A teacher teaches two classes with 8 students each. Each student has a 95% chance of passing their class independent of the other students. Find the probability that, in exactly one of the two classes, all 8 students pass.

Answer:

m = [tex]\frac{2K}{v^2}[/tex]

Step-by-step explanation:

Given mass (m ) varies directly as K and inversely as v² then the equation relating them is

m = [tex]\frac{kK}{v^2}[/tex] ← k is the constant of variation

To find k use the condition m = 10 when K = 80 and v = 4 , then

10 = [tex]\frac{80k}{4^2}[/tex] = [tex]\frac{80k}{16}[/tex] ( multiply both sides by 16 to clear the fraction )

160 = 80k ( divide both sides by 80 )

2 = k

m = [tex]\frac{2K}{v^2}[/tex] ← equation of variation

The expression of mass as a function of kinetic energy and velocity is m = 2K/V².

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

We have been given that the mass varies directly as the Kinetic energy (K) and inversely as the square of the velocity (V).

m ∝ K/V²

m = cK/V²

Here c is the constant of variation,

If the kinetic energy is 80 Joules and the velocity is 4 meters per second, then the mass is 10 kilograms.

We have to determine the value of c

Here m = 10 , K = 80 and V = 4 , then

Substitute the values in m =  cK/V²

10 = c(80)/4²

10 = c(80)/16

10 = 5c

c = 10/5

c = 2

Substitute the value of c = 2 in the equation of variation,

⇒ m = 2K/V²

Hence, the expression of mass as a function of kinetic energy and velocity is m = 2K/V².

Learn more about the expressions here:

brainly.com/question/13947055

#SPJ2

Answer:

B) 36

BA=CD

BA=9

AREA OF TRIANGLE ABC=1/2×b×h

63=1/2×b×9

126=b×9

b=14

BC=14

AD=BC

AE+ED=BC

AE=BC-ED

AE=14-6

AE=8

AREA OF TRIANGLE ACE= 1/2×AE×CD

= 1/2×8×9

=36

Answer:

48degrees

Step-by-step explanation:

From the circle geometry shown, traingle BDC is an isosceles triangle which shows means that their base angels are the same. Hence;

<B = <C

<CBD + <BCD + <D = 180

<BCD + <BCD + <D =180

2<BCD + <BDC = 180

Get <BCD;

<BCD+ <ECB = 90

<BCD + 48 = 90

<BCD = 90 - 48

<BCD = 42degrees

Get <BDC

2<BCD + <BDC = 180

2(42)+ <BDC = 180

84 + <BDC = 180

<BDC = 180 - 84

<BDC = 96

Since angle at the centre is twice that at the circumference, then;

<BAC = 1/2(<BDC )

<BAC = 96/2

<BAC = 48degrees

Answer:

108 meters squared or m^2

Step-by-step explanation:

* means multiply

15 is probably hypotenuse because its the longest

12 and 9 are probably base and height

area = base * height

area = 12 * 9

area = 108

Answer:

54m^2

Step-by-step explanation:

Step-by-step explanation:

Measure the width, length and height of the shipping box in inches. Multiply the width, length and height of the box to calculate its volume in cubic inches. For example, if the box is 20 inches wide, 24 inches long and 16 inches high, then the volume is (20)(24)(16) = 7,680 cubic

Answer:

The volume of the shipping box would be 36 9/16

Step-by-step explanation:

One method to find the volume of the shipping box would be (l)(w)(h)

one we plug in our dimensions the equation would become 3 1/4 x 3 x 3 3/4

To simplify this we would first

Multiply

3 1/4 x 3 x 3 3/4 = 39/4 x 3 3/4

The bolded parts are the pieces we are working on

3 1/4 as an improper fraction is 13/4

13/4 x 3 = 13 x 3/4 = 39/4

- The second step would be to

Convert the mixed number to an improper fraction.

3 3/4  = ( 3 × 4 ) / 4 + 3/4 = 12 + 3 / 4 = 15/4

Now we have to Multiply

39/4 x 15/4 =  39 x 15 / 4 x 4 = 585/16

Lastly, we have to simplify

585/16 = 36 9/16

Answer:

x/8

Step-by-step explanation:

First, we are given "the quotient of...". This means that we are dividing something/something else. If two numbers are given in the phrase "something and something else", the first number given will be the something, and the second number will be the something else.

