A. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols.
The red die shows 1 and the numbers add to 4.
How many elements does it contain?
B. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 2; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.]
The numbers do not add to 2.
How many elements does it contain?
C. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 2; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 11 or the red die shows a 1.
How many elements does it contain?
D. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 5; C: at least one of the numbers is 1; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 5, or they add to 9, or at least one of them is 1.
How many elements does it contain?

Question:- how many 50 cents coins are there in $10.50

Answer:-

Total amount-> $ 10.50

So amount in cents

$ 1 is equal to 100 cents

$10.50 is equal to 1050 cents

According to the question

[tex]Number \: of \: the \: 50 \: cents= \frac{ Total \: cents}{ 50 \: cents } \\ [/tex]

[tex]Number \: of \: the \: 50 \: cents = \frac{1050}{50} \\ Number \: of \: the \: 50 \: cents = 21 \: [/tex]

Answer:

7/5 is greater than 4/5

Answer:

[tex]\frac{4}{5}[/tex]  <  [tex]\frac{7}{5}[/tex]

Work Shown:

(9^x)/(3^y)

( (3^2)^x )/(3^y)

( 3^(2x) )/( 3^y )

3^(2x-y)

3^2 .... use the equation 2x-y = 2

9

Answer:

Credit remaining after 21 minutes = $30.4

Step-by-step explanation:

Credit remaining on a phone card is a linear function of the total calling time.

When graphed, let the linear function representing the line is,

y = mx + b

Where 'm' = slope of the line

b = y-intercept

From the graph,

Slope of the line = -0.12

y = -0.12x + b

If this line passes through a point (33, 28.96),

28.96 = -0.12(33) + b

b = 28.96 + 3.96

b = 32.92

Therefore, the linear function is,

f(x) = -0.12x + 32.92

where x = calling time

Credit left in the card after 21 minutes,

f(21) = -0.12(21) + 32.92

      = -2.52 + 32.92

      = $30.4

Answer:

number of successes

                 [tex]k = 235[/tex]

number of failure

                 [tex]y = 265[/tex]

The   criteria are met    

A

    The sample proportion is  [tex]\r p = 0.47[/tex]

B

    [tex]E =4.4 \%[/tex]

C

What this mean is that for N number of times the survey is carried out that the which sample proportion obtain will differ from  the true population proportion will not  more than 4.4%

Ci  

   [tex]r = 0.514 = 51.4 \%[/tex]

 [tex]v = 0.426 = 42.6 \%[/tex]

D

   This 95% confidence interval  mean that the the chance of the true    population proportion of those that are happy to be exist within the upper   and the lower limit  is  95%

E

  Given that 50% of the population proportion  lie with the 95% confidence interval  the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time

F

 Yes our result would support the claim because

            [tex]\frac{1}{3 } \ of N < \frac{1}{2} (50\%) \ of \ N , \ Where\ N \ is \ the \ population\ size[/tex]

Step-by-step explanation:

From the question we are told that

     The sample size is  [tex]n = 500[/tex]

     The sample proportion is  [tex]\r p = 0.47[/tex]

Generally the number of successes is mathematical represented as

             [tex]k = n * \r p[/tex]

substituting values

             [tex]k = 500 * 0.47[/tex]

            [tex]k = 235[/tex]

Generally the number of failure  is mathematical represented as

           [tex]y = n * (1 -\r p )[/tex]

substituting values

           [tex]y = 500 * (1 - 0.47 )[/tex]

           [tex]y = 265[/tex]

for approximate normality for a confidence interval  criteria to be satisfied

          [tex]np > 5 \ and \ n(1- p ) \ >5[/tex]

Given that the above is true for this survey then we can say that the criteria are met

  Given that the confidence level is  95%  then the level of confidence is mathematically 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]

Generally the margin of error is mathematically represented as  

                [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p}{n} }[/tex]

substituting values

                 [tex]E = 1.96 * \sqrt{ \frac{0.47 (1- 0.47}{500} }[/tex]

                 [tex]E = 0.044[/tex]

=>               [tex]E =4.4 \%[/tex]

What this mean is that for N number of times the survey is carried out that the proportion obtain will differ from  the true population proportion of those that are happy by more than 4.4%

