Please answer fast! :)

Please Answer Fast! :)

Answers

Answer 1

Answer:

D

Step-by-step explanation:

The fastest way to solve this probelm would be to plug in each x value into these equations untill it outputs the correct two y values.

When you plug 3 into equation D the entire right side it will become.

y-1=0

y=1, which is true.

When you plug 6 into that equation.

y-1=5

y=6 which is also true.

Answer 2

im sorry but the thing is i cant translate these words but the answer is D


Related Questions

the number 73 can be written as the sum of 73 consecutive integers. What are the greatest and the smallest of those numbers?

Answers

Answer:

-35 and 37

Step-by-step explanation:

If you start with negative 35 and count up (including zero), you’ll cancel out when you get to positive 35 and have 71 numbers.  Then you continue on with 36 and 37 which equals 73, and you have 73 consecutive integers.

Solve for x² in x²-3x+2=0​

Answers

[tex]x^2-3x+2=0\\x^2-x-2x+2=0\\x(x-1)-2(x-1)=0\\(x-2)(x-1)=0\\x=2 \vee x=1\\\\x^2=4 \vee x^2=1[/tex]

Answer:

Step-by-step explanation:

First we try to factor x²-3x+2.

We have to look for two numbers that multiply to 2 and add -3.

The two numbers are -1 and -2.

(x-1)(x-2) = 0

x-1 = 0 -> x = 1

x-2 = -> x = 2

Now we find x^2.

(1)^2 = 1

(2)^2 =4

Using the digits 0-9, at most only one time each, fill in the boxes to

Answers

Answer:

2 * 3 + 4 * 5 = 26

5 * 7 + 1 * 8 = 43

Step-by-step explanation:

Given

_ * _ + _ * _ = _ _

Required

Fill in the boxes with digits 0 to 9

From the question we understand that the result must be two digits i.e. _ _

To solve this, we'll make use of trial by error method:

Fill the first two boxes wit 2 and 3: _ * _ becomes 2 * 3

Fill the next two boxes with 4 and 5: _ * _ becomes 4 * 5

So,we have

2 * 3 + 4 * 5

6 + 20

26

Hence, the first combination is 2 * 3 + 4 * 5 = 26

Another possible combination is:

Fill the first two boxes wit 5 and 7: _ * _ becomes 5 * 7

Fill the next two boxes with 1 and 8: _ * _ becomes 1 * 8

So,we have

5 * 7 + 1 * 8

35 + 8

43

Hence, another combination is 5 * 7 + 1 * 8 = 43

Note that; there are more possible combinations

20 POINTS! You are planning to use a ceramic tile design in your new bathroom. The tiles are equilateral triangles. You decide to arrange the tiles in a hexagonal shape as shown. If the side of each tile measures 9 centimeters, what will be the exact area of each hexagonal shape?

Answers

Answer:

210.33 cm^2

Step-by-step explanation:

We know that 6 equilateral triangles makes one hexagon.

Also, an equilateral triangle has all its sides equal.

If the tile of each side of the triangular tile measure 9 cm, then the height of the triangular tiles can be gotten using Pythagoras's Theorem.

The triangle formed by each tile can be split along its height, into two right angle triangles with base (adjacent) 4.5 cm and slant side (hypotenuse) of 9 cm. The height  (opposite) is calculated as,

From Pythagoras's theorem,

[tex]hyp^{2} = adj^{2} + opp^{2}[/tex]

substituting, we have

[tex]9^{2} = 4.5^{2} + opp^{2}[/tex]

81 = 20.25 + [tex]opp^{2}[/tex]

[tex]opp^{2}[/tex] = 81 - 20.25 = 60.75

opp = [tex]\sqrt{60.75}[/tex] = 7.79 cm  this is the height of the right angle triangle, and also the height of the equilateral triangular tiles.

