Richard and Stephen win some money and share it in the ratio 6:1. Richard gets £60 more than Stephen. How much did they get altogether?

Answer:

Yes,these two functions are the inverse of each other.

Step-by-step explanation:

They way of finding if two functions ([tex]f(x)\,\,and\,\,g(x)[/tex] ) are the inverse of each other is by studying if their composition renders in fact the identity. That is, we see if:

[tex]f(x) \,o \,g(x)=f(g(x))=x[/tex]

in our case:

[tex]f(g(x))=\frac{1}{g(x)+4} -9\\f(g(x))=\frac{1}{(\frac{1}{x+9} -4)+4}-9\\f(g(x))=\frac{1}{\frac{1}{x+9} }-9\\f(g(x))={x+9} -9\\f(g(x))=x[/tex]

The composition does render the identity, therefore, these two functions are indeed the inverse of each other

Answer:

Step-by-step explanation:

[tex](x-3)^2=49[/tex]

<=>

[tex](x-3)^2-49=0\\\\<=> (x-3)^2-7^2=0\\\\<=> (x-3-7)(x-3+7)=0\\<=> (x-10)(x+4)=0\\<=> x -10=0\ or \ x+4=0\\<=> x = 10 \ or\ x = -4[/tex]

solutions are -4 and 10

do not hesitate if you need further explanation

if you like my answer, tag it as the brainliest :-)

Answer:

a. P(X>695)=0.026

b. P(X<485)=0.44

Step-by-step explanation:

The question is incomplete:

a. higher than 695 on the test.

b. at most 485 on the test.

We have a normal distribution with mean 500 and standard deviation of 100 for the test scores. We will use the z-scores to calculate the probabilties with the standard normal distribution table.

a. We want to calculate the probability that a randomly selected student scores higher than 695.

We calculate the z-score and then we calculate the probability:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{695-500}{100}=\dfrac{195}{100}=1.95\\\\\\P(X>695)=P(z>1.95)=0.026[/tex]

a. We want to calculate the probability that a randomly selected student scores at most 485.

We calculate the z-score and then we calculate the probability:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{485-500}{100}=\dfrac{-15}{100}=-0.15\\\\\\P(X<485)=P(z<-0.15)=0.44[/tex]

Answer:

b. external validity

Step-by-step explanation:

External Validity is the applicability of the results of an experiment to the real world. Most times, there are threats to the validity of an experiment which could result in little or no effect on the general population. For example, if the method of selection reflects a measure of bias, then this could affect the result. Also if the participants are taking different aspects of the same test, it could also affect its validity as they may not be able to make a correct conclusion. If the sample size is not reflective of the entire population, it could also pose a threat to the validity of the experiment.

John's experiment is weak in its external validity because it cannot be generalized to the entire population of customers. He has to identify the threats to the validity of his experiment and correct them. For example, the sample selection may be biased.

Answer:

b. 0.25

c. 0.05

d. 0.05

e. 0.25

Step-by-step explanation:

if the waiting time x follows a uniformly distribution from zero to 20, the probability that a passenger waits exactly x minutes P(x) can be calculated as:

[tex]P(x)=\frac{1}{b-a}=\frac{1}{20-0} =0.05[/tex]

Where a and b are the limits of the distribution and x is a value between a and b. Additionally the probability that a passenger waits x minutes or less P(X<x) is equal to:

[tex]P(X<x)=\frac{x-a}{b-a}=\frac{x-0}{20-0}=\frac{x}{20}[/tex]

Then, the probability that a randomly selected passenger will wait:

b. Between 5 and 10 minutes.

[tex]P(5<x<10) = P(x<10) - P(x<5)\\P(5<x<10) = \frac{10}{20} -\frac{5}{20}=0.25[/tex]

c. Exactly 7.5922 minutes

[tex]P(7.5922)=0.05[/tex]

d. Exactly 5 minutes

[tex]P(5)=0.05[/tex]

e. Between 15 and 25 minutes, taking into account that 25 is bigger than 20, the probability that a passenger will wait between 15 and 25 minutes is equal to the probability that a passenger will wait between 15 and 20 minutes. So:

[tex]P(15<x<25)=P(15<x<20) \\P(15<x<20)=P(x<20) - P(x<15)\\P(15<x<20) = \frac{20}{20} -\frac{15}{20}=0.25[/tex]

Answer:

The correct answer will be Option B (multinomial population).

Step-by-step explanation:

Other given options are not connected to the given situation. So that Option B seems to be the perfect solution.

Answer:

The probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.

Step-by-step explanation:

The complete question is:

There are 103 students in a physics class. The instructor must choose two students at random.

Students in a Physics Class

Academic Year          Physics majors           Non-Physics majors

Freshmen                              17                                     15

Sophomores                         20                                    14

Juniors                                   11                                      17

Seniors                                   5                                       4

What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.