The 95% confidence interval is mathematically represented as

          [tex]\r p - E < p < \r p + E[/tex]

substituting values

        [tex]0.47 - 0.044 < p < 0.47 + 0.044[/tex]

         [tex]0.426 < p < 0.514[/tex]

The upper limit of the 95% confidence interval is  [tex]r = 0.514 = 51.4 \%[/tex]

The lower limit of the   95% confidence interval is  [tex]v = 0.426 = 42.6 \%[/tex]

This 95% confidence interval  mean that the the chance of the true population proportion of those that are happy to be exist within the upper and the lower limit  is  95%

Given that 50% of the population proportion  lie with the 95% confidence interval  the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time

Yes our result would support the claim because

            [tex]\frac{1}{3 } < \frac{1}{2} (50\%)[/tex]

Answer:

9.488

Step-by-step explanation:

The critical value is found by first assessing which statistical test should be used.

We are interested in investigating relationship between social activity and education so chi-square test would be appropriate.

We have 3 rows and 3 columns. The degree of freedom for chi-square critical value is (r-1)(c-1)=(3-1)(3-1)=2*2=4

Chi-square critical value(0.05,4)= 9.488

Answer:

[tex]x = 3.6[/tex]

Step-by-step explanation:

To find the area of a rectangle, you multiply its length by its width. The formula is [tex]lw = a[/tex].

We already know the length, 5, and the area, 18, so we can plug it into the equation.

[tex]5\cdot w=18[/tex]

We can simplify this equation by dividing both sides by 5.

[tex]5\cdot w \div5 = 18\div5\\\\w = 3.6[/tex]

Hope this helped!

Answer: x= 13

Step-by-step explanation:

F + V = E + 2

⇨ 9 + 14 = E + 2

⇨ 23 = E + 2

⇨ 23 - 2 = E

⇨ 21 = E

Hence , the number of edges in polyhedron is 21.

The number of edges of a polyhedron with 9 faces and 14 vertices have will be 21.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

here, we have,

Using Euler's formula, the number of the edges does a polyhedron with 9 faces and 14 vertices have

We know the formula for the edges of the polyhedron will be

By Euler's Formula

F + V = E + 2

The number of faces, vertices, and edges of a polyhedron are denoted by the letters F, V, and E.

Then we have

Solution

F = 9

V = 14

E = ?

Substuting the values

⇨ 9 + 14 = E + 2

⇨ 23 = E + 2

⇨ 23 - 2 = E

⇨ 21 = E

Hence , the number of edges in polyhedron is 21.

More about the polygon link is given below.

brainly.com/question/17756657

#SPJ2

9514 1404 393

Answer:

  D. 72 heads in 100 flips

Step-by-step explanation:

A probability calculator will tell you the probabilities of the given outcome with a fair coin are ...

  A: 0.0625

  B: 0.04395

  C: 0.15498

  D: 3.9×10^-6

__

It is "improbable" that a fair coin will give 72 heads in 100 flips. So, it is reasonable to assume the coin is not fair if that is the result.

Answer:

option C . 5

Step-by-step explanation:

For two points (x1,y1) and (x2,y2) divided by a point p in ratio m:n then coordinates of that point is given by

p    :  (nx1+mx2)/(m+n),  (ny1+my2)/(m+n),  

Given

x coordinate of P (-3)

x  coordinate of Q (a) since we have to find it , let it be a

x coordinate of R(-1)\

ratio = 1:3

_______________________________________

Using the above formula to find the point of division

we can get value of x coordinate for point Q

x  coordinate of R = 3*-3 + 1*a/(1+3)

-1 = (-9 + a)/4

=> -4 = -9 +a

=>a = -4+9 = 5

Thus, x  coordinate of Q is 5

Answer:

1 pound of Oranges = $2

1 pound of Bananas = $2

Step-by-step explanation:

O = Oranges

B = Bananas

=> 5o + 2b = 14

=> 2b = 14 - 5o

=> b = 14/2 - 5/2o

=> b = 7 - 2.5o

3o + 6b = 18

=> 3o + 6( 7 - 2.5o ) = 18

=> 3o + 42 - 15o = 18

=> -12o + 42 = 18

=> -12o = -24

=> -o = -2

=> o = 2

One pound of oranges costs $2.

