Solve for x. Question 12 options: A) 8 B) 5 C) 14 D) 10

Answer:

the probability of no defects in 10 feet of steel = 0.1353

Step-by-step explanation:

GIven that:

A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two.

Let consider β to be the average value for defecting

So;

β = 2

Assuming Y to be the random variable which signifies the anticipated number of defects in a 10-foot segment of this roll.

Thus, y follows a poisson distribution as number of defect is infinite with the average value of β = 2

i.e

[tex]Y \sim P( \beta = 2)[/tex]

the probability mass function can be represented as follows:

[tex]\mathtt{P(y) = \dfrac{e^{- \beta} \ \beta^ \ y}{y!}}[/tex]

where;

y =  0,1,2,3 ...

Hence,  the probability of no defects in 10 feet of steel

y = 0

[tex]\mathtt{P(y =0) = \dfrac{e^{- 2} \ 2^ \ 0}{0!}}[/tex]

[tex]\mathtt{P(y =0) = \dfrac{0.1353 \times 1}{1}}[/tex]

P(y =0) = 0.1353

Answer:

Step-by-step explanation:

Hello, this is false.

The first step of a mathematical induction proof is to prove the statement for the initial value, which is most of the time for n = 0 or n = 1.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

Initial population in 2018 = 25,000

Annual growth rate (in %) = 4%

Yearly Increment in population = 4% of 25000

= 4/100 * 25000

= 250*4

= 1000

This means that the population increases by 1000 on yearly basis.

To determine what the  population will be in 2033, we need to first know the amount of years we have between 2018 and 2033.

Amount of years we have between 2018 and 2033 = 2033-2018

= 15 years

After 15 years, the population will have increased by 15*1000 i.e 15,000 more than the initial population.

Hence the population in 2033 will be Initial population + Increment after 15years = 25,000+15000 = 40,000 population.

Answer:

[tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]

Step-by-step explanation:

Given

[tex]log_{17}(52.875)[/tex]

Required

Convert to base 10

To do this, we make use of the following logarithm laws;

[tex]log_ba = \frac{log_{10}a}{log_{10}b}[/tex]

In the given parameters;

[tex]a = 52.875[/tex]

[tex]b = 17[/tex]

Substitute these values in [tex]log_ba = \frac{log_{10}a}{log_{10}b}[/tex]

[tex]log_{17}52.875 = \frac{log_{10}52.875}{log_{10}17}[/tex]

Represent as a ratio

[tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]

Hence;

[tex]log_{17}(52.875)[/tex] is represented as [tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]

Expression  [tex]log_{17} 52.875[/tex] can be written as in form of ratio of log  [tex]\frac{log_{10} 52.875}{log_{10} 17}[/tex] .

Any logarithmic expression [tex]log_{a} b[/tex] can we written as in form of ratio of log on base 10.

                   [tex]log_{a} b=\frac{log_{10} b}{log_{10} a}[/tex]

Here logarithmic expression is,  [tex]log_{17} 52.875[/tex] comparing with above expression.

We get,    [tex]b=52.875,a=17[/tex]

Substitute values of a and b in above expression.

 We get,      [tex]log_{17} 52.875=\frac{log_{10} 52.875}{log_{10} 17}[/tex]

Learn more:

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Answer:

680

Step-by-step explanation:

Number of red beans = 30

Number of Blue beans = 30

Number of green beans = 30

How many color combinations of 15 beans have at least 6 green beans?

Since at least 6 of the beans must be green,

Then (15 - 6) = 9

Then, the remaining 9 could be either red, blue or green.

Therefore, C(9 + (9 - 1), 3)

C(17, 3) = 17C3

nCr = n! ÷ (n-r)! r!

17C3 = 17! ÷ (17 - 3)! 3!

17C3 = 17! ÷ 14!3!

17C3 = (17 * 16 * 15) / (3 * 2)

17C3 = 4080 / 6

17C3 = 680 ways

Using the combination formula, it is found that there are 17,157,323,000,000,000 color combinations of 15 beans have at least 6 green beans.

The order in which the beans are chosen is not important, hence, the combination formula is used to solve this question.

