Factorise fully for this

Answer:

Step-by-step explanation:

Since she will use 4 groups or class intervals, the the class width would be 20/4 = 5 hours

The class groups would be

1 to 5

5 to 10

10 to 15

15 to 20

The class mark for each class is the average of the minimum and maximum value of each class. Therefore, the class marks are

(1 + 5)/2 = 3

(5 + 10)/2 = 7.5

(10 + 15)/2 = 12.5

(15 + 20)/2 = 17.5

The frequency table would be

Class group Frequency

1 - 5 4

5 - 10 8

10 - 15 6

15 - 20 2

The total frequency is 4 + 8 + 6 + 2 = 20

Answer:

1/3 simplifed.

Step-by-step explanation:

To find the product of 3/7*7/9. We can multiply top and bottom. Top: 3*7=21 Bottom: 7*9=63. Our final answer is just the Top/Bottom= 21/63. We can also simplify this into 1/3 which is our final answer.

Step-by-step explanation:

In mathematics, the absolute value |x|, is the non-negative result of x without regard to its sign.

An absolute function, can never have a negative result.

By this alone, you can solve the question because the inequality is false, and therefore there are zero solutions.

Please see the attachment of f(x) = |x - 7|.

When you look at the graph, you can easily confirm that there is no value which can result in a negative y- coordinate like -2. In fact, that is the whole purpose of any absolute value or function. The result of an absolute function can never be negative.

Answer:

Thats not possible

Step-by-step explanation:

There is no:

Answer:

(-4,-7)

Step-by-step explanation:

Adding 1 to the x and subtracting 3 from the y we get

-5+1= -4

And

-4-3= -7

Answer:

53

Step-by-step explanation:

Plugging in 32 for z, you get:

(32)/2+37=x

16+37=x

x=53

Hope this helps!

The solution of the linear equation z/2 + 37 = x at x at z = 32 will be 53.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given below.

z/2 + 37 = x

Then the solution of the linear equation z/2 + 37 = x at z = 32. Then the equation will be

x = 32/2 + 37

x = 16 + 37

x = 53

Thus, the solution of the linear equation z/2 + 37 = x at z = 32 will be 53.

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Answer:

see below

Step-by-step explanation:

You could write it as 2+2+2+2+2 or 5+5 bc multiplication is like repeated addition.

Answer:

You can use the repeated additional as given below.

Step-by-step explanation:

2+2+2+2+2 or 5+5

Answer:

12

Step-by-step explanation:

8x=96

x=96/8

x=12

Answer:

12

Step-by-step explanation:

8x=96

96/8

x=12

so the the product of 8and 12=96

Answer:

0.9

Step-by-step explanation:

10% is equal to 0.1

The probability of having defective parts in a pile of parts is 0.1

Before the process is stopped, 1 part has to be defective.

In a pile of 9 parts, the probability that a part is defective 0.1 of 9, which is = 0.9 hence, approximately one (1) part will be defective in a pile of 9 parts and the process will be stopped.

Since there was no defective part among the first 6 parts, P(d) was 0

That is, probability of a defective part was zero.

Answer:

C: Multiply the first equation by -2

Step-by-step explanation:

-2 * (x + 3y = 16) = -2x-6y=-32

The resulting equation would be -2x-6y=-32

In the next if you add the two equations, you will successfuly eliminate x and can now solve for y.

-2x-6y=-32

2x + y = -18

Answer:

c

Step-by-step explanation:

x+3y=16________________eqn 1

2x+y=-18_______________eqn 2

multiply first equation by - 2

-2(x+3y=16)

-2x-6y= -32______________eqn 3

using elimination method

-2x-6y= -32

+

2x+y= -18

0-5y= -50

-5y= -50

divide both sides by -5

-5y/5= -50/5

y=10

substitute y in eqn 2 to find the value of x

2x+y= -18

2x+(10)= -18

2x+10= -18

2x= -18-10

2x= -28

divide both sides by 2

2x/2= -28/2

x= -14

Answer:

Dear Laura Ramirez

Answer to your query is provided below

Option D is correct.

Reason - Because of Hinge and Converse of Hinge theorem

Answer:

[tex]\boxed{\ 123 \ dollars\ }[/tex]

Step-by-step explanation:

its value decreases at a rate of 2% each month

in 2 years there are 12*2=24 months

so the Samsung worth [tex]200(0.98)^{24}\\[/tex]

it gives 123 rounded to the nearest dollar

Answer:

$123

Step-by-step explanation:

initial price= $200

value decrease rate= 2% = 0.98 times a month

time = 2 years

current value= $200*0.98²⁴= $123

Answer:

a) 20.44% probability that none of the selected adults say that they were too young to get tattoos.

b) 35.90% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c) 56.34% probability that the number of selected adults saying they were too young is 0 or 1.

d) No

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they say they were too young when they got their tattoos, or they don't say that. Each adult is independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

18% say that they were too young when they got their tattoos.

