Which option is correct and how would one solve for it?

The question is incomplete. Here is the complete question.

In a recent year, the socres for the reading portion of a test were normally distributed, with a mean of 23.3 and a standard deviation of 6.4. Complete parts (a) through (d) below.

(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 18. (Round to 4 decimal places as needed.)

(b) Find a probability that a random selected high school student who took the reading portion of the test has a score that is between 19.9 and 26.7.

(c) Find a probability that a random selected high school student who took the reading portion of the test ahs a score that is more than 36.4.

(d) Identify any unusual events. Explain your reasoning.

Answer: (a) P(X<18) = 0.2033

              (b) P(19.9<X<26.7) = 0.4505

              (c) P(X>36.4) = 0.0202

               (d) Unusual event: P(X>36.4)

Step-by-step explanation: First, determine the z-score by calculating:

[tex]z = \frac{x-\mu}{\sigma}[/tex]

Then, use z-score table to determine the values.

(a) x = 18

[tex]z = \frac{18-23.3}{6.4}[/tex]

z = -0.83

P(X<18) = P(z< -0.83)

P(X<18) = 0.2033

(b) x=19.9 and x=26.7

[tex]z = \frac{19.9-23.3}{6.4}[/tex]

z = -0.67

[tex]z = \frac{26.7-23.3}{6.4}[/tex]

z = 0.53

P(19.9<X<26.7) = P(z<0.53) - P(z< -0.67)

P(19.9<X<26.7) = 0.7019 - 0.2514

P(19.9<X<26.7) = 0.4505

(c) x=36.4

[tex]z = \frac{36.4-23.3}{6.4}[/tex]

z = 2.05

P(X>36.4) = P(z>2.05) = 1 - P(z<2.05)

P(X>36.4) = 1 - 0.9798

P(X>36.4) = 0.0202

(d) Events are unusual if probability is less than 5% or 0.05. So, part (c) has an unusual event.

The probability will be:

(a) 0.2038

(b) 0.4046

(c) 0.0203

(d) Event in part (c) is unusual.

According to the question,

Let,

(a)

The z-score for X=18 will be:

→ [tex]z = \frac{X- \mu}{\sigma}[/tex]

      [tex]= \frac{18-23.3}{6.4}[/tex]

      [tex]= -0.828[/tex]

So,

The probability will be:

→ [tex]P(X<18) = P(z < -0.828)[/tex]

                     [tex]= 0.2038[/tex]

(b)

The z-score for X=19.9 will be:

→ [tex]z = \frac{X -\mu}{\sigma}[/tex]

     [tex]= \frac{19.9-23.3}{6.4}[/tex]

     [tex]= -0.531[/tex]

The z-score for X=26.7 will be:

→ [tex]z = \frac{X -\mu}{\sigma}[/tex]

      [tex]= \frac{26.7-23.3}{6.4}[/tex]

      [tex]= 0.531[/tex]

So,

The probability will be:

→ [tex]P(19.9 < X< 23.3) = P(-0.531 < z< 0.531)[/tex]

                                   [tex]= 0.4046[/tex]

(c)

The z-score for X=36.4 will be:

→ [tex]z = \frac{X -\mu}{\sigma}[/tex]

     [tex]= \frac{36.4-23.3}{6.4}[/tex]

     [tex]= 2.047[/tex]

So,

The probability will be:

→ [tex]P(X > 36.4 )= P(z > 2.047)[/tex]

                       [tex]= 0.0203[/tex]

(d)

Just because it's probability value is less than 0.05, so that the events is "part c" is unusual.

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(a) The average value of f(x) on the closed interval [0, π] is

[tex]\displaystyle\frac1{\pi-0}\int_0^\pi f(x)\,\mathrm dx = \frac1\pi\int_0^\pi(8\sin(x)-4\sin(2x))\,\mathrm dx = \boxed{\frac{16}\pi}[/tex]

(b) By the mean value theorem, there is some c in the open interval (0, π) such that f(c) = 16/π. Solve for c :

8 sin(c) - 4 sin(2c) = 16/π

8 sin(c) - 8 sin(c) cos(c) = 16/π

sin(c) - sin(c) cos(c) = 2/π

Use a calculator to solve this. You should get two solutions, c ≈ 1.2382 and c ≈ 2.8081.

