(06.02)A six-sided number cube labeled 1 through 6 is rolled 200 times. An even number is rolled 115 times. Compare the theoretical probability of rolling an even number with the relative frequency of rolling an even number and select one of the statements below that best describes the situation. The theoretical probability and relative frequency are the same. The theoretical probability is larger than the relative frequency. The theoretical probability is smaller than the relative frequency. There is not enough information to determine the relative frequency.

Answer:

21

Step-by-step explanation:

The 5 smallest prime numbers are 1, 2, 3, 5, and 7.

So when multiplied it equals 105.

Divide by 42 and you get 2 21/42

So you have a remainder of 21

Answer:

6xy^2+10y^2z is the answer

Answer:

i). 10 levels of the bricks

ii). 320 bricks

Step-by-step explanation:

First level contains number of bricks = 50

Second level will contain = 50 - 4 = 46 bricks

Similarly, 3rd level will contain number of bricks = 46 - 4 = 42

Therefore, sequence formed for the number of bricks in each level of the wall will be,

50, 46, 42........14

This sequence is an arithmetic sequence having,

First term 'a' = 50

Common difference 'd' = 46 - 50 = (-4)

Last term of the sequence [tex]T_{n}[/tex]= 14

i). Expression representing last term will be,

  [tex]T_{n}=a+(n-1)d[/tex]

  Here [tex]T_{n}[/tex] = nth term

  a = first term

  n = number of term (Number of level of the wall)

  d = common difference

  By substituting these values in the formula,

  14 = 50 + (n - 1)(-4)

  14 - 50 = (-4)(n - 1)

  -36 = -4(n - 1)

  9 = (n - 1)  

  n = 9 + 1

  n = 10

ii). Number of bricks used in the wall = Sum of the sequence

   Expression for the sum of an arithmetic sequence is,

   [tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]

   [tex]S_n=\frac{10}{2}[2\times 50+(10-1)(-4)][/tex]

        = 5(100 - 36)

        = 320 bricks

Answer:

For x

We use cosine

cos 45° = 2/x

After solving

x = 2√2

Since we have the value of x we use it to get the value of y

we use cosine

cos 60° = 2√2/y

y =2√2/cos 60

y = 4√2

We use Pythagoras theorem to find z

(4√2)² = (2√2)² + z²

z² = 32 - 8

z² = 24

z = √24

z = 2√6

Therefore x = 2√2

y = 4√2

z = 2√6

Hope this helps.

Answer:

Not a random variable

Step-by-step explanation:

The last book a person read in City A is not a random variable because it is not a number as there is no numerical description for the outcome of this experiment.

Thus, the last book read by someone in City A is not a random variable.

Answer:

not random

Step-by-step explanation:

The question is incomplete. The complete question is as follows.

The city of Oakdale wishes to see if there is a linear relantionship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a pont estimate Kilowatt usage when the Temperature is 90 degrees outside?

Temperature(x)                       Kilowatts(y)

        73                                         680

        78                                         760

        85                                         910

        98                                         1510

        93                                         1170

        83                                         888

        92                                         923

        81                                          837

        76                                         600

       105                                        1800

Answer: The point estimate is 1132.5 Kilowatts

Step-by-step explanation: Regression analysis is used to find an equation that fits the data. Once this equation is found, it's used to make predictions. One of the regressions is linear regression.

To find the linear regression model:

1) Create a table with the following: ∑y; ∑x; ∑xy; ∑x²; ∑y²;

2) Use these equations to find coefficients a and b:

a = (∑y)(∑x²) - (∑x)(∑yx) / n(∑x²) - (∑x)²

b = n(∑xy) - (∑x)(∑y) / n(∑x²) - (∑x)²

3) Substitute the coefficients into the equation of form: y = a + bx

For the table above, the linear regression equation is:

y = - 2004 + 34.85x

When Temperature is 90, i.e. x = 90:

y = - 2004 + 34.85*90

y = 1132.5

The estimate Kilowatt is 1132.5.

Answer:

8 + 2x

Step-by-step explanation:

You are adding 8 to 2 times an unknown number.

Answer:

Step-by-step explanation:

The computer hardware company requires all of the chips purchased from its supplier of computer chips to meet the specification of 1.2 centimeters, with error margins of -0.1cm and +0.1cm

This means that the required length of computer chips is between 1.1cm - 1.3cm

Where 1.1cm = [1.2 - 0.1]

1.3cm = [1.2 + 0.1]

Based on the computer chips supplied last month, mean length was 0.9cm. This means that most of the chips were (in length) less than the lower boundary of 1.1cm.

The element that the production manager should consider in determining his company's ability to produce chips that meet specification is:

- The length of the chips.

The length of the chips his production team produces should be tailored to meet the length specification of his client.

