The domain of the following relation has how many elements?
[(1/2, 3.14/6), (1/2, 3.14/4), (1/2, 3.14/3), (1/2,3.14/2)]

a. 0
b. 1
c. 4​

Answer: The AP = 1, ⁷/₂, 6, ¹⁷/₂, 11 ..............

Step-by-step explanation:

From the first statement,

S₅ = ⁵/₂(2a + ( n - 1 )d }    = 30

       5(2a  + 4d )d           = 60

       10a    + 20d             = 60

reduce to lowest term to easy calculation by dividing through by 10

                      a + 2d       = 6 -----------------------------------1

second statement

sum of the next 4 terms inclusive

T₉  = ⁹/₂(2a + 8d )   = 69

        9(2a  + 8d )    = 30 + 69

            18a + 72d   = 99 x 2

            18a + 72d   = 198

divide through by 18 to reduce to lowest time

                a  + 4d    = 11 ------------------------------------------2

Now solve the two equation simultaneously to find a and d

                 a + 2d = 6

                 a + 4d = 11

                     -2d  = -5

                          d = ⁵/₂.

Now substitute  for d to get a

               a  + 2(⁵/₂) = 6

                a + 5       = 6

                           a   = 6 - 5

                            a = 1.

Therefore the AP = 1 , ⁷/₂ , 6 , ¹⁷/₂ , 11 , ..............

The AP if, The sum of the first 5 terms of an AP is 30 and the sum of the four terms from T6 to T9 is 69, is 1, ⁷/₂, 6, ¹⁷/₂, 11, and so on.

An ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is determined by the number of items.

Given:

The sum of the first 5 terms of an AP is 30,

Write the equations as shown below,

S₅ = ⁵/₂(2a + ( n - 1 )d }  = 30

5(2a  + 4d )d = 60

10a    + 20d = 60

reduce to lowest term to easy calculation by dividing through by 10

a + 2d = 6

T₉  = ⁹/₂(2a + 8d )   = 69  (sum of the next 4 terms inclusive)

9(2a  + 8d )  = 30 + 69

18a + 72d  = 99 x 2

18a + 72d = 198

a  + 4d    = 11

Solve the equation as shown below,

d = ⁵/₂, and   a = 1.

Therefore, the AP = 1, ⁷/₂, 6, ¹⁷/₂, 11, and so on.

To know more about the sequence:

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Answer:

Known:

• a book have front, back and 200 pages

• front= 0.7 mm

• back= 0.7 mm

• each page= 0,14 mm

ask:

calculate the minimum thickness...?

answer:

a. 200 p × 0,14 = 28 mm

b. front + back = 0.7+0.7= 1.4 mm

Thickness= 28+1,4 = 29,4 mm

I hope this helps

if u have question let me know in comments^_^

Answer:

measure

Step-by-step explanation:

The collection of quantitative or numerical data that describes a property of an object or event is called a measured/measurement.

The SI Unit is a metric system. An example of an SI Unit is the kilogram, centimeter, second, etc.

Measurements are made by comparing a particular quantity with an SI unit or assigning numbers to certain objects in a way that reflects its value.

Answer:

the answer is 4

Step-by-step explanation:

so 1 rotation is like a circle 1 unit circle requires 4 quadrant to be in this is the most simplified i can get

Answer:

Solution : 4

Step-by-step explanation:

The question asks us how many polar coordinates are possible for one rotation. For one rotation there will be 4 polar coordinates, one present in each quadrant such that,

( r, theta ), ( r, theta ), ( - r, theta ), ( - r, theta )

Respectively if theta was q say,

( r, q ), ( r, - q ), ( - r, q ), ( - r, -q )

Therefore there are 4 sets of polar coordinates for one rotation, in each of the 4 quadrants.

Answer:

He should find 24 defective lightbulbs.

Step-by-step explanation:

1. Divide the number of defective bulbs by the total number of bulbs for each section.

2. Make sure the number you get is the same each time.

3. Divide the guessed number of bulbs (24) by the total number of bulbs (336)

4. If the number you got for step 4 matches the number you got for step 3, then he is right

Answer:

The answer is A

Step-by-step explanation:

on NCCA

Answer: A,C, and D

Step-by-step explanation:

Answer:

the answer to this question may be option B, C and D

Answer:

The probability that none of the LED light bulbs are​ defective is 0.7374.

Step-by-step explanation:

The complete question is:

What is the probability that none of the LED light bulbs are​ defective?

Solution:

Let the random variable X represent the number of defective LED light bulbs.

The probability of a LED light bulb being defective is, P (X) = p = 0.03.