Combination formula:

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

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

Th total number of combinations of 15 beans from a set of 30 + 30 + 30 = 90 is:

[tex]C_{90,15} = \frac{90!}{15!75!} = 45795674000000000[/tex]

With less than 6 green, we have:

0 green:

[tex]C_{30,0}C_{60,15} = \frac{60!}{15!45!} = 53194089000000[/tex]

1 green:

[tex]C_{30,1}C_{60,14} = \frac{30!}{1!29!} \times \frac{60!}{14!46!} = 520376960000000[/tex]

2 green:

[tex]C_{30,2}C_{60,13} = \frac{30!}{2!28!} \times \frac{60!}{13!47!} = 2247585600000000[/tex]

3 green:

[tex]C_{30,3}C_{60,12} = \frac{30!}{3!27!} \times \frac{60!}{12!48!} = 5681396900000000[/tex]

4 green:

[tex]C_{30,4}C_{60,11} = \frac{30!}{4!26!} \times \frac{60!}{11!49!} = 9391696900000000[/tex]

5 green:

[tex]C_{30,5}C_{60,10} = \frac{30!}{5!25!} \times \frac{60!}{10!50!} = 10744101000000000[/tex]

Hence, the total for the number of combinations with less than 5 green is:

[tex]53194089000000 + 520376960000000 + 2247585600000000 + 5681396900000000 + 9391696900000000 + 10744101000000000 = 28638351000000000[/tex]

Subtracting the total amount of combinations from the number with less than 5 green, the number of combinations with at least 6 green is:

[tex]T = 45795674000000000 - 28638351000000000 = 17157323000000000[/tex]

There are 17,157,323,000,000,000 color combinations of 15 beans have at least 6 green beans.

A similar problem is given at https://brainly.com/question/24437717

Answer:

D

Step-by-step explanation:A set is said to be closed under an operation when the application of the operation between any two elements of the set leads to an element that belongs to the same set. If a set is closed under an operation, it is said to have the closure property of that operation. When we combine two rational expressions by adding, subtracting, multiplying, or dividing, we get a rational expression. This pattern indicates that rational expressions are closed for all four operations.

Since they are multiples if 12

The possibilities are

12, 12, 156

12,24,144

12,36,132

12,48,120

12,60,108

12,72,96

12,84,84

24,24,132

24,36,120

24,48,108

24,60,96

24,72,84

36,36,108

36,48,96

36,60,84

36,72,72

48,48,84

48,60,72

60,60,60

Hence the probability is 1/19 or 0.0526

Answer:

D). (-4,-8)​

Step-by-step explanation:

An image at (8,-4) if rotated at an angle of 90° wipl have another location.

First of all, an image at (8,-4) is in the fourth quadrant, and if it's to rotate clockwise at 90° iths supposed to be in the third quadrant.

And in the third quadrant both x and y is negative.

So the new position is at (-4,-8)​

Answer:

The 95% confidence interval is  [tex]10.5 < \mu <13.3[/tex]

Step-by-step explanation:

From the question we are told that

     The  sample size is  [tex]n = 41[/tex]

      The  sample mean is  [tex]\= x = 11.9 \ hr[/tex]

       The standard deviation is  [tex]\sigma = 4.5[/tex]

For  a  95% confidence interval the confidence level is  95%

Given that the confidence level is 95% then the level of significance can be mathematically represented as

                  [tex]\alpha = 100 - 95[/tex]

                  [tex]\alpha = 5 \%[/tex]

                  [tex]\alpha = 0.05[/tex]

Next we obtain the critical values of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table

     The values is

                             [tex]Z_{\frac{\alpha }{2} } = 1.96[/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 = 1.96 * \frac{ 4.5 }{ \sqrt{41} }[/tex]  

                           [tex]E = 1.377[/tex]

The 95% confidence interval is mathematically represented as

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

substituting values

         [tex]11.9 - 1.377 < \mu <11.9 + 1.377[/tex]

         [tex]10.5 < \mu <13.3[/tex]

Answer:

The answer is

Step-by-step explanation:

To find the equation of the line that passes through two points , first find the slope and then use the formula

y - y1 = m(x - x1)

where m is the slope

(x1 , y1) are any of the points

To find the slope of the line using two points we use the formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Slope of the line using points

(2, -7) and (8, -4) is

Now the equation of the line using point (2 , - 7) and slope 1/2 is

We have the final answer as

Hope this helps you

Answer:   He must sell 7 cabinets.

Step-by-step explanation:

So it gives us the equations y= 400x + 1400  and the equations  y=600x and to find the break even point we need to set the two equations equal each other to solve for x.

