The scores for a particular examination are normally distributed with a mean of 68.5% and a standard deviation of 8.2%. What is the probability that a student who wrote the examination had a mark between 80% and 100%? Give your answer to the nearest hundredth.

Answer:

12

Step-by-step explanation:

Given the data :

X : 10,8,18,17,7

The mean value of scores obtained can be obtained thus :

Mean = ΣX / n

n = sample size = 5

Mean = ΣX / n = (10+8+18+17+7) / 5

Mean = 60 / 5 = 12

[tex]\\ \sf\longmapsto 112^2[/tex]

[tex]\\ \sf\longmapsto (100+12)^2[/tex]

[tex]\\ \sf\longmapsto 100^2+2(100)(12)+12^2[/tex]

[tex]\\ \sf\longmapsto 10000+2400+144[/tex]

[tex]\\ \sf\longmapsto 12400+144[/tex]

[tex]\\ \sf\longmapsto 12544[/tex]

112²

(a + b)² = (a² + 2ab + b²)

⇛112²

⇛(100 + 12)²

⇛(100)² + 2 × 100 × 12 + (12)²

⇛10000 + 2400 + 144

⇛12400 + 144

⇛12544

Answer:

750,. is answer

I hope it helps

If the scale factor is 30, then all you have to do is multiply each measurement by the scale factor. In this case, 4 · 30 = 120.

These are variables on your graph

Answer:

0.05x + 0.1(55 - x) = 3.9

Step-by-step explanation:

There are 55 coins.

Let x = number of nickels.

The number of dimes is 55 - x.

The value of a nickel is $0.05, and the value of a dime is $0.10.

The value of x nickels is 0.05x

The value of 55 - x dimes is 0.1(55 - x)

The total value of the coins is 0.05x + 0.1(55 - x)

The total value of the coins is $3.90

0.05x + 0.1(55 - x) = 3.9

Answer:

15 cm

Step-by-step explanation:

Since the traingles are similar, we can find the ratio between the side lengths, and it will be the same for each side.

We can use the side length 9 and 15 to find this ratio. 15/9=5/3. So, the ratio of a side length of the larger triangle to the smaller one is 5/3, so our equation becomes 5/3 = 25/x. Use any method you like to find that x=15.

Hope this helped,

~cloud

9514 1404 393

Answer:

  d) 10.38%

Step-by-step explanation:

The multiplier for four quarters of quarterly compounding is ...

  (1 +10%/4)^4 = 1.025^4 = 1.103812890625

This is about 1 + 10.38%.

The effective rate of interest is about 10.38% per annum.

9514 1404 393

Answer:

  a. Definition of bisector.

Step-by-step explanation:

Line l is a line through the midpoint M. We can conclude it is a bisector, because, by definition, a bisector is a line through the midpoint.

The conclusion is justified by the definition of a bisector.

Answer:

115

Step-by-step explanation:

You divide 230 by 2 cause there are two peoples. I hope that helps :)

Answer:

$147

Step-by-step explanation:

0.15x = $22.05

Divide both sides by 15

22.05/0.15 = $147

Answer:

15.534% decrease

Step-by-step explanation:

Find the new number of boys and girls on the honor roll:

56(0.75) = 42 boys

150(0.88) = 132 girls

Find the new total number of students on the honor roll:

42 + 132 = 174

Find the percent decrease by dividing the difference in the number of students by the original number.

There were originally 206 total students on the honor roll. Find the difference:

206 - 174 = 32

Divide this by the original amount:

32/206

= 0.15534

So, the number of students on the honor roll decreased by approximately 15.534%

Answer:

D. Height

General Formulas and Concepts:

Geometry

Area of a Circle: A = πr²

Step-by-step explanation:

In order to find the area of a circle, we must follow the formula. Out of all the options given, height is not incorporated into the formula.

It wouldn't make sense to use height anyways since it would be 3-dimenional and we're talking 2-dimensional.

∴ our answer is D.

Answer:

No, because the ratio of pay to hours is not the same for each pair of value.