This means that [tex]p = 0.18[/tex]

Eight adults who regret getting tattoos are randomly selected

This means that [tex]n = 8[/tex]

a. Find the probability that none of the selected adults say that they were too young to get tattoos.

This is P(X = 0).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{8,0}.(0.18)^{0}.(0.82)^{8} = 0.2044[/tex]

20.44% probability that none of the selected adults say that they were too young to get tattoos.

b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.

This is P(X = 1).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{8,1}.(0.18)^{1}.(0.82)^{7} = 0.3590[/tex]

35.90% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c. Find the probability that the number of selected adults saying they were too young is 0 or 1.

Either a. or b.

20.44 + 35.90 = 56.34

56.34% probability that the number of selected adults saying they were too young is 0 or 1.

d. It we randomly select 9 adults. Is 1 a significantly low number who day that they were too young to get tattoos?

Now [tex]n = 9[/tex]

It is significantly low if it is more than 2.5 standard deviations below the mean.

The mean is [tex]E(X) = np = 9*0.18 = 1.62[/tex]

The standard deviation is [tex]\sqrt{V(X)} = \sqrt{n*p*(1-p)} = \sqrt{9*0.18*0.82} = 1.15[/tex]

1 > (1.62 - 2.5*1.15)

So the answer is no.

Answer:

8.55 days for a decay rate parameter of 8.1% per day

Step-by-step explanation:

Assuming a decay rate parameter of  8.1% per day

the general equation for radioactive decay is;

N = N₀e^(-λt)

x - decay constant (λ) - rate of decay 

t-  time 

N - amount remaining after t days , since we are calculating the half life, amount of time it takes for the substance to to be half its original value, its N₀/2

N₀ - amount initially present 

substituting the values 

N₀/2 = N₀e^(-0.081t)

0.5 = e^(-0.081t)

ln (0.5) = -0.081t

-0.693 = -0.081t

t = 0.693 / 0.081  = 8.55

half life of substance is 8.55 days 

Answer: The graph is

The graph is plotted and attached.

A function is a law that relates a dependent and an independent variable.

The function is y = 3/4 x + 5

The slope of the line is (3/4)

and the y intercept is 5.

The graph is plotted and attached with the answer.

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Answer:

5 units

Step-by-step explanation:

P=2(w)+2(2w-1)

28=2w+4w-2

30=6w

w=5

Answer:

5

Step-by-step explanation:

Answer:

The answer is C.

Step-by-step explanation:

You have to divide it by 2 :

∠XYZ = 148° ÷ 2

= 74°

Answer:

The answer is 3.01 x 10’23

Step-by-step explanation:

I got the answer to wrong and guessed the first one and it was correct

Answer:

the number of possible reading schedules is 1.064301638 × 10¹²

Step-by-step explanation:

Given that :

The English teacher needs to pick 10 books to put on her reading list for the next school year.

If the English teacher picks at most  3 poetry books i.e no  more than 3 poetry books from 8 books. and other books are picked from (6+4+4 ) = 14 books

Thus; the number of ways to pick the books are :

[tex]\left[\begin{array}{c}8\\0\\ \end{array}\right] \ \left[\begin{array}{c}14\\10\\ \end{array}\right]+ \left[\begin{array}{c}8\\1\\ \end{array}\right] \left[\begin{array}{c}14\\9\\ \end{array}\right] + \left[\begin{array}{c}8\\2\\ \end{array}\right] \left[\begin{array}{c}14\\8\\ \end{array}\right] + \left[\begin{array}{c}8\\3\\ \end{array}\right] \left[\begin{array}{c}14\\7 \\ \end{array}\right][/tex]

[tex]= [ \dfrac{8!}{0!(8-0)!}* \dfrac{14!}{10!(14-10!)} ] + [ \dfrac{8!}{1!(8-1)!}* \dfrac{14!}{9!(14-9)!}]+ [ \dfrac{8!}{2!(8-2)!}* \dfrac{14!}{8!(14-8)!}] + [ \dfrac{8!}{3!(8-3)!}* \dfrac{14!}{7!(14-7)!}][/tex]

[tex]= [ 1*1001]+[8*2002]+[28*3003]+[56*3432][/tex]

[tex]\mathbf{= 293293}[/tex]

However, to determine how many reading schedules that are possible we use the relation:

Number of ways to pick a book × [tex]^{10}P_{10}[/tex]

[tex]= 293293* \dfrac{10!}{(10-10)!}[/tex]

= 293293 ×  10!

= 1.064301638 × 10¹²

Thus , the number of possible reading schedules is 1.064301638 × 10¹²

Answer:

2.143

Step-by-step explanation:

An urn contains 8 black and;

6 pink balls.

5 balls are randomly drawn from the urn in succession, with replacement.