400x + 1400 = 600x

-400x               -400x

1400 = 200x

 x = 7    

Answer: blank 1:  3   Blank 2:  8   blank 3:  1.5    blank 4:   0.25

Step-by-step explanation:

5 times 8=15

4 times 8=32

6 times 1.5=9

12 times 0.25=3

The complete equation is

5⋅____3__=15

4⋅___8___=32

6⋅___1.5___=9

12⋅__0.25____=3

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number.

Multiplication Formula

The multiplication formula is expressed as, Multiplicand × Multiplier = Product; where:

Learn more about multiplication here:

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Answer:

Length = Width = 7 cm

Step-by-step explanation:

Volume of a triangular prism is represented by the formula,

Volume = (Area of the triangular base) × height

588 = 49 × h

h = [tex]\frac{588}{49}[/tex]

h = 12 cm

We have to find the side length of a rectangular prism having same volume.

Volume = Area of the rectangular base × height

588 = (l × b) × h [l = length and b = width ]

588 = (l × b) × 12

l × b = 49 = 7 × 7

Therefore, length = width = 7 cm may be the side lengths of the rectangular prism to have the same volume.              

Answer:

[tex]\frac{5x-4}{x(x^2+7)^2} = \frac{A}{x} + \frac{Bx+C}{x^2+7} + \frac{Dx+E}{(x^2+7)^2}[/tex]

Step-by-step explanation:

Given the expression [tex]\frac{5x-4}{x(x^2+7)^2}[/tex], we are to re-write the expression in form of a partial fraction.

Before we write in form of a partial fraction, we need to note the expression at the denominator. Since the expression in parenthesis is a quadratic equation, the equivalent numerator must be a linear expression.

Also the quadratic equation is a repeated form since it is squared. This means that we are to repeat the quadratic equation twice when writing as a partial fraction.

[tex]\frac{5x-4}{x(x^2+7)^2} = \frac{A}{x} + \frac{Bx+C}{x^2+7} + \frac{Dx+E}{(x^2+7)^2}[/tex]

From the above partial fraction, it can be seen that x² + 7 in parenthesis was repeated twice and their equivalent expressions at the numerator are  both linear i.e Bx+E and Dx+ E where A, B, C, D and E are the unknown constant.

Answer:

the answer is c

Step-by-step explanation:

Answer: a. 43

b. 27

c.  34.8

d. 45

e. 17.72

f. First quartile = 23

Second quartile = 27

Third quartile =43

Step-by-step explanation:

The given set of data:  24, 43, 65, 12, 31, 78, 43, 24, 25, 18, 29, 53, 18, 23, 20, 43, 53, 25

Arrange in Ascending order:

12 ,18,18 , 20 ,23 ,24 , 24 ,25 , 25 , 29, 31, 43, 43 , 43 , 53 , 53, 65 , 78

Total data points: n= 18 ( even)

a. Mode= Most repeated data value = 43

i.e. mode =43

b. Median = [tex]\dfrac{(\frac{n}{2})^{th}\text{term}+(\frac{n}{2}+1)^{th}\text{term}}{2}[/tex]

[tex]=\dfrac{(\frac{18}{2})^{th}\text{term}+(\frac{18}{2}+1)^{th}\text{term}}{2}\\\\=\dfrac{9^{th}\text{term}+10^{th}\text{term}}{2}\\\\=\dfrac{25+29}{2}\\\\=27[/tex]

i.e. median = 27

c. Mean = (sum of data points)÷n

Sum =12+18+18 + 20 +23 +24 + 24 +25 + 25 + 29+ 31+ 43+ 43 + 43 + 53 + 53+ 65 + 78=627

Mean = 627 ÷ 18 ≈34.8

i.e. Mean = 34.8

d. Mid range = [tex]\dfrac{\text{Maximum value +Minimum value}}{2}[/tex]

[tex]=\dfrac{78+12}{2}\\\\=\dfrac{90}{2}\\\\=45[/tex]

e. Standard deviation =[tex]\sqrt{\dfrac{\sum (x-mean)^2}{n}}[/tex][tex]\sum (x-\mean)^2=(12-34.8)^2+(18-34.8)^2+(18 -34.8)^2+( 20 -34.8)^2+(23 -34.8)^2+(24 -34.8)^2+( 24 -34.8)^2+(25 -34.8)^2+2( 25 -34.8)^2+( 29-34.8)^2+( 31-34.8)^2+( 43-34.8)^2+( 43 -34.8)^2+( 43 -34.8)^2+( 53 -34.8)^2+( 53-34.8)^2+( 65 -34.8)^2+( 78-34.8)^2\\\\=5654.56[/tex]