The area of a triangle = [tex]\frac{1}{2} bh[/tex]

where b is the base = 9 cm

h is the height = 7.79 cm

substituting, we have

area = [tex]\frac{1}{2}[/tex] x 9 x 7.79 = 35.055 cm^2

Area of the hexagon that will be formed = 6 x area of the triangular tiles

==> 6 x 35.055 cm^2 = 210.33 cm^2

A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 80 indicated they like the taste. At 95% confidence, test to determine if at least 22% of the population will like the new soft drink.


Required:

Determine the p-value.

Answers

Answer: p-value of the test  = 0.167

Step-by-step explanation:

Given that,

sample size n = 400

sample success X = 80

confidence = 95%

significance level = 1 - (95/100) = 0.05

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.22

Hₐ : p < 0.22

P = x/n = 80/400 = 0.2

Standard deviation of proportion α = √{  (p ( 1 - p ) / n }

α = √ { ( 0.22 ( 1 - 0.22 ) / 400 }

α = √ { 0.1716 / 400 }

α = √0.000429

α = 0.0207

Test statistic

z = (p - p₀) / α

z = ( 0.2 - 0.22 ) / 0.0207

z = - 0.02 / 0.0207

z = - 0.9661

fail to reject null hypothesis.

P-value Approach

P-value = 0.167

As P-value >= 0.05, fail to reject null hypothesis.

Since test is left tailed so p-value of the test is 0.167. Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

PLEASE HELP 30 POINTS

How long will it take in hours for a car traveling from Tucson to Phoenix (120 km)
to reach Phoenix at a rate of 10km/hr.? How long would it take that car to circle the Earth
at the equator? (c= 2 nr) rof earth is 6,378 km.

Answers

Answer:

1. It would take the car to get from Tucson to Phoenix 12 hours.

2. for the car to go around the equator it would take 637 hours if it is still travelling at 10km/hr.

hope this helps

Step-by-step explanation:

1. 120 km divided by 10 = 12 hours

Which methods could you use to calculate the y-coordinate of the midpoint of vertical line segment with endpoints at (0,0) and (0,15)? Check all that apply

Answers

Answer:

Midpoint formula.

The midpoint formula is (x_1+x_2)/2 , (y_1+y_2)/2

Step-by-step explanation:

This is one method. A list wasn't provided.

(a) Use appropriate algebra and Theorem to find the given inverse Laplace transform. (Write your answer as a function of t.)
L−1 {3s − 10/ s2 + 25}
(b) Use the Laplace transform to solve the given initial-value problem.
y' + 3y = e6t, y(0) = 2

Answers

(a) Expand the given expression as

[tex]\dfrac{3s-10}{s^2+25}=3\cdot\dfrac s{s^2+25}-2\cdot\dfrac5{s^2+25}[/tex]

You should recognize the Laplace transform of sine and cosine:

[tex]L[\cos(at)]=\dfrac s{s^2+a^2}[/tex]

[tex]L[\sin(at)]=\dfrac a{s^2+a^2}[/tex]

So we have

[tex]L^{-1}\left[\dfrac{3s-10}{s^2+25}\right]=3\cos(5t)-2\sin(5t)[/tex]

(b) Take the Laplace transform of both sides:

[tex]y'(t)+3y(t)=e^{6t}\implies (sY(s)-y(0))+3Y(s)=\dfrac1{s-6}[/tex]

Solve for [tex]Y(s)[/tex]:

[tex](s+3)Y(s)-2=\dfrac1{s-6}\implies Y(s)=\dfrac{2s-11}{(s-6)(s+3)}[/tex]

Decompose the right side into partial fractions:

[tex]\dfrac{2s-11}{(s-6)(s+3)}=\dfrac{\theta_1}{s-6}+\dfrac{\theta_2}{s+3}[/tex]

[tex]2s-11=\theta_1(s+3)+\theta_2(s-6)[/tex]

[tex]2s-11=(\theta_1+\theta_2)s+(3\theta_1-6\theta_2)[/tex]

[tex]\begin{cases}\theta_1+\theta_2=2\\3\theta_1-6\theta_2=-11\end{cases}\implies\theta_1=\dfrac19,\theta_2=\dfrac{17}9[/tex]

So we have

[tex]Y(s)=\dfrac19\cdot\dfrac1{s-6}+\dfrac{17}9\cdot\dfrac1{s+3}[/tex]

and taking the inverse transforms of both sides gives

[tex]y(t)=\dfrac19e^{6t}+\dfrac{17}9e^{-3t}[/tex]

If f(x)=x/2-3and g(x)=4x^2+x-4, find (f+g)(x)

Answers

Step-by-step explanation:

(f+g)(x) = f(x) + g(x)

= x/2-3 + 4x²+x+4

= ..........