Solution:

There are a total of N = 103 students present in a Physics class.

Some of the students are Physics Major and some are not.

The instructor has to select two students at random.

The instructor first selects a senior Physics major and then a sophomore Physics major.

Compute the probability of selecting a senior Physics major student as follows:

[tex]P(\text{Senior Physics Major})=\frac{n(\text{Senior Physics Major}) }{N}[/tex]

                                        [tex]=\frac{5}{103}\\\\=0.04854369\\\\\approx 0.0485[/tex]

Now he two students are selected without replacement.

So, after selecting a senior Physics major student there are 102 students remaining in the class.

Compute the probability of selecting a sophomore Physics major student as follows:

[tex]P(\text{Sophomore Physics Major})=\frac{n(\text{Sophomore Physics Major}) }{N}[/tex]

                                        [tex]=\frac{20}{102}\\\\=0.1960784314\\\\\approx 0.1961[/tex]

Compute the probability that a senior Physics major and then a sophomore Physics major are chosen at random as follows:

[tex]P(\text{Senior}\cap \text{Sophomore})=P(\text{Senior})\times P(\text{Sophomore})[/tex]

                                     [tex]=0.0485\times 0.1961\\\\=0.00951085\\\\\approx 0.0095[/tex]

Thus, the probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.

Answer:

a number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10.

Step-by-step explanation:

Given : Statement  'The relationship between numbers divisible by 5 and 10'.

To find : What statement BEST explains the statement?

Solution :

First we study the divisibility rules,

Rule for the number divisible by 5 is that number must end in 5 or 0.

Rule for the number divisible by 10 is that number need to be even and divisible by 5, as the prime factors of 10 are 5 and 2 and the number to be divisible by 10, the last digit must be a 0.

According to the divisibility rules Option D is correct.

Therefore, The correct statement explains the relationship between numbers divisible by 5 and 10 is a number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10.

Answer:

17.85 feet.

Step-by-step explanation:

Area = 1/4 * 3.14 * r^2  where r is the radius

So r^2 = 19.625 / (1/4 * 3.14)

r^2 = 25

r = 5 feet.

The perimeter = 2r + 1/4 * 2* 3.14*r

= 2*5 + 7.85

= 17.85 feet.

Answer:

33.33%

Step-by-step explanation:

Add them together 8 plus 8 plus 8 which is 24 there are 8 tp so its 8/24 which is equal to 1/3 so the percent is

Answer:

I just do a' as a sample. You calculate b' and c'

Step-by-step explanation:

[tex]a'=\frac{b\times c}{a\bullet (b\times c)}, b' = \frac{c\times a}{a\bullet (b\times c)}, c' = \frac{a\times b}{a\bullet (b\times c)}[/tex]

Now, calculate b x c

[tex]\left[\begin{array}{ccc}i&j&k\\2&3&1\\1&-1&-2\end{array}\right] =<-5, 5,-5>[/tex]

[tex]a'=\frac{<-5,5,-5>}{<1, 2, 2>\bullet <-5, 5,-5>}=\frac{<-5, 5, -5>}{-5} =<1,-1,1>[/tex]

Answer:

x = 20

Step-by-step explanation:

The sum of the three angles in the diagram is 180 degrees since they form a straight line

x + 100 + 3x = 180

Combine like terms

100 +4x = 180

Subtract 100 from each side

100+4x-100 =180-100

4x= 80

Divide each side by 4

4x/4 = 80/4

x = 20

Answer:

538

Step-by-step explanation:

12 times 46 is 552 then 552 minus 14 is 538

:D

Answer:

x = 1/2 , y = 6

Explanation:

Step 1 - Align the equations and multiply the second row by 2

4x + 3y = 20

2x + y = 7

4x + 3y = 20

4x + 2y = 14

Step 2 - Subtract them both

4x + 3y = 20

4x + 2y = 14

y = 6

So, y = 6

Step 3 - Substitute y into the first equation

4x + 3y = 20

4x + 3(6) = 20

4x + 18 = 20

Step 4 - Subtract 18 from both sides

4x + 18 = 20

4x + 18 - 18 = 20 - 18

4x = 2

Step 5 - Divide both sides by 4

4x = 2

4x / 4 = 2 / 4

x = 2/4

So, x = 1/2

Answer:

The mean of depth is 12.75cm.

The variance of depth is of 13.02 cm².

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform distribution is:

[tex]M = \frac{a+b}{2}[/tex]

The variance of the uniform distribution is given by:

[tex]V = \frac{(b-a)^{2}}{12}[/tex]

Uniform distribution on the interval (6.5, 19)

This means that: [tex]a = 6.5, b = 19[/tex]

So

Mean:

[tex]M = \frac{6.5+19}{2} = 12.75[/tex]

The mean of depth is 12.75cm.