[tex]\sqrt{\dfrac{5654.56}{18}}=\sqrt{314.1422}\approx17.72[/tex]

f. First quartile = Median of first half (12 ,18,18 , 20 ,23 ,24 , 24 ,25 , 25)

= 23  (middle most value)

Second quartile = Median = 27

Third quartile = Median of second half (29, 31, 43, 43 , 43 , 53 , 53, 65 , 78)

= 43 (middle most value)

Correction:

P(AΔB) = P(A) + P(B) - 2P(AnB)

is what could be proven using the axioms of probability, and considering the case of symmetric difference given.

Answer:

P(AΔB) = P(A) + P(B) - 2P(AnB)

Has been shown.

Step-by-step explanation:

We are required to show that

P(AUB) = P(A) + P(B) - 2P(AnB)

directly using the axioms of probability.

Note the following:

AUB = (AΔB) U (AnB)

Because (AΔB) U (AnB) is disjoint, we have:

P(AUB) = P(AΔB) + P(AnB)..................(1)

But again,

P(AUB) = P(A) + P(B) - P(AnB)...............(2)

Comparing (1) with (2), we have

P(AΔB) + P(AnB) = P(A) + P(B) - P(AnB)

P(AΔB) = P(A) + P(B) - 2P(AnB)

Where AΔB is the symmetric difference of A and B.

Answer:

8 M&Ms and 9 Candy Bars

Step-by-step explanation:

$15 dollars could buy 15 candy bars, and there are 17 pieces of candy total.

Prioritizing the number of bars:

0.75 * 2 = 1.50

1.50 * 2 = 3

At least $3 were spend on M&Ms, meaning 4 M&Ms and 12 candy bars, which is only 16 candy pieces...

8 M&Ms and 9 candy bars is equivalent to 17 total candy pieces.

Answer:

0

Step-by-step explanation:

Answer:

≈ -0.821

Step-by-step explanation:

Given:

Then, the sample proportion is:

Hypothesis test:

Test statistics:

Answer:

Step-by-step explanation:

For b

To find side b we use the sine rule

a = 7

A = 23°

B = 32°

b = ?

Substitute the values into the above formula

That's

Divide both sides by sin 23°

b = 9.493573

To find side c we use sine rule

C = 125°

So we have

Divide both sides by sin 23°

c = 14.67521

Hope this helps you

Hello, please consider the following.

[tex]\displaystyle \forall x \in \mathbb{R}\\\\\dfrac{e^{2x}-1}{e^x-1}\\\\=\dfrac{(e^x)^2-1^2}{e^x-1}\\\\=\dfrac{(e^x-1)(e^x+1)}{e^x-1}\\\\=e^x+1\\\\\text{So, we can find the limit.}\\\\\lim_{x\rightarrow 0} \ {\dfrac{e^{2x}-1}{e^x-1}}\\\\=\lim_{x\rightarrow 0} \ {e^x+1}\\\\=e^0+1\\\\\large \boxed{\sf \bf \ =2 \ }[/tex]

Thank you

Answer:

The answer is "[tex]AB= \left[\begin{array}{cc} -2 &51 \\-8&33\\0&27&\end{array}\right][/tex]"

Step-by-step explanation:

If the value of A and B is:

[tex]A= \left[\begin{array}{cc}-1&6\\-4&5\\0&3\end{array}\right][/tex]

[tex]B=\left[\begin{array}{cc}2&3\\0&9\end{array}\right][/tex]

Find the value of A[tex]\times[/tex]B:

[tex]AB =\left[\begin{array}{cc}-1 \times 2+6 \times 0 &-1 \times 3+6 \times 9\\ -4 \times 2+5 \times 0& -4 \times 3+5 \times 9\\ 0 \times 2+3 \times 0&-1 \times 2+3\times 9\end{array}\right] \\ \\\\AB =\left[\begin{array}{cc}-2+0 &- 3+54\\ -8+0& -12+45\\ 0+ 0&-2 +27\end{array}\right] \\ \\[/tex]

[tex]AB= \left[\begin{array}{cc} -2 &51 \\-8&33\\0&27&\end{array}\right][/tex]

Answer:

16 yard line

Step-by-step explanation:

The football team is starting on the 10 yard line. In the first play, they move up to the 24 yard line. Then in the second play, they go back to the 12 yard line since they lost 12 yards. Then in the third play, they gain 4 yards so you add 4 to 12. They end up at the 16 yard line after the third play. This means that they're going to start their fourth play at the 16 yard line.