The first number listed is x. Therefore, we have

x/something else.

Next, we are given "and 8", so we have x/8 as our expression

The length of the confidence interval is the margin of error, which is the ratio of the standard deviation and the square root of sample size. Hence, to reduce the length of confidence interval by half, Quadruple the sample size.

Recall :

Evaluating an hypothetical scenario :

Let standard deviation, σ = 2

Sample size = 50

Margin of Error = 2/√50 = 0.554

Using Quadruple of the sample size : (50 × 4) = 200 samples

(0.227 ÷ 0.554) = 0.5

Therefore, increasing the sample size, reduces the margin of error. Hence, using quadruple the sample size, will reduce the margin of error by half.

Learn more : https://brainly.com/question/13403969

Answer:

Step-by-step explanation:

Slope of line through (0,-1) and (1,2) = (-1 - 2)/(0 - 1) = 3

Point-slope equation for line of slope 3 that passes through (0,-1):

y+1 = 3(x-0)

When x = 2:

y+1 = 3(2-0)

y = 3·2 - 1 = 5

When x = 3:

y+1 = 3(3-0)

y = 3·3-1 = 8

9514 1404 393

Answer:

Step-by-step explanation:

The equations can be written in factored form and vertex form to see the x-intercepts, axis of symmetry, and extreme value.

The y-intercept is the constant in the equation in standard form.

The axis of symmetry is the vertical line through the vertex.

__

f(x) = x² -2x -8 = (x -4)(x +2) = (x -1)² -9

  x-intercept (-2, 0), y-intercept (0, -8), axis of symmetry x = 1

__

g(x) = x² +6x +8 = (x +2)(x +4) = (x +3)² -1

  x-intercept (-2, 0), y-intercept (0, 8), minimum value -1

__

h(x) = -x² +2x = -(x)(x -2) = -(x -1)² +1

  axis of symmetry x = 1

_____

Additional comment

We have only listed the intercepts, axis, and extreme where the values match a label.

Answer:

Region C

Step-by-step explanation:

y ≤ ¼ x + 3 maps the areas C and D including the common boundary line

y ≥ -x + 5 maps the areas B and C including the common boundary line

The common area mapped is C plus its boundaries

Answer:

$.08 per mile

Step-by-step explanation:

$2.25          gallon

------------ * ---------------

gallon          28 miles

$2.25

-------------

28 miles

$.080357143 per mile

Rounding to the nearest cent

$.08 per mile

Answer:

48 NO seña hfjxsmisns sisbxbd

Step-by-step explanation:

Answer:

ask in English then I can help u

Answer:

6 (-5 + 6x)

Step-by-step explanation:

Rewrite the number 30 as 6×5 and 36 as 6×6

Factor out the common number, which is 6

so, 6 (-5 + 6x)

Answer:

-6(5-6x).

Just factor out -6 from the expression. Thank you!

Answer:

[tex]\cos(11x)[/tex]

Step-by-step explanation:

Given

[tex]\cos 5x\ \cos 6x- \sin\ 5x \sin 6x[/tex]

Required

Express as a single function

In trigonometry, we have:

[tex]\cos(A + B) = \cos A\cos B - \sin A \sin B[/tex]

By comparison, we have

[tex]\cos(5x + 6x) = \cos 5x\cos 6x - \sin 5x \sin 6x[/tex]

[tex]\cos(11x) = \cos 5x\cos 6x - \sin 5x \sin 6x[/tex]

9514 1404 393

Answer:

  4.8 years

Step-by-step explanation:

Solving the compound interest formula for the number of years gives ...

  t = log(A/P)/(n·log(1 +r/n))

where principal P invested at rate r compounded n times per year produces value A after t years.

  t = log(24805/22000)/(365·log(1 +0.025/365)) ≈ 4.800

The loan was for 4.8 years.

This is a relative frequency question. Applying the concept, we get that the relative frequency of gluten free breads sold at store A compared to those sold at all stores combined is 0.1667.

Relative frequency:

The relative frequency of a to b is given by a divided by b.

In this question:

a: Gluten free breads sold at store A

b: Gluten free breads sold at all stores combined.