A stationary point at x = 3 means the derivative dy/dx = 0 at that point. Differentiating, we have

dy/dx = 6x ² + 2ax + b

and so when x = 3,

0 = 54 + 6a + b

or

6a + b = -54 … … … [eq1]

The curve passes through the point (4, 2), which is to say y = 2 when x = 4. So we also have

2 = 128 + 16a + 4b - 30

or

16a + 4b = -96

4a + b = -24 … … … [eq2]

Eliminate b by subtracting [eq2] from [eq1] and solve for a, then for b :

(6a + b) - (4a + b) = -54 - (-24)

2a = -30

a = -15   ===>   b = 96

Step-by-step explanation:

The graph clearly has a positive slope. So Answer D couldn't be correct. Next: the y-intercept of this line is (0, -2), so b in the formula y = mx÷ b must be -2.

Therefore the correct equation of this line is

y = x - 2 (choice a)

The null and alternate hypotheses are

H0 : u = 0.44  vs   Ha: u > 0.44

Null hypothesis: 44% of readers own a personal computer.

Alternate Hypothesis : greater than 44% of readers own a personal computer.

This is one tailed test and the critical region for this one tailed test for the significance level 0.1 is  Z >  ±1.28

The given values are

p1= 0.54 , p2= 0.44 ; q2= 1-p2= 0.56

Using z test

Z = p1-p2/√p2(1-p2)/n

Z= 0.54-0.44/ √0.44*0.56/200

z= =0.1/ 0.03509

z=  2.849

Since the calculated value of Z=  2.849 is greater than Z= 1.28  reject the null hypothesis therefore there is sufficient evidence to support the executive's claim.

Null hypothesis is rejected

There is sufficient evidence to support the executive's claim at 0.10 significance level.

https://brainly.com/question/2642983

Answer:

120

Step-by-step explanation:

720÷6

why?

becoz 6= 1+5

1 is the cosy of the chair

5 is the cost of the desk

Answer:

0 is the answer measure 1

Answer:

Farah: x

Ibtisam: x-3

Muna: 2(x-3) or 2x-6

Sum of all their ages: 4x-6

Step-by-step explanation:

Farah is x, so we don't need an expression for that.

Ibtisam is 3 years younger than Farah, which means that we need to subtract 3 from Farah, and that would be Ibtisam's age. x-3.

Muna is 2 TIMES Ibtisam's age, so we need to multiply whatever expression taht was used for Ibtisam by 2. Put brackets around the equation with 2 outside: 2(x-3). Solve and you get 4x-6

Now, you have all their ages in expression form, now you need to simplify by adding:

x+x+2x-6

We cannot simplify -6, so we put that aside. Add all the x's and you get 4x, insert the minus 6 at the end:

4x-6

Hope this helps!

--Applepi101

Answer:

a) X -3

b) 4x - 9

Step-by-step explanation:

a) Farah's age is X so Ibtisam will be X - 3 old since he is 3years younger than Farah

b) Farah is X years old

Ibtisam is X - 3 years old

Muna is 2(X -3) since she is 2 times older than Ibtisam.

the sum of Thier ages will be

X + X -3 + 2(x-3)

= 2x - 3 + 2x - 6

= 4x - 9

One mathematical idea I've always been curious about is "integration and derivation".

Integration is about assimilating different variables. Derivation is a mathematical process whereby a result is gotten from some initial assumptions.

Integration is used everyday in different aspects of our lives. For example, if a person is travelling from let's say point A to point B, the speed used by the person might vary but through integration, one can easily get the accurate speed.

Through the division of equations into smaller bits, once can use integration to get the answer that one seeks. Architect can use integration in building the right structures at the exact places where the structures fits.

Likewise derivatives can be used by businesses in assessing whether a profit or loss will be made for a particular transaction or sale of product.

You can read more on:

https://brainly.com/question/14295614

Answer:

opposite angles

Step-by-step explanation:

They are formed in the intersection of lines AD and BD.

Answer:

opposite angles

Step-by-step explanation:

they are formed in the intersection of lines AD and BD. two figures are called similar if they have same shape however have different size.

Answer:

[tex]-32^\frac{3}{5} = -8[/tex]

Step-by-step explanation:

Given

[tex]-32^\frac{3}{5}[/tex]

Required

The equivalent expression

We have:

[tex]-32^\frac{3}{5}[/tex]

Rewrite as:

[tex]-32^\frac{3}{5} = (-32)^\frac{3}{5}[/tex]

Expand

[tex]-32^\frac{3}{5} = (-2^5)^\frac{3}{5}[/tex]

Remove bracket

[tex]-32^\frac{3}{5} = -2^\frac{5*3}{5}[/tex]

[tex]-32^\frac{3}{5} = -2^3[/tex]

[tex]-32^\frac{3}{5} = -8[/tex]

Answer:

In the picture below.