A random sample of n = 10 LED light bulbs is selected.

The event of a specific LED light bulb being defective is independent of the other bulbs.

The random variable X thus follows a Binomial distribution with parameters n = 10 and p = 0.03.

The probability mass function of X is:

[tex]P(X=x)={10\choose x}(0.03)^{x}(1-0.03)^{10-x};\ x=0,1,2,3...[/tex]

Compute the probability that none of the LED light bulbs are​ defective as follows:

[tex]P(X=0)={10\choose 0}(0.03)^{0}(1-0.03)^{10-0}[/tex]

                [tex]=1\times 1\times 0.737424\\=0.737424\\\approx 0.7374[/tex]

Thus, the probability that none of the LED light bulbs are​ defective is 0.7374.

Answer:

5/2

Step-by-step explanation:

5^(-3). 2^2.5^6 / (2^3.5^2)

By the law of indices,

=5^(-3+6-2).2^(2-3)

=5^1.2^(-1)

=5. 2^-1

=5/2

Answer:

9%

Step-by-step explanation:

12x=6y eq 1

18x=9y eq 2

Answer:

m = 15

Step-by-step explanation:

m/9 + 2/3 = 7/3

Subtract 2/3 from each side

m/9 + 2/3  -2/3= 7/3 -2/3

m/9 = 5/3

Multiply each side by 9

m/9 *9 = 5/3 *9

m = 15

Answer:

d. 60000000000

Step-by-step explanation:

Answer:

The answer is D. 60,000,000,000

Step-by-step explanation:

Answer:   maximum "safe"  Force = 415.58 N

Step-by-step explanation:

Length = 1.2 m

lower bound is 1.15 (because it rounds up to 1.2)

upper bound is 1.24 (because it rounds down to 1.2)

Note: 1.25 would round up to 1.3

width = 2.5 m

lower bound is 2.45 (because it rounds up to 2.5)

upper bound is 2.54 (because it rounds down to 2.5)

Note: 2.55 would round up to 2.6

Pressure = 150 N/m²

lower bound is 147.5 (because it rounds up to 150)

upper bound is 152.4 (because it rounds down to 150)

Note: 152.5 would round up to 155

Max "safe" Force means minimum Area and minimum Pressure (lower bounds)

Force = Area x Pressure

           = length x width x Pressure

           = 1.15 x 2.45 x 147.5

           = 415.58

Answer:

A) P(Betty is first in line and mary is last) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))

B) The method used is Relative frequency approach.

Step-by-step explanation:

From the question, we are told a sample of n kids line up for recess.

Now, the order in which they line up is random with each ordering being equally likely. Thus, this means that the probability of each kid to take a position is n(total of kids/positions).

Since we are being asked about 3 kids from the class, let's assign a letter to each kid:

J: John

B: Betty

M: Mary

A) Now, we want to find the probability that Betty is first in line or Mary is last in line.

In this case, the events are not mutually exclusive, since it's possible that "Betty is first but Mary is not last" or "Mary is last but Betty is not first" or "Betty is the first in line and Mary is last". Thus, there is an intersection between them and the probability is symbolized as;

P(B₁ ∪ Mₙ) = P(B₁) + P (Mₙ) - P(B₁ ∩ Mₙ) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))

Where;

The suffix 1 refers to the first position while the suffix n refers to the last position.

Also, P(B₁ ∩ Mₙ) = P(B₁) × P(Mₙ/B₁)

This is because the events "Betty" and "Mary" are not independent since every time a kid takes his place the probability of the next one is affected.

B) The method used is Relative frequency approach.

In this method, the probabilities are usually assigned on the basis of experimentation or historical data.

For example, If A is an event we are considering, and we assume that we have performed the same experiment n times so that n is the number of times A could have occurred.

Also, let n_A be the number of times that A did occur.

Now, the relative frequency would be written as (n_A)/n.

Thus, in this method, we will define P(A) as:

P(A) = lim:n→∞[(n_A)/n]

Given this pair of probabilities, the probability that Mary is the first is  n(A) = n-1!, while the probability that Betty is last is  n(A) = n-1!

There are n! ways of making this arrangement

We have probability of A: Betty is the first person in this line

Probability of B: Mary is the last person

A U B = p(A) + p(B) - p(A ∩ B)

n(A) = n-1 that is given that Betty is the first person on the line.

then n(A) = n-1!

As the last person on the line P(B) = n-1!

Probability of (A∩B) =( n-2)!  this has Mary as the first and Betty as the last person.

Remaining students that would have to be on this line are n-2

Prob(A∪B) = n(A ∪ B)/n!