Answer:

20-39 ⇒ 5

40-59 ⇒ 3

60-79 ⇒ 5

80-99 ⇒ 10

Answer:

20-39: 5

40-59: 3

60-79: 5

80-99: 10

Step-by-step explanation:

If you just added up, you can find all the values.

Answer:

''0 is neither a rational number nor an irrational number.''

Step-by-step explanation:

Zero is a rational number. Zero can be written as a fraction, where p/q = 0, where p = 0 and q is any non-zero integer. Hence, 0 is a rational number.

Answer:

[tex]\boxed{\sf \ \ age = 10\ \ }[/tex]

Step-by-step explanation:

Hello,

let's write the mean computation, we note x the age of the additional person

[tex]\dfrac{14+14+18+18+22+x}{6}=16[/tex]

[tex]<=> 14+14+18+18+22+x = 6*16=96\\\\<=> x = 96 - ( 14+14+18+18+22)= 10[/tex]

So the age of the person is 10

hope this helps

Answer:

10

Step-by-step explanation:

The mean is the sum of terms divided by number of terms.

Let x be the age of the person who entered the room.

(14+14+18+18+22+x)/6 = 16

(x + 86)/6 = 16

x + 86 = 96

x = 10

The age of the person who entered the room is 10.

Answer:

please see the attached picture for full solution...

Hope it helps...

Good luck on your assignment....

Answer:

A. Negative 32  dollars

Step-by-step explanation:

Kendra has a debt. Doubt means that the balance is Negative.

If the debt is greater than 25 USD . Kendra's debt has to be more negative than 25 . Amoung all other numbers only debt  32 is more negative than 25.

Answer:

I think it would be 32

Step-by-step explanation:

So she can pay the debt off

Answer:

  3

Step-by-step explanation:

Those wearing a shirt of another color are ...

  1 - 5/8 -1/4 = 8/8 -5/8 -2/8 = 1/8

of the total number of students in the classroom

  (1/8)×(24 students) = 3 students . . . . wearing another color

_____

Alternate solution

With the given information, you know ...

  (5/8)(24) = 15 . . . students wear blue

  (1/4)(24) = 6 . . . . students wear white

  24 -15 -6 = 3 . . . students wear another color

Answer:

96 ft^2

Step-by-step explanation:

volume=l^3

l=4

4x4x4=64

Surface area (4x4)=16

16x6=96

Answer:

SA =96 ft^2

Step-by-step explanation:

The volume of a cube is given by

V = s^3

64 = s^3

Take the cube root of each side

64 ^ 1/3 = s^3 ^ 1/3

4 =s

The side length si 4

The surface area of a cube is

SA = 6 s^2

SA = 6 * 4^2

SA = 6 * 16

SA =96 ft^2

Answer:

  appropriately writing the proportion can reduce or eliminate steps required to solve it

Step-by-step explanation:

The proportion ...

  [tex]\dfrac{A}{B}=\dfrac{C}{D}[/tex]

is equivalent to the equation obtained by "cross-multiplying:"

  AD = BC

This equation can be written as proportions in 3 other ways:

  [tex]\dfrac{B}{A}=\dfrac{D}{C}\qquad\dfrac{A}{C}=\dfrac{B}{D}\qquad\dfrac{C}{A}=\dfrac{D}{B}[/tex]

  Effectively, the proportion can be written upside-down and sideways, as long as the corresponding parts are kept in the same order.

I find this most useful to ...

  a) put the unknown quantity in the numerator

  b) give that unknown quantity a denominator of 1, if possible.

__

The usual method recommended for solving proportions is to form the cross-product, as above, then divide by the coefficient of the variable. If the variable is already in the numerator, you can simply multiply the proportion by its denominator.

Example:

  x/4 = 3/2

Usual method:

  2x = 4·3

  x = 12/2 = 6

Multiplying by the denominator:

  x = 4(3/2) = 12/2 = 6 . . . . . . saves the "cross product" step

__

Example 2:

  x/4 = 1/2 . . . . we note that "1" is "sideways" from x, so we can rewrite the proportion as ...

  x/1 = 4/2 . . . . . . written with 1 in the denominator

  x = 2 . . . . simplify

Of course, this is the same answer you would get by multiplying by the denominator, 4.

The point here is that if you have a choice when you write the initial proportion, you can make the choice to write it with x in the numerator and 1 in the denominator.

Answer:

False, it is easier to isolate x.