Answer:

(D) 48​

Step-by-step explanation:

Let English book = x

Let french book = y

In 1995 x= 10

Y= 7

In 1996

Y = 2x

Total book read in the two years

0.6(Total) = y

0.4(total) = x

We don't know the exact amount of books read in 1996.

Total = 10 + 7 +x +2x

Total = 17+3x

0.6(total) = 7+2x

0.6(17+3x) = 7+2x

10.2 +1.8x= 7+2x

10.2-7= 2x-1.8x

3.2= 0.2x

3.2/0.2= x

16= x

So she read 16 English book

And 16*2 = 32 french book Making it a total of 16+32= 48 books in 1996

Answer:

40.63

Step-by-step explanation:

31.25+9.38= 40.63

Hope this helps

Answer: 40.63

Look at the image for shown work.

Answer:

a

   [tex]\= x = 18.5[/tex]  ,  [tex]\sigma = 5.15[/tex]

b

 [tex]15.505 < \mu < 21.495[/tex]

c

 [tex]14.93 < \mu < 22.069[/tex]

Step-by-step explanation:

From the question we are are told that

    The  sample data is  21, 14, 13, 24, 17, 22, 25, 12

     The sample size is  n  = 8

Generally the ample mean is evaluated as

        [tex]\= x = \frac{\sum x }{n}[/tex]

        [tex]\= x = \frac{ 21 + 14 + 13 + 24 + 17 + 22+ 25 + 12 }{8}[/tex]

         [tex]\= x = 18.5[/tex]

Generally the standard deviation is mathematically evaluated as

         [tex]\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}[/tex]

[tex]\sigma = \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}[/tex]

[tex]\sigma = 5.15[/tex]

considering part b

Given that the confidence level is  90% then the significance level is evaluated as

         [tex]\alpha = 100-90[/tex]

         [tex]\alpha = 10\%[/tex]

         [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex]  from the normal distribution table the value is  

     [tex]Z_{\frac{ \alpha }{2} } = 1.645[/tex]

The margin of error is mathematically represented as

      [tex]E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

=>    [tex]E =1.645 * \frac{5.15 }{\sqrt{8} }[/tex]

=>     [tex]E = 2.995[/tex]

The 90% confidence interval is evaluated as

       [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

       [tex]18.5 - 2.995 < \mu < 18.5 + 2.995[/tex]

       [tex]15.505 < \mu < 21.495[/tex]

considering part c

Given that the confidence level is  95% then the significance level is evaluated as

         [tex]\alpha = 100-95[/tex]

         [tex]\alpha = 5\%[/tex]

         [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex]  from the normal distribution table the value is  

     [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

The margin of error is mathematically represented as

      [tex]E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

=>    [tex]E =1.96 * \frac{5.15 }{\sqrt{8} }[/tex]

=>     [tex]E = 3.569[/tex]

The 95% confidence interval is evaluated as

       [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

       [tex]18.5 - 3.569 < \mu < 18.5 + 3.569[/tex]

       [tex]14.93 < \mu < 22.069[/tex]

Answer:

15/22

Step-by-step explanation:

Of the 66 students who have no chores, 45 have a curfew.  So the probability is 45/66 = 15/22.

Answer:

x and y can have many values

Step-by-step explanation:

-24x - 12y = -16

Then: 24x + 12y = 16

We know: 6x + 3y = 4

X and Y can have a lot of valoues.

6x + 3y = 4

3 ( 2x + y) = 4

2x + y= 4/3

2x+y= 1.333...

Answer:

8 pounds of cheaper candy,

17.5 pounds of expensive candy

Step-by-step explanation:

Let's define some variables. Let's say the amount of pounds of candy that sells for $2.20/lb is x, and the $7.30 is y. Now we can write some equations!

x + y = 25.5

[tex]\frac{2.2x + 7.3y}{25.5} = 5.7[/tex]

We can start substitution. We can say that x = 25.5 - y. Plugging this into our second equation, we get:

y = 17.5

Plugging this in, we find that:

x = 8.