What is the probability that all the 5 balls drawn from the urn are pink?

The probability that all the 5 balls drawn is pink is 5 × 6/14 = 30/14 = 2.143 (rounded off to 3 decimal places)

The probability of drawing 5 pink balls is 0.271

Since the balls are replaced after each draw, the probability of drawing a pink ball each time is always  

6/14

=3/7

Since we are drawing 5 balls, the probability of drawing 5 pink balls with replacement is

[tex](3/7)^{5}[/tex]

≈0.2706

Rounding to 3 decimal places, the probability is  0.271

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Answer: The answer is choice 3

Step-by-step explanation:

i think the answer is c

Step-by-step explanation:

i don't think u would want a whole explanation

Answer:

|-a|=|a|

Step-by-step explanation:

The lines beside the a's mean that you are trying to find the absolute value of what's inside. The absolute value of something is the distance it is from 0. You can't have a negative distance so anything inside of absolute value line are positive.

Therefor this is how we can solve this.

|-a| __ |a|

  a __ a

a=a

Answer:

someone already answered

Step-by-step explanation:

srry

Answer:

x < 11

Step-by-step explanation:

[tex]5(x+4)<75 \\ open \: the \: bracket \: using \: 5 \\ 5x + 20 < 75 \\ subtract \: - 20 \: from \: both \: sides \: [/tex]

[tex]5x + 20 - 20 < 75 - 20 \\ 5x < 55 \\ divide \: both \: sides \: of \: the \: equation \: \\ by \: 5[/tex]

[tex] \frac{5x}{5} < \frac{55}{5} \\ x < 11[/tex]

The required solution of inequality is,

⇒ x < 11

We have to simplify the expression,

⇒ 5 (x + 4) < 75

We can simplify it by definition of inequality as,

⇒ 5 (x + 4) < 75

⇒ 5x + 20 < 75

Subtract 20 both side,

⇒ 5x + 20 - 20 < 75 - 20

⇒ 5x < 55

⇒ 5x - 55 < 0

⇒ 5 (x - 11) < 0

⇒ x - 11 < 0

⇒ x < 11

Therefore, The required solution of inequality is,

⇒ x < 11

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Answer:

5

Step-by-step explanation:

There are two ways you can solve this. First is to just count all the numbers in the list given that are within the range 15-19. This is an inclusive range meaning the numbers 15 and 19 are a part of it. The second method is to count how many numbers are in the list given and count all the numbers that have already been put on the table. There are 19 total numbers, and 14 have already been counted. If you subtract you are left with 5 numbers that are within the range. So the answer is 5.

Explanation:

One method is to count all of the values that are between 15 and 19. Those values are highlighted in the diagram below. There are 5 values marked.

An alternative method is to note there are 19 values total. The items in the given table add to 5+2+1+2+4 = 14, so there must be 19-14 = 5 items missing to completely fill out the table.

Answer:

Sorry, I cant understand rewrite it again.

Answer:

Poisson distribution

Step-by-step explanation:

Given that :

There is an average of 0.1 flaws per square meter of cloth

So X = the number of flaws in a bolt of 2000 square meters of cloth.

The objective is to deduce how is X distributed.

Well, we can say X undergoes Poisson distribution.

Because, the flaw can be randomly positioned on the cloth and also dictate  how many times the event is likely to occur within a specified period of time.

Most time Poisson distribution is majorly used for independent events.

An independent is an event which contains two types of events occuring at a time say event [tex]E_1[/tex] and event [tex]E_2[/tex] and the event [tex]E_1[/tex] does not in any way affects the occurrence of the event [tex]E_2[/tex] .

Answer:

D.) Converges; 256

Step-by-step explanation:

x0= 192

x1 = 48 = 192/4

x2 = 12 = 192/(4 x 4)

Therefore, this series can be written as:

[tex]x_n = \frac{192}{4^n}[/tex]

Applying limits at infinity:

[tex]\lim_{n \to \infty} x_n= \lim_{n \to \infty} (\frac{192}{4^n}) = \frac{192}{\infty}=0[/tex]

Since the terms of the series tend to zero, we can affirm that the series converges.

The sum of an infinite converging series is:

[tex]S=\frac{x_0}{1-r} \\S=\frac{192}{1-\frac{1}{4} }\\S=256[/tex]

Thus, the answer is D.) Converges; 256

Answer:

That would be just 0 because anything multiplied by 0 is 0.

Answer:

4 ( a+2)

Step-by-step explanation:

The average rate of change is

(f(a) - f(2))/(a-2)

f(a) = 4a^2 -8

f(2) = 4*2^2 -8 = 4*4 -8 = 16-8 = 8

(4a^2 - 8  - 8))/(a-2)

(4a^2 -16) / (a-2)

Factor the numerator

4( a^2 -4) / (a-2)

4( a-2)(a+2) / (a-2)

Cancel

4 ( a+2)