Help I’m really bad at this

Answers

Answer:

72

Step-by-step explanation:

The formula for surface area is SA = 2lw + 2wh + 2lh

W = width

L= length

H = height

A = 2(wl + hl + hw)

2·(6·3+2·3+2·6)

Simplify that down to get the answer 72

The graph of F(x), shown below in pink, has the same shape as the graph of
G(x) = x3, shown in gray. Which of the following is the equation for F(x)?

Answers

Greetings from Brasil...

In this problem we have 2 translations: 4 units horizontal to the left and 3 units vertical to the bottom.

The translations are established as follows:

→ Horizontal

F(X + k) ⇒ k units to the left

F(X - k) ⇒ k units to the right

→ Vertical

F(X) + k ⇒ k units up

F(X) - k ⇒ k units down

In our problem, the function shifted 4 units horizontal to the left and 3 units vertical to the bottom.

F(X) = X³

4 units horizontal to the left: F(X + 4)

3 units vertical to the bottom: F(X + 4) - 3

So,

F(X) = X³

F(X + 4) - 3 = (X + 4)³ - 3

The transformed function is f ( x ) = ( x + 4 )³ - 3 and the graph is plotted

What happens when a function is transformed?

Every modification may be a part of a function's transformation.

Typically, they can be stretched (by multiplying outputs or inputs) or moved horizontally (by converting inputs) or vertically (by altering output).

If the horizontal axis is the input axis and the vertical is for outputs, if the initial function is y = f(x), then:

Vertical shift, often known as phase shift:

Y=f(x+c) with a left shift of c units (same output, but c units earlier)

Y=f(x-c) with a right shift of c units (same output, but c units late)

Vertical movement:

Y = f(x) + d units higher, up

Y = f(x) - d units lower, d

Stretching:

Stretching vertically by a factor of k: y = k f (x)

Stretching horizontally by a factor of k: y = f(x/k)

Given data ,

Let the function be represented as g ( x )

Now , the value of g ( x ) = x³

And , the transformed function has coordinates as A ( -4 , -3 )

So , when function is shifted 4 units to the left , we get

g' ( x ) = ( x + 4 )³

And , when the function is shifted vertically by 3 units down , we get

f ( x ) = ( x + 4 )³ - 3

Hence , the transformed function is f ( x ) = ( x + 4 )³ - 3

To learn more about transformation of functions click :

https://brainly.com/question/26896273

#SPJ7

Round 1, 165.492 to the nearest hundredth.

Answers

Answer:

1, 165.500

Step-by-step explanation:

1, 165.492 rounded to the nearest hundredth is 1, 165.500 because the hundredth space in the decimal is 5 or above, so the whole decimal gets rounded to the nearest hundred, which in this case, would be .500.

165.492 is the correct answer

Answer 9 and 11 with explanation on how you solved it.

Answers

Answer:

(9). Range; {8, 5, 2, -1, -4}

(10). Range; {-15, -7, 1, 9, 17}

Step-by-step explanation:

Domain of a function is (x-values) determined by the input values and Range of a function is determined by the (y-values) output values of the function.