Variance:

[tex]V = \frac{(19 - 6.5)^{2}}{12} = 13.02[/tex]

The variance of depth is of 13.02 cm².

Answer:

[tex]-x^5+9x^4-18x^3=0\\-x^3(x^2-9x+18)=0\\-x^3(x-3)(x-6)=0\\\\\\\\x=0\\x=3\\x=6[/tex]

Answer:  The correct answer is:  " 2x² " .

________________________________

Step-by-step explanation:

________________________________

We are asked:  "What is the sum of:  "x + x² + 2" and "x² − 2 − x" ?

Since we are to find the "sum" ;

  →  We are to "add" these 2 (two) expressions together:

     →     (x + x² + 2) +  (x² − 2 − x) ;

Note:  Let us rewrite the above, by adding the number "1" as a coefficient to:  the values "x" ; and "x² " ;  since there is an "implied coefficient of "1" ;

            → {since:  "any value" ; multiplied by "1"; results in that exact same value.}.

            →     (1x + 1x² + 2) +  (1x² − 2 − 1x) ;

Rewrite as:

             →     1x + 1x² + 2) +  (1x² − 2 − 1x) ;

Now, let us add the "coefficient" , "1" ; just before the expression:

             "(1x² − 2 − 1x)" ;  

         {since "any value", multiplied by "1" , equals that same value.}.

And rewrite the expression; as follows:

            →     (1x + 1x² + 2) +  1(1x² − 2 − 1x) ;

Now, let us consider the following part of the expression:

                     →  " +1(1x² − 2 − 1x) " ;

________________________________

Note the distributive property of multiplication:

   →  " a(b+c) = ab + ac " ;

and likewise:

   →  " a(b+c+d) = ab + ac + ad " .

________________________________

So; we have:

→  " +1(1x² − 2 − 1x) " ;

  = (+1 * 1x²)  +  (+1 *-2) + (+1*-1x) ;

  =       + 1x²    +    (-2)     +  (-1x) ;

  =       +1x²    −    2   −  1x  ;

  ↔    ( + 1x²  −  1x  −  2)

Now, bring down the "left-hand side of the expression:

1x + 1x² + 2 ;

and add the rest of the expression:

     →  1x  +  1x²  +  2  +   1x²  −  1x  −  2 ;

________________________________

Now, simplify by combining the "like terms" ; as follows:

   +1x² + 1x² = 2x²  ;

   +1x −  1x = 0 ;  

   + 2 −  2  = 0 ;

________________________________

The answer is: " 2x² " .

________________________________

Hope this is helpful to you!

   Best wishes!

________________________________

Answer:

The correct answer is:  " 2x² " .

________________________________

Step-by-step explanation:

________________________________

We are asked:  "What is the sum of:  "x + x² + 2" and "x² − 2 − x" ?

Since we are to find the "sum" ;

 →  We are to "add" these 2 (two) expressions together:

    →     (x + x² + 2) +  (x² − 2 − x) ;

Note:  Let us rewrite the above, by adding the number "1" as a coefficient to:  the values "x" ; and "x² " ;  since there is an "implied coefficient of "1" ;

           → {since:  "any value" ; multiplied by "1"; results in that exact same value.}.

           →     (1x + 1x² + 2) +  (1x² − 2 − 1x) ;

Rewrite as:

            →     1x + 1x² + 2) +  (1x² − 2 − 1x) ;

Now, let us add the "coefficient" , "1" ; just before the expression:

            "(1x² − 2 − 1x)" ;  

        {since "any value", multiplied by "1" , equals that same value.}.

And rewrite the expression; as follows:

           →     (1x + 1x² + 2) +  1(1x² − 2 − 1x) ;

Now, let us consider the following part of the expression:

                    →  " +1(1x² − 2 − 1x) " ;

________________________________

Note the distributive property of multiplication:

  →  " a(b+c) = ab + ac " ;

and likewise:

  →  " a(b+c+d) = ab + ac + ad " .

________________________________

So; we have:

→  " +1(1x² − 2 − 1x) " ;

 = (+1 * 1x²)  +  (+1 *-2) + (+1*-1x) ;

 =       + 1x²    +    (-2)     +  (-1x) ;

 =       +1x²    −    2   −  1x  ;

 ↔    ( + 1x²  −  1x  −  2)

Now, bring down the "left-hand side of the expression:

1x + 1x² + 2 ;

and add the rest of the expression:

    →  1x  +  1x²  +  2  +   1x²  −  1x  −  2 ;

________________________________

Now, simplify by combining the "like terms" ; as follows:

  +1x² + 1x² = 2x²  ;

  +1x −  1x = 0 ;  

  + 2 −  2  = 0 ;

________________________________

The answer is: " 2x² " .