So,

5 (2) + 2b = 14

=> 10 + 2b = 14

=> 2b =4

=> b = 2

One pound of bananas also costs $2.

Answer:

[tex]\huge\boxed{x+y=-2}[/tex]

Step-by-step explanation:

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

where

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points (-2, 0) and (1, -3).

Substitute:

[tex]x_1=-2;\ y_1=0;\ x_2=1;\ y_2=-3[/tex]

[tex]m=\dfrac{-3-0}{1-(-2)}=\dfrac{-3}{1+2}=\dfrac{-3}{3}=-1\\\\y-0=-1(x-(-2))\\\\y=-(x+2)[/tex]

[tex]y=-x-2[/tex]         add x to both sides

[tex]x+y=-2[/tex]

Answer:

$275 a month

Step-by-step explanation:

Let x represent how much each friend is paying.

The amount Jane pays can be represented by 2x, since she is paying double than her friends.

Add together these terms and set them equal to 550. Then, solve for x:

x + x + 2x = 550

4x = 550

x = 137.5

So, each friend is paying $137.50. Double this to find how much Jane is paying:

137.5(2)

= 275

So, Jane is paying $275 a month

Answer:

The full answer is 4.40625 but rounded it would be 4.41

Answer:

Step-by-step explanation:

x² - 5x - 36

To factor the expression rewrite -5x as a difference

That's

x² + 4x - 9x - 36

Factor out x from the expression

x( x + 4) - 9x - 36

Factor out -9 from the expression

x( x + 4) - 9( x+ 4)

Factor out x + 4 from the expression

The final answer is

Hope this helps you

Answer:

[tex] \boxed{(x - 9) \: (x + 4) }[/tex]

Option A is the correct option.-

Step-by-step explanation:

( See the attached picture )

Hope I helped!

Best regards!

Answer:

answer below

Step-by-step explanation:

1. price per gallon of gasoline and total cost of gasoline

2. distance from a door and height of a wheelchair ramp

perfect positive linear relationship:

this is a relation that exists between two variables. The pearson correlation is used to check this relationship and if the relationship is 1.0 then it is established that a positive linear relationship exists

negative linear relationship

this is a relationship between variables where the pearson correlation is less than 0. if the value is -1.0 then a negative linear relatioship exists.

price per gallon of gasoline and total cost of gasoline move in the same direction so it is positive.

distance from a door and height of a wheelchair ramp are negative because they do not move in the same direction.

Answer:

Rs. 80 is owed.

Step-by-step explanation:

Principle (P) = 2000

Time (T) = 2 years

Rate (R) = 2%

Interest (I) = ?

Here,

I = (P×T×R) / 100

= (2000×2×2) / 100

= (8000) / 100

= Rs. 80

Answer:

P= 2000

T= 2

R=2÷100

I = PTR

= 2000×2×2÷100

2÷100=0.02

2000×2×0.02= 80

So i is 80

Answer:

The minimum sample size is [tex]n = 2123[/tex]

Step-by-step explanation:

From the question we are told that

    The margin of error is  [tex]E = 0.028[/tex]

Given that the confidence level is  99% then the level of significance is evaluated as

        [tex]\alpha = 100 - 99[/tex]

        [tex]\alpha = 1 \%[/tex]

        [tex]\alpha =0.01[/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} } = 2.58[/tex]

Now let  assume that the sample proportion is  [tex]\r p = 0.5[/tex]

  hence  [tex]\r q = 1 - \r p[/tex]

=>            [tex]\r q = 0.50[/tex]

   Generally the sample size is mathematically represented as

                [tex]n =[ \frac{Z_{\frac{ \alpha }{2} }}{ E} ]^2 * \r p * \r q[/tex]

                [tex]n =[ \frac{2.58}{ 0.028} ]^2 * 0.5 * 0.5[/tex]

              [tex]n = 2123[/tex]

Answer:

Step-by-step explanation: h(t) = -16t2 + 144

h(1) = -16(12) + 144 = 128 ft

h(2) = -16(22) + 144 = 80 ft

h(2) - h(1) = 80 - 128 = -48 ft

It fell 48 ft between t = 1 and t = 2 seconds.