Answer:

16 yards.

Step-by-step explanation:

They start at 10 yards. They are moving towards the 50 yard line, so gaining yards will add to the 10 yards instead of subtract from the 10 yards.

In the first play, they gain 14 yards. 10 + 14 = 24 yards.

In the second play, they lose 12 yards. 24 - 12 = 12 yards.

In the third play, they gain 4 yards. 12 + 4 = 16 yards, which is where they start their fourth play.

Hope this helps!

Answer:

3/11

Step-by-step explanation:

In the above question, we have the following information

Total number of balls = 12

White balls = 4

Blue balls = 3

Red balls = 5

We are to find the chance of probability that if we select 3 balls, all the three are selected.

Hence,

Probability ( all the three balls are selected) = P(White ball) × P(Blue ball) × P( Red ball)

Probability ( all the three balls are selected) = 4/12 × 3/11 × 5/10

= 60/1320

= 1/22

The number of ways by which we can selected all the three balls is a total of 6 ways:

WBR = White, Blue, Red

WRB = White, Red, Blue

RBW = Red, Blue, White

RWB = Red, White, Blue

BRW = Blue, Red, White

BWR = Blue, White, Red

Therefore, the chance that all three are selected :

1/22 × 6 ways = 6/22 = 3/11

Answer:

Step-by-step explanation:

[tex] \frac{2}{5} + p = \frac{4}{5} + \frac{3}{5} p[/tex]

Multiply through by the LCM

The LCM for the equation is 5

That's

[tex]5 \times \frac{2}{5} + 5p = 5 \times \frac{4}{5} + \frac{3}{5}p \times 5[/tex]

We have

2 + 5p = 4 + 3p

Group like terms

5p - 3p = 4 - 2

2p = 2

Divide both sides by 2

We have the final answer as

Hope this helps you

Answer:

0.079

Step-by-step explanation:

According to the given situation, the calculation of the value of k is presented as follows:

[tex]Q(t)= Q_0e^{-kt}\\\\ 0.5Q_0 = Q_0e^{-k(97.7)}\\\\ 0.5 = e^{-k(87.7)}[/tex]

now,

[tex]k = \frac{In0.5}{-87.7}[/tex]

After solving the above equation we will get the value of k.

= 0.079

Therefore for determining the value of k we simply solve the above equation i.e. by considering all the information mentioned in the question

Answer:

3.5e^-0.0079t

Step-by-step explanation:

None, Good luck mate

Answer:

No, each outcome is equally likely regardless of the previous outcome.

Answer:

The second option.

Step-by-step explanation:

The first option consists of a line that extends at both opposite sides to infinity, with no precise end.

The third option is a ray that has an endpoint of A, and extends to infinity towards B.

The fourth option is a line segment. It has two endpoints, B and A.

The second portion is a ray that has an endpoint B, and extends towards A in one direction, to infinity.

The answer is the 2nd option.

Question:

A research center poll showed that 78% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?

The probability that someone does not believe that it is morally wrong to not report all income on tax returns is . (Type an integer or a decimal.)

Answer:

[tex]q = 0.22[/tex]

Step-by-step explanation:

Given

Let p represent the given proportion

p = 78%

Required

Determine the probability that someone holds a contrary belief

Start by converting the given proportion to decimal

[tex]p = 78\%[/tex]

[tex]p = \frac{78}{100}[/tex]

[tex]p = 0.78[/tex]

In probability, the sum of opposite probability is equal to 1

Represent the probability that someone holds a contrary belief with q

So;

[tex]p + q = 1[/tex]

Make q the subject of formula

[tex]q = 1 - p[/tex]

Substitute 0.78 for p

[tex]q = 1 - 0.78[/tex]

[tex]q = 0.22[/tex]

Hence, the probability that someone does not believe is 0.22