Answer:

±7 sqrt(2) = x

Step-by-step explanation:

98 - x^2 = 0

Add x^2 to each side

98 =x^2

Take the square root of each side

±sqrt(98) = sqrt(x^2)

±sqrt(49*2) = x

±7 sqrt(2) = x

Answer:

[tex]\huge \boxed{{x = \pm 7\sqrt{2} }}[/tex]

Step-by-step explanation:

[tex]98-x^2 =0[/tex]

[tex]\sf Add \ x^2 \ to \ both \ sides.[/tex]

[tex]98=x^2[/tex]

[tex]\sf Take \ the \ square \ root \ of \ both \ sides.[/tex]

[tex]\pm \sqrt{98} =x[/tex]

[tex]\sf Simplify \ radical.[/tex]

[tex]\pm \sqrt{49} \sqrt{2} =x[/tex]

[tex]\pm 7\sqrt{2} =x[/tex]

[tex]\sf Switch \ sides.[/tex]

[tex]x= \pm 7\sqrt{2}[/tex]

Answer: The cube with side length of 12cm is alone in one plate, the other 3 cubes are in the other plate.

Step-by-step explanation:

We have 4 cubes with side lengths of:

6cm, 8cm, 10cm and 12cm.

Now, some things you need to know:

If we want a scale to be balanced, then the mass in both plates must be the same.

The volume of a cube of side length L is:

V = L^3

And the mass of an object of density D, and volume V is:

M = D*V.

As all the cubes are of the same material, all of them have the same density, so the fact that we do not know the value of D actually does not matter here.

Then we want to forms two groups of cubes in such a way that the total volume in each plate is the same (or about the same), the volumes of the cubes are:

Cube of 6cm:

V = (6cm)^3 = 216cm^3

Cube of 8cm:

V = (8cm)^3 = 512cm^3

Cube of 10cm:

V = (10cm)^3 = 1000cm^3

cube of 12cm

V = (12cm)^3 =  1728cm^3

First, if we add the volumes of the first two cubes, we have:

V1 = 216cm^3 + 512cm^3 = 728cm^3

Now we can see that we add 1000cm^3 the volume will be equal to the volume of the larger cube, so here we can also add the cube with side length of 10cm

Then the volume of the 3 smaller cubes together is:

V1 = 216cm^3 + 512cm^3 + 1000cm^3 = 1728cm^3.

Then, if we want to have the same volume in each plate, then we need to have the 3 smaller cubes in one plate, and the larger cube in the other plate.

Answer:

204

Step-by-step explanation:

To simplify the shape, you can do multiple things. I've opted to shave down both prongs to take it from a 'T' shape to a rectangular prism.

For height of the prongs, take 4 from 6.

6 - 4 = 2

Divide by 2 as there are 2 prongs.

2 / 2 = 1

Remember L * W * H

6 * 3 * 1 = 18

Remember that there are two prongs!

3 + 4 = 7

6 * 7 * 4 = 168

168 + 2(18) = 204

Answer:

b ≈ 9.2

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

b² = a² + c² = 6² +7² = 36 + 49 = 85 ( take the square root of both sides )

b = [tex]\sqrt{85}[/tex] ≈ 9.2 ( to the nearest tenth )

Answer:

9.22

Step-by-step explanation:

Since it's a 90° triangle [tex]c^{2} =a^{2} +b^{2}[/tex].

In this example they labeled the hypotenuse as b instead of c are equation is still the same just put the correct variables in the right places.

[tex]b = \sqrt{6^{2} +7^{2} }[/tex]

b = 9.22

Answer:

0.9995

Step-by-step explanation:

10% = 0.10

1 - 0.10 = 0.9

n = number of light bulbs = 7

we calculate this using binomial distribution.

p(x) = nCx × p^x(1-p)^n-x

our question says at most 4 is defective

= (7C0 × 0.1⁰ × 0.9⁷) + (7C1 × 0.1¹ × 0.9⁶) + (7C2 × 0.1² × 0.9⁵) + (7C3 × 0.1³ × 0.9⁴) + (7C4 × 0.1⁴ × 0.9³)

= 0.478 + 0.372 + 0.1239 + 0.023 + 0.0026

= 0.9995

we have 0.9995 probability that at most 4 light bulbs are defective.

Answer:

The area of ΔABC= 6.667 square units

Step-by-step explanation:

ΔABC is similar to ΔMNO.

