piece-wise functions

Answer:

r = (An−nP)/P

Step-by-step explanation:

A = P(1 + nr)

Divide P on both sides.

A/P = 1 + nr

Subtract 1 on both sides.

A/P - 1 = nr

Divide n on both sides.

A/P/n - 1/n = r

(An−nP)/P = r

The answer is, r = (An−nP)/P

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

here, we have,

given that,

A = P(1 + nr)

Divide P on both sides.

A/P = 1 + nr

Subtract 1 on both sides.

A/P - 1 = nr

Divide n on both sides.

A/P/n - 1/n = r

(An−nP)/P = r

hence, answer is (An−nP)/P = r.

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Answer:

$9,000

Step-by-step explanation:

The worth of the estate = $72,000

The client leaves half of his estate to charity, and 1/8 to each of his four children.

Therefore, the amount each of the child will receive

[tex]=\dfrac18 \times \$72,000\\\\=\$9,000[/tex]

Each child will receive $9,000.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

I assume you are asking for the new salary.

To find 1%, divide 62900 by 100.

629

Multiply this by 3.

1887

Add this to the original answer.

64787

Answer:

D

Step-by-step explanation:

THEY AVOID STUFF THAT HURTS THEIR BUISSNESS AND THEY HAVE TO TAKE RISKS THAT CAN LEAVE THEM BROKE

Answer:

Null hypothesis:[tex]p \leq 0.5[/tex]  

Alternative hypothesis:[tex]p > 0.5[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing we got:

[tex]z=\frac{0.512-0.5}{\sqrt{\frac{0.5(1-0.5)}{344}}}=0.445[/tex]  

Step-by-step explanation:

Information given

n=344 represent the random sample taken

X=176 represent the anumber of boys babies

[tex]\hat p=\frac{176}{344}=0.512[/tex] estimated proportion of boys babies

[tex]p_o=0.5[/tex] is the value that we want to check

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypotheis to verify

We want to check if the true proportion of boys is less than 50% then the system of hypothesis are .:  

Null hypothesis:[tex]p\leq 0.5[/tex]  

Alternative hypothesis:[tex]p > 0.5[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing we got:

[tex]z=\frac{0.512-0.5}{\sqrt{\frac{0.5(1-0.5)}{344}}}=0.445[/tex]  

Answer:

p= 0.5

p>0.5

Step-by-step explanation:

Answer:

i = 77.5°

k = 77.5°

j = 102.5°

h = 155°

Step-by-step explanation:

Since we have an isosceles triangle, we know that ∠i and ∠k are equal. So,

180 - 25 = 2x

155 = 2x

x = 77.5

So m∠i = m∠k = 77.5°

To find m∠j, we use Supplementary Angles:

180 - 77.5 = 102.5°

To find m∠h, we also use Supplementary Angles:

180 - 25 = 155°

Answer:

x = 90

y = 100

z = -10

Step-by-step explanation:

To find x and y in the above parallelogram ABCD as shown above, recall that one of the properties of a parallelogram is: the consecutive angles in a parallelogram are supplementary.

This means that the sum of angle A and angle B in the parallelogram ABCD = 180°.

Thus,

(x + 30)° + (x - 30)° = 180°

Solve for x

x + 30 + x - 30 = 180

x + x + 30 - 30 = 180

2x = 180

Divide both sides by 2

2x/2 = 180/2

x = 90

=>Find y:

Also, recall that opposite angles in a parallelogram are congruent.

This means, angle A and angle C in parallelogram ABCD above are equal.

Thus,

(x + 30)° = (y + 20)°

Plug in the value of x to solve for y

90 + 30 = y + 20

120 = y + 20

Subtract 20 from both sides

120 - 20 = y

100 = y

y = 100

=>Find z, if z = x - y

z = 90 - 100

z = -10

Answer:

see below

Step-by-step explanation:

9 dollars / 33 lbs = .272727 dollars per lb

.39 / 1 lbs = .39 per lb

The large bag is less expensive

Answer:

  y = 5 (x + 2)

Step-by-step explanation:

Equations with a different x-coefficient will graph as lines that intersect the given one, so will form a system with one solution.

The equation with the same slope and y-intercept (y = 5(x -2)) will graph as the same line, so will form a system with infinite solutions.

The line with the same slope and a different y-intercept will form a system with no solutions:

  y = 5 (x + 2)

Answer:

B

Step-by-step explanation:

got it on edge

Answer:

A lies along the positive x-axis and B lies along negative x - axis .

Step-by-step explanation:

They tell us that we have two vectors, A and B. And they give us a series of conditions for this, now, what would be the correct possibility.