= 2(n-2)/n(n-1)

This is the theory that talks about the chances or the likelihood of an event occuring in a pair of events.

Read more on probability here: https://brainly.com/question/24756209

Answer:

eddfdgdccggģdffcdrrfxddxcvgfx

Answer:

The area of the house is A. 1,108

Answer:

72/n^5r

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

13)

● 2d^3 × c^6 × 8d^5 × c^2

Isolate the similar terms

● (2×8)× (d^3 × d^5)×(c^6×c^2)

● 16 × d^(3+5) × c^(6+2)

● 16 × d^8 × c^8

● 16 × (dc)^8

● 16(dc)^8

■■■■■■■■■■■■■■■■■■■■■■■■■■

● 8n×r^(-4) ×9×n^(-6)×r^3

Isolate the similar terms

● (8×9)× (r^(-4)×r^3) × (n×n^(-6))

● 72 × r^(-4+3) × n^(1-6)

● 72 × r^-1 × n^(-5)

● 72 ×(1/r) × (1/n^5)

● 72/(r×n^5)

Answer:

35/14

Step-by-step explanation: 35/14

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

35/14 is your answer.

Answer:

10 girls.

Step-by-step explanation:

Boys: 5x

Girls: 2x

next... 5x + 2x = 35

7x= 35

x=5

Answer. 10 girls.

Answer:

Within the factors hindering expression in music, tempo is the most important number of factors such as your mood.

Step-by-step explanation:

If one wants to convey a message, they should try these:

a) Use real life

b) introduce symbolism

c) convey sensory disruption, e.t.c.

Hope these helps.

The answer is 1/2 because there are total 10 questions. So, the probability of getting 5 correct answers is 5/10 that is 1/2.

Mark me as brainleist

Answer:

The 99%  confidence interval is  [tex]97.94 < \mu < 98.26[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  110

     The  sample mean is  [tex]\= x = 98.1 \ F[/tex]

       The standard deviation is  [tex]\sigma = 0.64 \ F[/tex]

Given that the confidence level is  99% the level of significance i mathematically 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, the values is  

          [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]

Generally the margin of error is mathematically represented as

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

substituting values

          [tex]E = 2.58 * \frac{ 0.64}{\sqrt{110} }[/tex]

          [tex]E = 0.1574[/tex]

Generally the  99% confidence interval  is mathematically represented as

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

substituting values

             [tex]98.1 - 0.1574 < \mu < 98.1 + 0.1574[/tex]

             [tex]97.94 < \mu < 98.26[/tex]

Answer:

Step-by-step explanation:

Answer:

90% confidence interval for the difference between the two population means

( -23.4166 , -6.5834)

Step-by-step explanation:

Step(i):-

Given first sample size n₁ = 100

Given mean of the first sample x₁⁻ = 178

Standard deviation of the sample S₁ = 35

Given second sample size n₂= 100

Given mean of the second sample x₂⁻ = 193

Standard deviation of the sample S₂ = 37

Step(ii):-

Standard error of two population means

        [tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{s^{2} _{1} }{n_{1} }+\frac{s^{2} _{2} }{n_{2} } }[/tex]

       [tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{(35)^{2} }{100 }+\frac{(37)^{2} }{100 } }[/tex]

        [tex]se(x^{-} _{1} -x^{-} _{2} ) = 5.093[/tex]

Degrees of freedom

ν  = n₁ +n₂ -2 = 100 +100 -2 = 198

t₀.₁₀ = 1.6526

Step(iii):-

90% confidence interval for the difference between the two population means

[tex](x^{-} _{1} - x^{-} _{2} - t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2}) , x^{-} _{1} - x^{-} _{2} + t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2})[/tex]

(178-193 - 1.6526 (5.093) , 178-193 + 1.6526 (5.093)

(-15-8.4166 , -15 + 8.4166)

( -23.4166 , -6.5834)

Answer:

[tex]x {}^{2} - 2x = 48[/tex]

[tex]x { }^{2} - 2x - 48 = 0[/tex]

using quadratic formula,

[tex] - b \frac{ + }{ - } \sqrt{b {}^{2} - 4ac} \div 2a[/tex]

[tex]2 + \sqrt{196} \div 2[/tex]

[tex]2 + 14 \div 2[/tex]

[tex]x = 8[/tex]

or

[tex]x = - 6[/tex]

Answer:

The temperature of the 5th day was 3°C

Step-by-step explanation:

Mean temperature of the first 4 days = 8°C

Note that:

Mean = Sum of temperatures ÷ number of days

∴ 8 = sum of temperature ÷ 4

[tex]= 8 = \frac{sum\ of\ temperatures}{4}[/tex]

[tex]= sum\ of\ temperatures\ = 8\ \times\ 4 = 32[/tex]

Therefore the sum of the first 4 days = 32

Let the temperature of the next day (the fifth day) be m

Hence,

sum of the temperatures of first 5 days = 32 + m - - - - (1)

Next, the sum of the first 5 days can be calculated from the given average of the first 5 days as follows:

Mean temperature of the first 5 days = 7

[tex]Mean = \frac{sum\ of\ temperatures}{number \ of\ days}\\\\7 = \frac{sum\ of\ temperatures}{5} \\sum\ of\ temperatures\ = \ 7\ \times\ 5\ = 35\\sum\ of\ temperature\ of\ the\ first\ 5\ days\ =\ 35 - - - - - (2)[/tex]

Now, you will notice that equation (1) = equation (2)

∴ 32 + m = 35

m = 35 - 32 = 3

therefore, the temperature of the 5th day was 3°C

Answer:

53

Step-by-step explanation:

i used an angle of 45 degrees.

Distance from ground = 3feets

Angle = 45⁰

U is the initial velocity = 80ft/sec

g = 32

The question wants us to vfind maximum height

We have

r(t) = (80cos45⁰)ti + [3 + 80sin45⁰]t - 0.5(32)t²

We know cos 45 is also sin45 = 1/√2

r(t) = (40√2)ti + [3+40√2]t - 16t²

When we differentiate with respect to t:

r'(t) = (40√2)i + (40√2 - 32t)

= 40√2 =32t

t = 40√2/32

t= 20√2/16

We put the value of t into (3 + 40√2)t -16t²

When we substitute and simplify this we have

3 + 56.57 + 1.77 -16 +8

= 53.34

Which is approximately 53.

Answer:

Nothing further, the simplest answer is 32 1/2

Step-by-step explanation:

The required value of the tanФ is given as -3/4. C option is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.

here,
Tan(180 - Ф) = -tanФ = perpendicular / base

From figure,  perpendicular= 12 and  base = 16
-tanФ = 12 / 16
tanФ = -3/4

Thus, the required value of the tanФ is given as -3/4. C option is correct.

Learn more about trigonometry equations here:

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Answer:

The minimum sample size is  [tex]n =135[/tex]

Step-by-step explanation:

From the question we are told that

   The confidence interval is [tex]( lower \ limit = \ 0.44,\ \ \ upper \ limit = \ 0.51)[/tex]

    The margin of error is  [tex]E = 0.1[/tex]

Generally the sample  proportion can be mathematically evaluated as

     [tex]\r p = \frac{ upper \ limit + lower \ limit }{2}[/tex]

    [tex]\r p = \frac{ 0.51 + 0.44}{2}[/tex]

    [tex]\r p = 0.475[/tex]

Given that the confidence level is  98% then the level of significance can be mathematically evaluated as

         [tex]\alpha = 100 - 98[/tex]

        [tex]\alpha = 2\%[/tex]

        [tex]\alpha =0.02[/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} } = 2.33[/tex]

Generally the minimum sample size is evaluated as

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

     [tex]n =[ \frac { 2.33}{0.1} ]^2 * 0.475(1- 0.475 )[/tex]

     [tex]n =135[/tex]

Answer:

The  t-statistic is [tex]t = 0.6956[/tex]

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 22 \ minutes[/tex]

       The standard deviation is  [tex]s = 7.043[/tex]

       The  given data is  23, 35, 17, 30, 20, and 19.

Generally the sample mean is mathematically evaluated as

      [tex]\= x = \frac{23+ 35+17+ 30+ 20+ 19 }{6}[/tex]

     [tex]\= x =24[/tex]

The t-statistic is mathematically evaluated as

       [tex]t = \frac{ \= x - \mu }{\frac{s}{ \sqrt{n} } }[/tex]

=>   [tex]t = \frac{ 24 - 22 }{\frac{ 7.043}{ \sqrt{6} } }[/tex]

=>   [tex]t = 0.6956[/tex]

Answer: 0.70

Step-by-step explanation:

Answer:

1. a)

2. e)

3. c)

Step-by-step explanation:

1.

HD^2 = 9^2 - 7^2

HD^2 = 32

AD^2 = HD^2 + 2^4

AD^2 = 36

AD = 6

2.

PT^2 = 8(8 + OE)

144 = 64 + 8OE

OE = 10

R = OE = 10

3.

x^2 = 41^2 - 9^2

x = 40