²
≈ 3.14 * 16 square inches
≈ 50.24 square inches

Therefore, the correct answer is not listed among the given options. The area of the circle is approximately 50.24 square inches.

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Final answer:

The area of a circle with an 8-inch diameter is calculated using the formula A = πr². The correct area is around 50.27 square inches, not one of the provided options.

Explanation:

The question asks for the area of a circle with a diameter of 8 inches. To find the area, we use the formula A = πr², where π is approximately 3.14159, and r is the radius of the circle. Since the diameter is 8 inches, the radius (r) is half of that, which is 4 inches.

To calculate the area:

Divide the diameter by 2 to find the radius: 8 inches / 2 = 4 inches.Square the radius: 4 inches ² = 16 square inches.Multiply by π (pi): π × 16 square inches ≈ 50.26548 square inches.

The area of the circle is approximately 50.27 square inches, which means none of the given options A, B, C, or D is correct.

Determine if the function is an even function, an odd function or neither. y=-5x^(2)-2x+6

Answers

By definition we have:
A function is even if, for each x in the domain of f, f (- x) = f (x). The even functions have reflective symmetry through the y-axis.
A function is odd if, for each x in the domain of f, f (- x) = - f (x). The odd functions have rotational symmetry of 180º with respect to the origin.
For y = -5x ^ (2) -2x + 6 we have:
f (-x) = - 5 (-x) ^ (2) -2 (-x) +6
f (-x) = - 5x ^ (2) + 2x + 6
Answer:
the function is neither

Answer:

Step-by-step explanation:

a man owned 75 shares of stock worth $50 each the corporation declared a dividend of 8% payable in stock how many shares did he then own

Answers

Final answer:

After receiving an 8% stock dividend on his initial 75 shares, the man will own a total of 81 shares.

Explanation:

The question is asking how many shares the man will own after a corporation where he holds stock declared a dividend payable in stock. The man initially owned 75 shares of stock, each worth $50, and the corporation declared an 8% dividend. To find out how many additional shares he receives as a dividend, we calculate 8% of his 75 shares:

Additional shares = 8% of 75 = 0.08 × 75 = 6 shares.

The man will then own his original 75 shares plus the 6 additional shares, for a total of:

Total shares owned = 75 + 6 = 81 shares.

You save $15,000.00. You place one-third in a savings account earning a 4.6% APR compounded annually. You then invest one quarter of the remaining balance in a 3-year U.S. Treasury bond earning a 5.2% APR compounded annually and the rest in a stock plan. Your stock plan increases in value 3% the first year, decreases 8% in value the second year, and increases 6% in value the third year. What is the balance of the savings account by the end of the third year?

$4,618.81

$2,910.63

$5,722.23

$3,910.02

Answers

Scenario:
1. You deposited 1/3 of 15,000 or 5,000 in a savings account that earns 4.6% compounded annually. If 5,000 is already in the savings account, there is still 10,000 left.
2. One-fourth(1/4) of 10,000 or 2,500 is invested in 3-year US Treasury bond earning 5.2% compounded annually. If 2,500 is invested, there is still 7,500 left.
3. The 7,500 was invested in the stock market.

For the savings account
The amount of money deposited in the savings account after three years will be
[tex]F_2=P\left(1+r\right)^t=5,000\left(1+0.046\right)^3=5,722.23[/tex]

Therefore, the balance of the savings account after three years is $5,722.23.

In a family with 8 children, excluding multiple births, what is the probability of having 7 boys and 1 girl, in any order? assume that a boy is as likely as a girl at each birth

Answers

there is a 7/8 chance there will be boys and a 1/8 chance there will be a girl

Final answer:

The probability of having 7 boys and 1 girl in a family with 8 children is 1/128.

Explanation:

To find the probability of having 7 boys and 1 girl in a family with 8 children, we can use the concept of combinations. There are 8 children in total, and we want to choose 7 boys and 1 girl from them. The probability of having a boy or a girl at each birth is 50%, so we can use the binomial coefficient to calculate the probability. The formula for the binomial coefficient is C(n, k) = n! / (k!(n-k)!), where n is the total number of children and k is the number of boys we want. Plugging in the values, we get C(8, 7) = 8! / (7!(8-7)!) = 8. Therefore, the probability of having 7 boys and 1 girl in any order in a family with 8 children is 8 / 2^8 = 1 / 128.

PLEASE PLEASE PLEASE HELP ME WITH ALGEBRA 1 PLEASE!?!?!?!?!!!?!?!?!?!?! I WILL GIVE LOTS OF POINTS AND BRAINLEST PLEEEEEEEEEEEEEEEEASE!!?!?!?!?!?!!?!?!?!?

What are the different ways you can solve a system of linear equations in two variables? What is the process for solving a system using each method?

Answers

Im actually learning this myself atm, The three methods most commonly used to solve systems of equation are substitution, elimination and augmented matrices. Substitution is a method of solving systems of equations by removing all but one of the variables in one of the equations and then solving that equation. Elimination is another way to solve systems of equations by rewriting one of the equations in terms of only one variable. The elimination method achieves this by adding or subtracting equations from each other in order to cancel out one of the variables. Augmented matrices can also be used to solve systems of equations. The augmented matrix consists of rows for each equation, columns for each variable, and an augmented column that contains the constant term on the other side of the equation. For example, the augmented matrix for the system of equations 2x + y = 4, 2x - y = 0 is [[2 1], [2 -1]...[4, 0]], Good luck!

Hey mate

It is
________________________________
[tex]2x + y = 4, 2x - y = 0 is [[2 1], [2 -1] [4, 0][/tex]

Hope I helped have a good day

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