A lies along the positive x-axis and B lies along negative x - axis .

This is because when both vectors will be in x axis but opposite to each other, then the angle between them will be 180 ° and cos180 ° is -1.

Answer:

Total money raised by the students = $324

Step-by-step explanation:

Raffle tickets sold by Melissa = 18

'Jonah sold half as many tickets as Melissa'

Jonah sold the raffle tickets = [tex]\frac{1}{2}\times 18=9[/tex]

'Shona sold 1.5 times as many as Melissa'

Tickets sold by Shona = 1.5 × 18 = 27

Total number of raffle tickets sold by all of them = 18 + 9 +27 = 54

Since, each ticket cost = $6

Therefore, total money raised by the students = Total number of tickets sold × Cost of each ticket

= 54 × 6

= $324

Answer:

Option D is correct.

This statement shows the use of relative difference.

Step-by-step explanation:

Taking each of the answer choices one at a time

- Absolute Change

This expresses the exact value of alterations or modifications that happen to a particular quantity. It gives exactly how much the value of the same quantity has changed at different times or conditions. The statement in this question compares two different quantities (price of new CD burner at two different stores), hence it doesn't give the absolute change.

- Absolute Difference

This expresses the exact value of the difference between two quantities. The statement in the question on its own cannot give us the absolute value of the difference between the cost of new CD burner at the two stores being compared. Hence, this isn't the correct answer.

- Relative Change

Thìs expresses how much a particular quantity has changed with respect to its value at some other period of time or under some other condition(s). The question in this statement compares two different quantities and isn't the right answer.

- Relative Difference

This expresses the difference between two quantities wit respect to or relative to one of the two quantities being compared. This is exactly what the statement in the question expresses by saying that the new CD burner costs 12% less at the new electronics store.

It compares the telative difference of the new CD burner at the new and old electronics store.

Hope this Helps!!!

Answer:

Hello please your question is in-complete attached is the complete question

degree of freedom = -62.90 ( e )

Step-by-step explanation:

The formula for calculating the F-statistic/test statistic is

test - statistic  = Coef ( LBW) / SE Coef ( LBW )

                       = -0.72399 / 0.01151

                       = - 62.90

the degree of freedom the F-statistic has = -62.90

F-statistic test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. the value of the test can be gotten from running an ANOVA test or regression analysis on the statistical models

Using the definition of degrees of freedom, it is found that the F-statistic has 63 df.

When a hypothesis is tested, the number of degrees of freedom is one less than the sample size.

In this problem, the sample size is of n = 64.

Hence:

df = n - 1 = 64 - 1 = 63

The F-statistic has 63 df.

A similar problem is given at https://brainly.com/question/16194574

The element X will take 22.10 minutes to decay to 26 grams.

The radioactive radiations are the radiations that an atom nucleus releases.

It is a sequence of numbers which have common difference.

The decaying acts like an arithmetic progression in which a=670,d=-30.45 (per minute decaying) and n we have to find with the an value of 26 gram.

So, the formula of nth term of an arithmetic progression is

nth term=a+(n-1)d

26=670+(n-1)*(-30.45)

-644=-30.45n+30.45

-674.45=-30.45n

n=22.10 (after rounding off)

Hence the element X would take 22.10 minutes to decay to 26 grams.

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Answer:

y=a(.5)^{\frac{t}{h}}

y=a(.5)

h

t

​

y=30 \hspace{15px} a=670 \hspace{15px} h=11 \hspace{15px} t=?

y=30a=670h=11t=?

30=670(.5)^{\frac{t}{11}}

30=670(.5)

11

t

​

\frac{30}{670}=\frac{670(.5)^{\frac{t}{11}}}{670}

670

30

​

=

670

670(.5)

11

t

​

​

0.0447761=(.5)^{\frac{t}{11}}

0.0447761=(.5)

11

t

​

\log(0.0447761)=\log((.5)^{\frac{t}{11}})

log(0.0447761)=log((.5)

11

t

​

)

\log(0.0447761)=\frac{t}{11}\log(.5)

log(0.0447761)=

11

t

​

log(.5)

Power Rule.

11\log(0.0447761)=t\log(.5)

11log(0.0447761)=tlog(.5)

Multiply by 11.