(9). For the given function,

    f(x) = -3x + 2

    If the Domain of this function is a set of values,

    {-2, -1, 0, 1, 2}

    For Range,

    x       -2        -1         0        1       2

    f(x)     8         5        2       -1      -4

   Therefore, Range of the function 'f' will be; {8, 5, 2, -1, -4}

(11). f(x) = 4x + 1

    Domain is {-4, -2, 0, 2, 4}

    Table for input-output values will be,

    x      -4        -2         0        2        4

    f(x)  -15        -7          1        9        17

    Therefore, Range of the function will be {-15, -7, 1, 9, 17}

c. What is f (-5)?
When the function is f(x) =-3x+7

Answers

Answer:

f(-5) = 22

Step-by-step explanation:

f(x) =-3x+7

Let x = -5

f(-5) =-3*-5+7

      = 15 +7

       =22

There are 4 roads leading from Bluffton to Hardeeville, 10 roads leading from Hardeeville to Savannah, and 5 roads leading from Savannah to Macon. How many ways are there to get from Bluffton to Macon

Answers

Answer: 200 ways

Step-by-step explanation:

From the given information:

Total number of roads leading from Bluffton to​ Hardeeville = 4

Total number of roads leading from Hardeeville to​ Savannah = 10

Total number of roads leading from Savannah to Macon = 5

We need to find the total number of ways to get from Bluffton to​ Macon.

Total number of ways to get from Bluffton to​ Macon = 4 * 10 * 5

= 200

Therefore, there are 200 required number of ways to get from Bluffton to​ Macon.

How many months does it take for $700 to double at simple interest of 14%?
• It will take
number.
months to double $700, at simple interest of 14%.

Answers

It will approximately take 7 months to double $700 at a %14 interest rate.
700•.14=98
98 divided into 700= 7.14

Plzz help i cant figure this out..

Answers

Answer:

[tex]\large \boxed{\mathrm{B. \ \ \{-10, -6, 10\} }}[/tex]

Step-by-step explanation:

The domain is the x values.

D = {-1, 0, 4}

y = 4(-1) - 6 = -4 - 6 = -10

y = 4(0) - 6 = 0 - 6 = -6

y = 4(4) - 6 = 16 - 6 = 10

The range is the y values.

R = {-10, -6, 10}

Write each expression in a simpler form that is equivalent to the given expression. Let g be a nonzero number. 1/g^1 or 1/g-1

Answers

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

Apply rule : [tex]a^1 =a[/tex]

[tex]\displaystyle \frac{1}{g^1 } =\frac{1}{g}[/tex]

[tex]\displaystyle \frac{1}{g^{-1}}[/tex]

Apply rule : [tex]\displaystyle a^{-b}=\frac{1}{a^b}[/tex]

[tex]\displaystyle \frac{1}{\frac{1}{g^1 } }[/tex]

Apply rule : [tex]\displaystyle \frac{1}{\frac{1}{a} } =a[/tex]

[tex]\displaystyle \frac{1}{\frac{1}{g^1 } }=g[/tex]

Answer:

[tex]\frac{1}{g^1}[/tex]

= [tex]\frac{1}{g}[/tex]

[tex]\frac{1}{g - 1}[/tex]

= [tex]\frac{g^1}{1}[/tex]

= [tex]\frac{g}{1}[/tex]

= g

Hope this helps!

Select the best answer for the question . 7. At a public swimming pool , the probability that an employee is a lifeguard is P(L) = 0.85 , and the probability that an employee is a teenager is P(T) = 0.58 . What's the probability that an employee is a lifeguard , given that the employee is a teenager ? O A. There isn't enough information given. O B. 1.47 OC. 0.68 O D.0.49​

Answers

Answer:

D)  0.49

Step-by-step explanation:

0.85 * 0.58 = 0.49

The probability is:

D  0.49

In a recent survey of drinking laws, a random sample of 1000 women showed that 65% were in favor of increasing the legal drinking age. In a random sample of 1000 men, 60% favored increasing the legal drinking age. Test the claim that the percentage of men and women favoring a higher legal drinking age is different at (alpha 0.05).