The scale factor from ΔMNO to ΔABC is 3∕2

the area of ΔMNO is 10 square units,

The area of ΔABC/the area of ΔMNO

= 2/3

The area of ΔABC/10= 2/3

The area of ΔABC= 2/3 * 10

The area of ΔABC= 20/3

The area of ΔABC= 6 2/3

The area of ΔABC= 6.667 square units

Answer:

22.5 square units

Step-by-step explanation:

i multiplied 10 by 2 to get 20 and went with the closest answer and got it right.

i dont know how to do math but i guess it worked

Answer:

The total   profit is [tex]p = 17x + 2124[/tex]

Step-by-step explanation:

From the question we are told that

   The profit made on each mp3 is  k  =  $35

    The profit made on each mp3 is  y =  $18

     The total amount sold is   n  =  118

 Now given that the amount of mp3 sold is x then the amount of  DVD sold is mathematically evaluated as

                      [tex]n - x[/tex]

Now the profit made on the x number of mp3 sold is  

                      [tex]x * 35 = 3x[/tex]

And the the profit made from the n-x number of  DVD  sold is  18 (n-x ) =  18 - 18x

 So the total profit made last week from the sales of both mp3 and DVD  is  

                   [tex]p = 35x + 18n - 18x[/tex]

                    [tex]p = 17x + 18(118)[/tex]

                    [tex]p = 17x + 2124[/tex]

Answer:

[tex]a_n = 8 + (n - 1) (-6)[/tex]

Step-by-step explanation:

Given

[tex]a_1 = 8[/tex]

Recursive: [tex]a_{n} = a_{n-1} - 6[/tex]

Required

Determine the formula

Substitute 2 for n to determine [tex]a_2[/tex]

[tex]a_{2} = a_{2-1} - 6[/tex]

[tex]a_{2} = a_{1} - 6[/tex]

Substitute [tex]a_1 = 8[/tex]

[tex]a_2 = 8 - 6[/tex]

[tex]a_2 = 2[/tex]

Next is to determine the common difference, d;

[tex]d = a_2 - a_1[/tex]

[tex]d = 2 - 8[/tex]

[tex]d = -6[/tex]

The nth term of an arithmetic sequence is calculated as

[tex]a_n = a_1 + (n - 1)d[/tex]

Substitute [tex]a_1 = 8[/tex] and [tex]d = -6[/tex]

[tex]a_n = a_1 + (n - 1)d[/tex]

[tex]a_n = 8 + (n - 1) (-6)[/tex]

Hence, the nth term of the sequence can be calculated using[tex]a_n = 8 + (n - 1) (-6)[/tex]

Hey  There!

Answer:

Step-by-step explanation:

HCF

If HCF is  ''9'' that means that ''9'' is the divisible of two numbers.

So 18 and 19 can be divided by 9 and that's the highest divisible for both factors.

And always remeber the answer is a ''Prime factor.''

LCM

If LCM is ''3'' that means ''3'' is the lowest common multiple out of  two numbers.

Hope this helps!

Have a nice Day!:)

Answer:

C. $37.76

Step-by-step explanation:

30% of $49.95

=30/100×49.95

=$14.99

selling price = 49.95 -14.99

= $34.96

8% sales tax included

=8/100×34.96

=$2.80

new price= 34.96+2.80

=$37.76

Answer:

work is pictured and shown

Answer:

D) 9 cm

Step-by-step explanation:

EDGE 2020

(D) 9 cm.

Therefore, the correct answer is (D) 9 cm.

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Answer:

C = 2pie(r)

r= d/2= 13/2= 6.5

C = 2*3.14*6.5

C= 41

Step-by-step explanation:

Answer:

a. Quadratic--[tex]y=x^{2}[/tex]

b. Absolute Value--[tex]y=|x|[/tex]

c. Linear--[tex]y=x[/tex]

d. Reciprocal Squared--[tex]y=\frac{1}{x^{2} }[/tex]

e. Cubic--[tex]y=x^{3}[/tex]

f. Square Root--[tex]y=\sqrt{x}[/tex]

g. Reciprocal--[tex]y=\frac{1}{x}[/tex]

h. Cube root--[tex]y=\sqrt[3]{x}[/tex]

Answer:

Step-by-step explanation:

y=[tex]x^{2}[/tex] is quadratic

y=x  is an absolute value

y= |x| os linear

y= [tex]\frac{1}{x}[/tex] is reciprocal

y= [tex]x^{3}[/tex] is cubic

y= [tex]\sqrt{x}[/tex] is square root

y= [tex]\frac{1}{x^{2} }[/tex] is reciprocal squared

y= [tex]\sqrt[3]{x}[/tex] is cube root

Answer:

A) C = 1/96

B) P(x<=1, y<=1) = 1/128 or 0.0078125 to 7 places

C) P(x+y<=1) = 5/2305, or 0.0021701 to 7 places

Step-by-step explanation:

f(x,y) = C x (1+y)

A)

To find C, we need to integrate the volume under region bound by

0 <= x <= 4, and

0 <= y <= 4

This volume equals 1.0.

Find integral,

int( int(f(x,y),x=0,4), y = 0,4) = 96C

therefore C = 1/96

or

F(x,y) = x (1+y) / 96  ............................(1)

B)

P(x<=1, y<=1)

Repeat the integral, substitute the appropriate limits,

P = int( int(F(x,y),x=0,1), y = 0,1)

= 1/128 or 0.0078125

P(x<=1, y<=1) = 1/128 or 0.0078125 to 7 places

C)

P(x+y<=1)

From the function, we know that this is going to be less than one half of the probability in (B), closer to 1/4 of the previous.

It will be again a double integral, as follows:

P = int( int(F(x,y),x=0,1-y), y = 0,1)

= 5/2304

= 0.0021701 (to 7 decimals)

P(x+y<=1) = 5/2305, or 0.0021701 to 7 places

Answer:

Multiply/divide both sides by the same non-zero constant

Step-by-step explanation:

5x = 20

Divide each side by 5

5x/5 = 20/5

x = 4

To obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"

Given the equations :

To obtain the value ; x = 4 from A

Here, the constant value which can be used is 5 in other to isolate 'x'

5x/5 = 20/5

x = 4

Therefore, to obtain (B) from (A) "Multiply/divide both sides by the same non-zero constant"

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Answer:

13/6

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

   = (6 - -7)/(1 - -5)

   = ( 6+7)/ (1+ 5)

   = 13/6

Answer:

∠A and ∠G is the pair of vertical angles.

Step-by-step explanation:

From the figure attached,

Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.

Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."

Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ≅ ∠F are the vertical angles.

From the given options,

∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.

Answer:

a

Step-by-step explanation:

Answer:

C° = 71.6056

Step-by-step explanation:

Law of Cosines: c² = a² + b² - 2abcosC°

Step 1: Plug in known variables

29² = 30² + 15² - 2(30)(15)cosC°

Step 2: Evaluate

841 = 900 + 225 - 900cosC°

-59 = 225 - 900cosC°

-284 = -900cosC°

71/225 = cosC°

cos⁻¹(71/225) = C°

C° = 71.6056

And we have our answer!

Answer:

  79.0°

Step-by-step explanation:

The Law of Cosines is used for this purpose. It tells you ...

  a² = b² +c² -2bc·cos(A)

Solving for A gives ...

  cos(A) = (b² +c² -a²)/(2bc) = (15² +29²-30²)/(2(15)(29)) = 166/870

Using the inverse cosine function, we find the angle to be ...

  A = arccos(166/870) ≈ 79.00026°

  A ≈ 79.0°

Answer:

[tex]g(x) = 0.5^{(x+3)}[/tex]

Step-by-step explanation:

Assuming f(x) = [tex]0.5^{x}[/tex] is a correct interpretation of f(x),

the way to translate three units to the left is to change x to x+3.  This gives our answer:   [tex]g(x) = 0.5^{(x+3)}[/tex]

Answer:

B. g(x) = (1/2)⁽ˣ⁺³⁾

Hope this helps!

Step-by-step explanation:

Answer:

3^x( 2-3^x)

Step-by-step explanation:

f(x) = 3^x and g(x) = 3^2x - 3^x

h(x) = f(x) - g(x)

       3^x - ( 3^2x - 3^x)

Distribute the minus sign

         3^x - 3^2x + 3^x

     2 * 3^x - 3 ^ 2x

Rewriting

We know that 3^2x = 3^x * 3^x

2 * 3^x - 3^x* 3^x

Factoring out 3^x

3^x( 2-3^x)