Step-by-step explanation:

6y+x=3

x=3-6y

Answer: 6811

Step-by-step explanation:

in this problem the values are 8800 and -2900 and the respective probabilities are 0.83 and 0.17

--

so the expected profit o# sum = (x*P(x))=8800*(0.83)+(-2900)*(0.17)=6811

Answer:

[tex]\frac{25}{16}[/tex]

Step-by-step explanation:

[tex](-\frac{5}{4})^2\\\\ \text {Apply power of a fraction rule: } (\frac{a}{b})^x=\frac{a^x}{b^x}\\\\(-\frac{5}{4})^2 = \frac{-5^2}{4^2}=\frac{25}{16}\\\\\boxed{(-\frac{5}{4})^2=\frac{25}{16}}[/tex]

Answer:

1/3

Step-by-step explanation:

hello,

probability of 1 = 1/6

probability of 2 = 1/6

probability of 1 or 2 = 1/6+1/6 as probability of 1 and 2 = 0

so the answer is 2/6=1/3

Answer:

2/5

Step-by-step explanation:

2 red, 3 yellow, 4 green, 6 blue marbles. = 15 marbles

P( blue) = blue / total

             =6/15

             =2/5

Answer:

(56 )log3 x

Step-by-step explanation:

We know that  log a^b = bloga

8log3 x^7 = (7*8 )log3 x = 56 log3 x

Answer:

56 log3 x

Step-by-step explanation:

8 log3 x^7 can be rewritten as log3 x^(7*8) = log3 x^56 or 56 log3 x

Step-by-step explanation:

sin²α − sin⁴α

Factor out sin²α.

sin²α (1 − sin²α)

Use Pythagorean theorem.

(1 − cos²α) cos²α

Distribute.

cos²α − cos⁴α

Answer:

a. They are empty set.

b. they are finite set.

Solution,

a. A={ prime number between 6 and 7}

There are not any number between 6 and 7.

So there will be no Elements.

A={ }

It is empty set.

Empty set are those set which doesn't contain any Element.

b.B={multiples of 2 less than 20}

B={2,4,6,8,10,12,14,16,18}

It is a finite set.

Finite set are those set which we can count easily.

Hope this helps...

Good luck on your assignment...

Answer:

[tex]\boxed{\sf \ \ \ \dfrac{4}{5} \ \ \ }[/tex]

Step-by-step explanation:

when the equation is like y = ax + b

the slope is a

in this case we have

[tex]y \ = \ \dfrac{4}{5}x\ \ - \ 3[/tex]

so the slope is

[tex]\dfrac{4}{5}[/tex]

Answer:

0.48% probability that all four are new

Step-by-step explanation:

The homes are chosen "without replacement", which means that after a home is visited, it is not elegible to be visited again. So we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

Total of 10 homes, so N = 10.

We want 4 new, so x = 4.

In total, there are 4 new, so k = 4.

Sample of four homes, so n = 4.

Then

[tex]P(X = 4) = h(4,10,4,4) = \frac{C_{4,4}*C_{6,0}}{C_{10,4}} = 0.0048[/tex]

0.48% probability that all four are new

The calculated probability is "0.0048".

From a total of [tex]N=10\ \ \text{homes},\ r=4[/tex] are completely new while 6 are not.

Let X indicate the series of innovative dwellings in a sample of[tex]n=4[/tex] homes.

X is the next step. Algebraic distribution for parameters[tex]N=10, r=4, \ \ and\ \ n = 4[/tex] Only integer values in this range: can be given to a hypergeometric random variable.

[tex]\to [ \max {(0,\,n+r-N)}, \min {(n,\,r)} ] = [ 0, 4 ] \\\\ \to P( X = 4) \\\\ \to N=10\\\\ \to r=4\\\\ \to n = 4[/tex]

[tex]\to \bold{P(X=k) = \dfrac{\binom{r }{ k}{\binom{N-r} {n-k}}}{\binom{N}{n}}} \\\\\to P(X =4 ) = \dfrac{\binom{r }{ 4}{\binom{N-r} {n-4}}}{\binom{N}{n}} \\\\[/tex]

                   [tex]= \dfrac{\binom{4 }{ 4}{\binom{10-4} {4-4}}}{\binom{10}{4}}\\\\= \dfrac{\binom{4 }{ 4}{\binom{6} {0}}}{\binom{10}{4}} \\\\= \dfrac{ 1 \times 1}{210} \\\\= \dfrac{ 1}{210} \\\\= \dfrac{1}{210} \\\\= 0.004762[/tex]

Using the excel function:

[tex]\text{HYPGEOM.DIST( k, n, r, N. cumulative)}[/tex]  for calculating the [tex]P_{X} (4)[/tex]:

[tex]\to \text{HYPGEOM.DIST( 4, 4, 4, 10, FALSE) = 0.0047619047619}[/tex]

[tex]\to P(X= 4 ) = \frac{1}{210} = { 0.0048 }[/tex]

Find out more information about the probability here:

brainly.com/question/2321387

Answer:

[tex]j^4k[/tex]

Step-by-step explanation:

[tex]3j^4k-2jk^3+jk^3-2j^4k+jk^2\\2j^4k-2j^4k-2jk^3+jk^3+jk^3\\j^4k[/tex]

Answer:

4

Step-by-step explanation:

give me brainliest

Answer: 15

Step-by-step explanation:

to find the area multiply the length by height

in this case it’s 5ft and 3ft

5 • 3 = 15

A=15