Answers

Answer:

Step-by-step explanation:

Given that:

Let sample size of women be [tex]n_1[/tex]  = 1000

Let the proportion of the women be [tex]p_1[/tex] = 0.65

Let the sample size of the men be [tex]n_2[/tex] = 1000

Let the proportion of the mem be [tex]p_2[/tex]  = 0.60

The null and the alternative hypothesis can be computed as follows:

[tex]H_0: p_1 = p_2[/tex]

[tex]H_0a: p_1 \neq p_2[/tex]

Thus from the alternative hypothesis we can realize that this is a two tailed test.

However, the pooled sample proportion p = [tex]\dfrac{p_1n_1+p_2n_2 } {n_1 +n_2}[/tex]

p =[tex]\dfrac{0.65 * 1000+0.60*1000 } {1000 +1000}[/tex]

p = [tex]\dfrac{650+600 } {2000}[/tex]

p = 0.625

The standard error of the test can be computed as follows:

[tex]SE = \sqrt{p(1-p) ( \dfrac{1} {n_1}+ \dfrac{1}{n_2} )}[/tex]

[tex]SE = \sqrt{0.625(1-0.625) ( \dfrac{1} {1000}+ \dfrac{1}{1000} )}[/tex]

[tex]SE = \sqrt{0.625(0.375) ( 0.001+0.001 )}[/tex]

[tex]SE = \sqrt{0.234375 (0.002)}[/tex]

[tex]SE = \sqrt{4.6875 * 10^{-4}}[/tex]

[tex]SE = 0.02165[/tex]

The test statistics is :

[tex]z =\dfrac{p_1-p_2}{S.E}[/tex]

[tex]z =\dfrac{0.65-0.60}{0.02165}[/tex]

[tex]z =\dfrac{0.05}{0.02165}[/tex]

[tex]z =2.31[/tex]

At level of significance of 0.05  the critical value for the z test will  be in the region between - 1.96 and 1.96

Rejection region: To reject the null hypothesis if z < -1.96 or z > 1.96

Conclusion: Since the value of z is greater than 1.96, it lies in the region region. Therefore we reject the null hypothesis and we conclude that  the percentage of men and women favoring a higher legal drinking age is different.

find the area of the figure pictured below. 3.8ft 8.3ft 7.4ft 3.9ft

Answers

The can be divided into two rectangles, one having length [tex]8.3[/tex] and width $3.8$

Another with, dimensions $7.4-3.8=3.6$ and $3.9$

Area of first rectangle=$3.8\times8.3=31.54$

Area of second rectangle =$3.6\times3.9=14.04$

Total area $=31.54+14.04=45.58$ ft²

Answer:

45.58 ft^2

Step-by-step explanation:

We can split the figure into two pieces

We have a tall rectangle that is 3.8 by 8.3

A = 3.8 * 8.3 =31.54 ft^2

We also have a small rectangle on the right

The dimensions are ( 7.4 - 3.8) by 3.9

A = 3.6*3.9 =14.04 ft^2

Add the areas together

31.54+14.04

45.58 ft^2

The function fix) = (x - 4)(x - 2) is shown.
What is the range of the function?
8
all real numbers less than or equal to 3
all real numbers less than or equal to -1
all real numbers greater than or equal to 3
all real numbers greater than or equal to - 1
6
2
16
2
14
COL
40
8
G D​

Answers

Answer:

The range of the function f(x)= (x-4)(x-2) is all real numbers greater than or equal to -1

Step-by-step explanation:

How many ways can you arrange your 3 statistics books, 2 math books, and 1 computer science book on your bookshelf if (a) the books can be arranged in any order

Answers

Answer:

720 different ways.

Step-by-step explanation:

Permutation has to do with arrangement. For example, in order to arrange 'n' objects in any order, this can only be done in n! ways since there is no condition or restriction on how to arrange the objects.

n! = n(n-1)(n-2)... (n-r)!

If there are 3 statistics books, 2 math books, and 1 computer science book on your bookshelf, the total number of books altogether is 3 + 2 + 1 = 6 books.

The number of ways that 6 books can be arranged in any order is 6!.

6! = 6(6-1)(6-2)(6-3)(6-4)(6-5)

6! = 6*5*4*3*2*1

6! = 120*6

6!= 720 different ways.