Step-by-step explanation:

From the commenter and answer above, confirmed on edge 2022.

Answer:

3/4

Step-by-step explanation:

There are 13 hearts in a 52 deck.

52-13=39

39/52=3/4

The probability that you are not dealt a heart from the deck of cards is 3/4.

Probability determines the chances that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that you are not dealth with a heart = 1 - (number of hearts / total number of cards)

1 - 13/52 = 39/52 =  3/4

To learn more about probability, please check: https://brainly.com/question/13234031

Answer:

-(x+6) (x-8)

Step-by-step explanation:

-(x^2-2x-48)

two values the multiply to get 48 and the difference of those two numbers gives you -2.

6,-8

6 x -8 =-48

6-8=-2

In this case we factored out the negative so leave it outside

-(x+6) (x-8)

Answer:

-1(x-8)(x+6) is the answer just took the test

Step-by-step explanation:

9514 1404 393

Answer:

  B(8, 4)

Step-by-step explanation:

Reflection across the origin negates both coordinate values.

  (x, y) ⇒ (-x, -y) . . . . . reflection across the origin

  A(-8, -4) ⇒ B(8, 4)

Answer:

Hello,

P(B)=0.65

Step-by-step explanation:

If P(A+B) means P(A∪B)=0.93 then you may read below.

Let's say x=P(B)

A and B being independent, P(A∩B)=P(A)*P(B)=0.8*x

Since P(A∪B)=P(A)+P(x)-P(A∩B) ,

0.93=0.8+x-0.8*x

0.2*x=0.13

x=0.65

Answer:

Step-by-step explanation:

point est. 0.307824427

99% 2.58

Confidence Interval - "P" values  

(0.2914 , 0.3243 )  

Answer:

(a)

[tex]\begin{array}{cccccc}x & {1} & {3} & {4} & {6} & {12} \ \\ P(x) & {0.30} & {0.10} & {0.05} & {0.15} & {0.40} \ \end{array}[/tex]

(b)

[tex]P(3 \le x \le 6) = 0.30[/tex]

[tex]P(4 \le x)=0.60[/tex]

Step-by-step explanation:

Given

[tex]F(x) = \left[\begin{array}{ccc}0& x<1 &\\0.30&1 \le x<3 &\\0.40&3 \le x < 4& &0.45 &4 \le x<6 &\\0.60 & 6 \le x < 12 & & 1 & 12 \le x\end{array}\right[/tex]

Solving (a): The pmf

This means that we list out the probability of each value of x.

To do this, we simply subtract the current probability value from the next.

So, we have:

[tex]\begin{array}{cccccc}x & {1} & {3} & {4} & {6} & {12} \ \\ P(x) & {0.30} & {0.10} & {0.05} & {0.15} & {0.40} \ \end{array}[/tex]

The calculation is as follows:

[tex]0.30 - 0 = 0.30[/tex]

[tex]0.40 - 0.30 = 0.10[/tex]

[tex]0.45 - 0.40 = 0.05[/tex]

[tex]0.60 - 0.45 = 0.15[/tex]

[tex]1 - 0.60 = 0.40[/tex]

The x values are gotten by considering where the equality sign is in each range.

[tex]1 \le x < 3[/tex] means [tex]x = 1[/tex]

[tex]3 \le x < 4[/tex] means [tex]x = 3[/tex]

[tex]4 \le x < 6[/tex] means [tex]x=4[/tex]

[tex]6 \le x < 12[/tex] means [tex]x = 6[/tex]

[tex]12 \le x[/tex] means [tex]x = 12[/tex]

Solving (b):

[tex](i)\ P(3 \le x \le 6)[/tex]

This is calculated as:

[tex]P(3 \le x \le 6) = F(6) - F(3-)[/tex]

From the given function

[tex]F(6)= 0.60[/tex]

[tex]F(3-) = F(1) = 0.30[/tex]

So:

[tex]P(3 \le x \le 6) = 0.60 - 0.30[/tex]

[tex]P(3 \le x \le 6) = 0.30[/tex]

[tex](ii)\ P(4 \le x)[/tex]

This is calculated as:

[tex]P(4 \le x)=1 - F(4-)[/tex]

[tex]P(4 \le x)=1 - F(3)[/tex]

[tex]P(4 \le x)=1 - 0.40[/tex]

[tex]P(4 \le x)=0.60[/tex]