Step-by-step explanation:

Answer:

Step-by-step explanation:

draw it out and use trig function to solve for the angle. Keep in mind, after getting trig, need to do inverse

Answer:

27 stuffed bears

Step-by-step explanation:

Erin: 55   Su: 15

Erin: 55-7=48 ( 7 will be kept for herself)

Erin and her sisters: 48/4= 12

Each sister besides Erin and Su have 12

Su: 15+12=27

Thus, Su will have 27 stuffed bears

Answer:

31 Stuffed Bears

Step-by-step explanation:

55 - 7 = 48

48 / 3 = 16

16 + 15 = 31

Sue has 31 stuffed bears

Answer:

$120.52

Margin of error M.E = $120.52

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

x+/-M.E

Where M.E = margin of error

M.E = zr/√n

Given that;

Mean x = $1,873

Standard deviation r = $550

Number of samples n = 80

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

M.E = (1.96 × $550/√80) = 120.5240639872

M.E = $120.52

Margin of error M.E = $120.52

Answer:

The 99% confidence interval for the percentage of Phoenix residents who support mandatory sick leave for food handlers is between 85.40% and 92.60%.

Step-by-step explanation:

Confidence interval for the proportion:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 500, \pi = \frac{445}{500} = 0.89[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.89 - 2.575\sqrt{\frac{0.89*0.11}{500}} = 0.8540[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.89  + 2.575\sqrt{\frac{0.89*0.11}{500}} = 0.9260[/tex]

For the percentage:

Multiply the proportion by 100.

0.8540*100 = 85.40%

0.9260*100 = 92.60%

The 99% confidence interval for the percentage of Phoenix residents who support mandatory sick leave for food handlers is between 85.40% and 92.60%.

Answer:

There were 210 downloads of the standard version.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the number of downloads of the standard version.

y is the number of downloads of the high-quality version.

The size of the standard version is 2.6 megabytes (MB). The size of the high-quality version is 4.2 MB. The total size downloaded for the two versions was 4074 MB.

This means that:

[tex]2.6x + 4.2y = 4074[/tex]

Yesterday, the high-quality version was downloaded four times as often as the standard version.

This means that [tex]y = 4x[/tex]

How many downloads of the standard version were there?

This is x.

[tex]2.6x + 4.2y = 4074[/tex]

Since [tex]y = 4x[/tex]

[tex]2.6x + 4.2*4x = 4074[/tex]

[tex]19.4x = 4074[/tex]

[tex]x = \frac{4074}{19.4}[/tex]

[tex]x = 210[/tex]

There were 210 downloads of the standard version.

Answer:

There are 5 number of temperature readings.

Step-by-step explanation:

9, 7, 9, 10, 9

5 readings recorded in the range of 6-10°C.

Answer:

[tex] 25.5 -3.3= 22.2[/tex]

[tex] 25.5 +3.3= 28.8[/tex]

And the confidence interval would be given by: [tex] 22.2\leq \mu \leq 28.8[/tex]

Step-by-step explanation:

[tex]\bar X=25.5[/tex] represent the sample mean for the sample  

ME= 3.3 represent the margin of error

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The margin of error is given by;

[tex] ME =t_{\alpha/2}\frac{s}{\sqrt{n}}= 3.3[/tex]

And the confidence interval would be given by:

[tex] 25.5 -3.3= 22.2[/tex]

[tex] 25.5 +3.3= 28.8[/tex]

And the confidence interval would be given by: [tex] 22.2\leq \mu \leq 28.8[/tex]

[tex]z_1z_2=(3+2i)(4+3i)=3\cdot4+2i\cdot4+3\cdot3i+2i\cdot3i[/tex]

[tex]z_1z_2=12+8i+9i+6i^2[/tex]

[tex]i^2=-1[/tex], so

[tex]z_1z_2=12+8i+9i-6=\boxed{6+17i}[/tex]

Answer:

The Answer is : 9(x2 + 6x + 9) = 103

Step-by-step explanation:

Option D on edge2020 i got a 100 on the quiz

The resulting quadratic equation is [tex](x+3)^2-103/9=0[/tex]

Given the quadratic equation [tex]9x^2 + 49x = 22 - 5x[/tex]

Write in standard form:

[tex]9x^2 + 49x = 22 - 5x\\ 9x^2 + 49x + 5x -22= 0\\ 9x^2+54x-22=0[/tex]

Divide through by 9

[tex]x^2+6x-22/9=0\\ [/tex]

complete the square to have:

[tex]x^2+6x-22/9+3^2-3^2=0\\ x^2+6x+3^2-9-22/9 = 0\\ (x+3)^2-103/9=0[/tex]

Hence the resulting quadratic equation is [tex](x+3)^2-103/9=0[/tex]

Learn more on completing the square here: https://brainly.com/question/1596209

Answer:it is b

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

In the attached file