Hence, the books on your shelf can be arranged in 720 different ways.

An urn contains two blue balls (denoted B1 and B2) and three white balls (denoted W1, W2, and W3). One ball is drawn, its color is recorded, and it is replaced in the urn. Then another ball is drawn and its color is recorded.

a. Let B1 W2 denote the outcome that the first ball drawn is B1 and the second ball drawn is W2. Because the first ball is replaced before the second ball is drawn, the outcomes of the experiment are equally likely. List all 25 possible outcomes of the experiment.

b. Consider the event that the first ball that is drawn is blue. List all outcomes in the event. What is the probability of the event?

c. Consider the event that only white balls are drawn. List all outcomes in the event. What is the probability of the event?

Answers

Answer:

(a) Shown below.

(b) The probability that the first ball drawn is blue is 0.40.

(c) The probability that only white balls are drawn is 0.36.

Step-by-step explanation:

The balls in the urn are as follows:

Blue balls: B₁ and B₂

White balls: W₁, W₂ and W₃

It is provided that two balls are drawn from the urn, with replacement, and their color is recorded.

(a)

The possible outcomes of selecting two balls are as follows:

B₁B₁          B₂B₁          W₁B₁          W₂B₁          W₃B₁

B₁B₂         B₂B₂          W₁B₂         W₂B₂          W₃B₂

B₁W₁         B₂W₁         W₁W₁         W₂W₁         W₃W₁

B₁W₂        B₂W₂         W₁W₂        W₂W₂         W₃W₂

B₁W₃        B₂W₃         W₁W₃        W₂W₃         W₃W₃

There are a total of N = 25 possible outcomes.

(b)

The sample space for selecting a blue ball first is:

S = {B₁B₁, B₁B₂, B₁W₁, B₁W₂, B₁W₃, B₂B₁, B₂B₂, B₂W₁, B₂W₂, B₂W₃}

n (S) = 10

Compute the probability that the first ball drawn is blue as follows:

[tex]P(\text{First ball is Blue})=\frac{n(S)}{N}=\frac{10}{25}=0.40[/tex]

Thus, the probability that the first ball drawn is blue is 0.40.

(c)

The sample space for selecting only white balls is:

X = {W₁W₁, W₂W₁, W₃W₁, W₁W₂, W₂W₂, W₃W₂, W₁W₃, W₂W₃, W₃W₃}

n (X) = 9

Compute the probability that only white balls are drawn as follows:

[tex]P(\text{Only White balls})=\frac{n(X)}{N}=\frac{9}{25}=0.36[/tex]

Thus, the probability that only white balls are drawn is 0.36.

ab-0.5bab−0.5ba, b, minus, 0, point, 5, b when a=1a=1a, equals, 1 and b=5b=5

Answers

Answer:

  2.5

Step-by-step explanation:

Put the values in place of the corresponding variables and do the arithmetic:

  ab - 0.5b = (1)(5) -0.5(5) = 5 - 2.5 = 2.5

Please help with this

Answers

The answer is C. Opposite sides have the exact same slope, and the shape is a quadrilateral.

help with math ASAP!

Answers

Answer:

1.)  [tex]\frac{1}{9^4}*9^3[/tex]

2.) [tex]\frac{1}{w^7}[/tex]

3.)

Step-by-step explanation:

When you have a negative exponent, rewrite:

[tex]x^{-a}=\frac{1}{x^a}[/tex]

Rewrite using this to change all negative exponents.

Answer:

Multiple Answers

Step-by-step explanation:

Note: When multiplying numbers with exponents, you add the exponents. When dividing numbers with exponents, you subtract exponents.When you have a negative exponent, flip the fraction and write it as a positive exponent.

1) -4 + 3= -1  

So we have  (9^-4) + (9^3)= (1/(9^1)

2) (1/w)^7

3) cannot read problem, but just apply the rules I wrote under "Note"

4) 14/y

5) cannot read problem,but just apply the rules I wrote under "Note"

6) 20d^4 n^? --Cannot read n exponents--.