It reaches the ground when h(t) = 0

0 = -16t2 + 144

t = √(144/16) s = 3s

It reaches the ground 3s after being dropped.

Answer:

51 miles

Step-by-step explanation:

hope it's clear and understandable

:)

Answer:

a) and b)  Look step by step explanation

c) z(s) = - 12,07

d) z(c) = - 1,64

e) Final decision: Reject H₀

Step-by-step explanation:

We assume Normal Distribution

Data:

Sample population  n   = 1200

Sample mean         μ  =    3

Sample Standard deviation   2,87

Claim mean      μ₀  =  4

α = 0,05  then from z-table we find  z(c) = 1,64   ( critical value )

We need to develop a one tail-test to the left

Test Hypothesis

The General Society developed a survey ( in all cases that is an indication of a sample)

Null hypothesis                    H₀                      μ   =  μ₀

Alternative hypothesis        Hₐ                       μ  <  μ₀

To calculate the  z(s)

z(s) =  ( μ  -  μ₀ )/ 2,87/√n

z(s) =  ( 3 - 4 )/ 2,87/√1200

z(s) =   -1 * 34,64 / 2,87

z(s) = - 12,07

To compare  z(s) and z(c)

z(s)  <  z(c)           - 12,07 < - 1,64

z(s) is in the rejection region (quite far away) we reject H₀

Data provide enough evidence to disprove the claim

Answer:

x < 12

Step-by-step explanation:

subtract 4 from both sides:

x + 4 < 16

   - 4     -4

x < 12

Answer:

x<4

Step-by-step explanation:

x+4 <16

x < 16

4

x<4

I hope this will help you

Answer:

I think :

c is 30 triangle

b is 60 triangle

d is 90 triangle

Answer:

535525-62635-$6#62626636$66$6$63663636$6$62

brainly is dustbin

Answer:

Step-by-step explanation:

To find the missing side in the question, we use the cosine rule

That's

Since we are finding a we use the formula

From the question

b = 2

c = 4

A = 78°

Substitute the values into the above formula

We have

a² = 2² + 4² - 2(2)(4) cos 78

a² = 4 + 16 - 16 cos 78

a² = 20 - 16cos 78

a² = 16.67341

Find the square root of both sides

a = 4.0833

We have the final answer as

Hope this helps you

Answer:

135 degrees

Step-by-step explanation:

3x+15 = 5x - 5 because of the alternate interior angles theorem.

20 = 2x

x = 10

3(10) + 15 = 30+15 = 45

Remember that a line has a measure of 180 degrees. So we can just subtract the angle we found from 180 degrees to get BFG.

180-45 = 135.

Answer:

The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.

Step-by-step explanation:

Let be [tex]f(m, b) = m\cdot b - m^{2}[/tex], if [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex], the value of the expression:

[tex]f(3.48,96.52) = (3.48)\cdot (96.52)-3.48^{2}[/tex]

[tex]f(3.48,96.52) = 323.779[/tex]

The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.

====================================================

Explanation:

Both AB and XY are the first two letters of ABC and XYZ respectively. So we have one fraction of AB/XY = 2/7.

AC and XZ are the first and last letters of ABC and XYZ respectively. We can form another fraction AC/XZ. I'm dividing in the same order of small over large to keep things consistent. As you can probably guess, the order of the letters ABC and XYZ are important so we see how the angles match up and how the proportional sides match up.

Because the triangles are similar, the two fractions formed earlier are equal to one another.

The equation we need to solve is AB/XY = AC/XZ

-----

AB/XY = AC/XZ

2/7 = 3/N ... plug in given values

2N = 7*3 .... cross multiply

2N = 21

N = 21/2 .... divide both sides by 2

N = 10.5

ZX is 10.5 units long.

Answer:

b)25

Step-by-step explanation:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Answer:

[tex]IQR=Q_{3}-Q_{1}[/tex]

Step-by-step explanation:

The inter-quartile range is a measure of dispersion of a data set.

It is the difference between the third and the first quartile.

[tex]IQR=Q_{3}-Q_{1}[/tex]

The 1st quartile (Q₁) is well defined as the mid-value amid the minimum figure and the median of the data set. The 2nd quartile (Q₂) is the median of the data. The 3rd quartile (Q₃) is the mid-value amid the median and the maximum figure of the data set.