2 + 7 + 3 = 12 gluten free breads sold.

2 sold at store A, so:

[tex]\frac{2}{12} = \frac{1}{6} = 0.1667[/tex]

Thus, the relative frequency of gluten free breads sold at store A compared to those sold at all stores combined is 0.1667.

Another example of a problem involving relative frequency you can check at https://brainly.com/question/20630951

Relative Frequency:

The relative frequency of gluten-free breads sold at Store A compared to those sold at all the stores combined is:

= 0.167

Data and Calculations:

Gluten-Free Breads at Different Stores

                           Gluten-Free         Not Gluten-

                               Breads            Free Breads

Store A                        2                          4

Store B                        7                         10

Store C                       3                         12

Since we are only considering Gluten-Free Breads at the three stores, we take the relevant data to calculate and compare their frequencies as follows:

                           Gluten-Free        Relative

                               Breads         Frequency

Store A                        2                0.167 (2/12) = 17%

Store B                        7                0.583 (7/12) = 58%

Store C                       3                0.250 (3/12) = 25%

Total Gluten-free     12                 1 = 100%

Thus, the relative frequency of gluten-free breads sold at Store A compared to those sold at all the stores combined is 0.167.

Answer:

H1 : μ ≠ 20000

Step-by-step explanation:

Given that :

Population mean salary, μ = 20,000

To test if mean salary is more or less Than population mean salary, μ, this means we are testing if the mean salary is different from 20,000

Hence, the hypothesis :

Null, H0 : The mean salary is 20000

Alternative, H1 : The mean salary is not 20000

Using notation :

H0 : μ = 20000

H1 : μ ≠ 20000

Hence, alternative hypothesis is : H1 : μ ≠ 20000

Answer:

[tex]A). \ \ \frac{(72\pi + 9\pi )}{4} \ in^2[/tex]

Step-by-step explanation:

Given;

radius of the circle, r = 9 inches

the part of the circle cut out = one-forth of the complete circle

the angle of the sector cut out θ= ¹/₄ x 360 = 90⁰

Area of the complete circle = πr² = π x 9² = 81π in²

Area of the sector cut out = [tex]= \frac{\theta }{360} \pi r^2 = \frac{90}{360} \pi (9^2) = \frac{1}{4} \times 81\pi = \frac{81 \pi}{4} = \frac{(72\pi + 9\pi)}{4} \ in^2[/tex]

Therefore, the only correct option is A. [tex]\frac{(72\pi + 9\pi )}{4} \ in^2[/tex]

Answer:

the answer would be 100,000,000

Greatest 8 Digit Number: 99,999,999

Adding 1 = 99999999+1

= 100,000,000

Must click thanks and mark brainliest

z = 3i / (-1 - i )

z = 3i / (-1 - i ) × (-1 + i ) / (-1 + i )

z = (3i × (-1 + i )) / ((-1)² - i ²)

z = (-3i + 3i ²) / ((-1)² - i ²)

z = (-3 - 3i ) / (1 - (-1))

z = (-3 - 3i ) / 2

Note that this number lies in the third quadrant of the complex plane, where both Re(z) and Im(z) are negative. But arctan only returns angles between -π/2 and π/2. So we have

arg(z) = arctan((-3/2)/(-3/2)) - π

arg(z) = arctan(1) - π

arg(z) = π/4 - π

arg(z) = -3π/4

where I'm taking arg(z) to have a range of -π < arg(z) ≤ π.

9514 1404 393

Answer:

  (a)  {(5, 2), (-4, 2), (3, 6), (0, 4), (-1, 2)}

Step-by-step explanation:

The only relation with no repeated x-values is the first one. The first relation is a function.

Answer:

The final price of the textbook rounded to the nearest dollar is $167

Step-by-step explanation:

To solve this problem, we need to find out what 13.5% of $147 equals.

13.5% = 0.135

0.135 x $147 = $19.845

$147 + 19.845 = 166.845

Round to the nearest dollar to get $167

Find the sale price by multiplying the original price by 70% then add the two prices together to get the total.

799 x 0.70 = 559.30

549 x 0.70 = 384.30

Total: 559.30 + 384.30 = $943.60

hope it helps

please mark Brainliest