7) cannot read problem

8) Cannot read problem

9) 90/z^4---only if exponents are 5,-3,and-6

10) 1/(9^5)

11) 54b^4

12) Cannot read problem

13) 16d^8c^8 ---if exponents are 5,3,6,2--

14) s^8

Hope this helps! Plz give brainly, I kinda need it.

For the regression equation, Ŷ = +20X + 200 what can be determined about the correlation between X and Y?

Answers

Answer:

There is a positive correlation between X and Y.

Step-by-step explanation:

The estimated regression equation is:

[tex]\hat Y=20X+200[/tex]

The general form of a regression equation is:

[tex]\hat Y=b_{yx}X+a[/tex]

Here, [tex]b_{yx}[/tex] is the slope of a line of Y on X.

The formula of slope is:

[tex]b_{yx}=r(X,Y)\cdot \frac{\sigma_{y}}{\sigma_{x}}[/tex]

Here r (X, Y) is the correlation coefficient between X and Y.

The correlation coefficient is directly related to the slope.

And since the standard deviations are always positive, the sign of the slope is dependent upon the sign of the correlation coefficient.

Here the slope is positive.

This implies that the correlation coefficient must have been a positive values.

Thus, it can be concluded that there is a positive correlation between X and Y.

A local statistician is interested in the proportion of high school students that drink coffee. Suppose that 20% of all high school students drink coffee.
What is the probability that out of these 75 people, 14 or more drink coffee?

Answers

Answer:

the probability that out of these 75 people, 14 or more drink coffee is 0.6133

Step-by-step explanation:

Given that:

sample size n = 75

proportion of high school students that drink coffee p = 20% = 0.20

The proportion of the students that did not drink coffee = 1 - p

Let X be the random variable that follows a normal distribution

X [tex]\sim[/tex] N (n, p)

X  [tex]\sim[/tex] N (75, 0.20)

[tex]\mu = np[/tex] = 75 × 0.20

[tex]\mu =[/tex] 15

[tex]\sigma = \sqrt{p (1-p) n}[/tex]

[tex]\sigma = \sqrt{0.20(1-0.20) 75}[/tex]

[tex]\sigma = \sqrt{0.20*0.80* 75}[/tex]

[tex]\sigma = \sqrt{12}[/tex]

[tex]\sigma = 3.464[/tex]

Now ; if 14 or more people drank coffee ; then

[tex]P(X \geq 14) = P(\dfrac{X-\mu }{\sigma} \leq \dfrac{X-\mu}{\sigma})[/tex]

[tex]P(X \geq 14) =P(\dfrac{14-\mu }{\sigma} \leq \dfrac{14-15}{3.464})[/tex]

[tex]P(X \geq 14) = P(Z \leq \dfrac{-1}{3.464})[/tex]

[tex]P(X \geq 14) = P(Z \leq -0.28868)[/tex]

From the standard normal z tables; (-0.288)

[tex]P(X \geq 14) = P(Z \leq 0.38667)[/tex]

[tex]P(X \geq 14) = 1 - 0.38667[/tex]

[tex]P(X \geq 14) = 0.61333[/tex]

the probability that out of these 75 people, 14 or more drink coffee is 0.6133

A bag contains five white balls and four black balls. Your goal is to draw two black balls. You draw two balls at random. Once you have drawn two balls, you put back any white balls, and redraw so that you again have two drawn balls. What is the probability that you now have two black balls? (Include the probability that you chose two black balls on the first draw.)

Answers

Answer:

Probabilty of both Black

= 1/6

Step-by-step explanation:

A bag contains five white balls and four black balls.

Total number of balls= 5+4

Total number of balls= 9

Probabilty of selecting a black ball first

= 4/9

Black ball remaining= 3

Total ball remaining= 8

Probabilty of selecting another black ball without replacement

= 3/8

Probabilty of both Black

=3/8 *4/9

Probabilty of both Black

= 12/72

Probabilty of both Black

= 1/6

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