\frac{11\log(0.0447761)}{\log(.5)}=\frac{t\log(.5)}{\log(.5)}

log(.5)

11log(0.0447761)

​

=

log(.5)

tlog(.5)

​

Divide by log(.5).

t=\frac{-14.838489}{-0.30103}

t=

−0.30103

−14.838489

​

t=49.29239\approx 49.3 \text{ minutes}

t=49.29239≈49.3 minutes

Step-by-step explanation:

Answer:

[tex]x^2-2x+1[/tex]

Step-by-step explanation:

=> (x-1)(x-1)

Using FOIL

=> [tex]x^2-x-x+1[/tex]

=> [tex]x^2-2x+1[/tex]

Answer:

Step-by-step explanation:

simply :

                     = x²-2x=1

Answer:

25%

Step-by-step explanation:

Total cards = 4

The number 4 = 1

p(4) = 1/4

In %age:

=> 25%

Answer:

25%

Step-by-step explanation:

There is only 1 four card from the 4 cards.

1 card out of 4 cards.

1/4 = 0.25

P(4) = 25%

Answer:

Step-by-step explanation:

When two variables vary inversely, it means that an increase in one would lead to a decrease in the other and vice versa. Since the volume of a gas, V in a container varies inversely with the pressure on the gas, P, if we introduce a constant of proportionality, k, the expression would be

V = k/P

If V = 370 in³ and P = 15psi, then

370 = k/15

k = 370 × 15 = 5550

The equation that relates the volume, V, to the pressure, P would be

V = 5550/P

if the pressure was increased to 25psi, the volume would be

V = 5550/25 = 222 in³

Answer:

v=5550/p

222

Step-by-step explanation:

Answer: 16 kph

Step-by-step explanation:

Average Speed = Total Distance/ Total Time

Distance = Speed x Time

The Distance between A and B is 20 kph

Time(A-B) = 1.5 hrs

Time(B-A) = 1 hour

Total Time = 2.5 hrs

Total Distance = 20 + 20 = 40 km

Average Speed = 40 km / 2.5 hrs = 16 kmph

Answer:

1/9

Step-by-step explanation:

The probability of picking a even number is 1/3

The probability of picking another even number is 1/3(if u put the first one back)

So u multiply 1/3 times 1/3 which gives u 1/9 which is ur answer hope this helps

Answer:

1/9

Step-by-step explanation:

3 cards total

1 even number

P(even) = even/total

                1/3

Put the card back

3 cards total

1 even number

P(even) = even/total

                1/3

P(even, replace, even) = P(even) * P(even) =1/3*1/3 = 1/9

Answer:

108 and 114

Step-by-step explanation:

Answer:

222

Step-by-step explanation:

We want the first two multiple of 6 that are greater than 103

103/6 =17 1/6

Rounding up

6*18 =108

The next  multiple will be 6* 19

6*19 =114

The sum is 108+114 =222

Answer:

(a + b + c)/2

Step-by-step explanation:

Number of kids in first class: a

Number of kids in second class: b

Number of kids in third class: c

The total number of kids in all classes is: a + b + c

The total number of kids is divided equally between 2 buses:

(a + b + c)/2

Answer:

(a + b + c)/2

Step-by-step explanation:

;)

Answer:

Part A

The population standard deviation is suitable for this dataset as it isnt given whether its a sample or a population distribution and it sure doesn't seem like the findings from such a dataset is to be generalized for some population distribution.

Part B

This is outrightly a population distribution of all the students in the middle school, So, the spread of the height of all students about a mean is best indicated using the population standard deviation.

Step-by-step explanation:

The spread of a dataset is usually the measure of dispersion, a measure of the way the distribution spreads out from a particular mean value.

The problem of which type of standard deviation one should calculate usually arises a lot in Statistics. As the name sounds, population standard deviation usually uses all of the distribution to compute while the sample standard deviation uses the data from the sample distribution

The best advice on when to use the population stamdard deviation formula is that

(1) we have the entire population or

(2) we have a sample of a larger population, but we are only interested in this sample and do not wish to generalize the statistical findings to the population.

The sample standard deviation formula is used when one has a sample of a larger population, one is not only interested in this sample and one wishes to generalize the findings to the population.

The population standard deviation is given as

σ = √[Σ(x - xbar)²/N]

Sample standard deviation

σ = √{[Σ(x - xbar)²]/N-1)}

The only difference is the N and (N-1).

So, for the questions presented,

Part A.

Here, it is evident that the findings for this dataset in the question is just for this dataset, hence,the population standard deviation is suitable for this dataset.

Part B

This is outrightly a population distribution of all the students in the middle school, So, the spread of the height of all students about a mean is best indicated using the population standard deviation.

Hope this Helps!!!

The Answer is 171 kg m/s

Answer:

Step-by-step explanation:

A type I error occurs when the researcher rejects the null hypothesis when it is actually true.

A type II error occurs when the research fails to reject the null hypothesis when it is not true.

In this case study,

The null hypothesis is the standard deviation is less that or equal to 13min.

The alternative hypothesis would be that the standard deviation is greater than 13mins.

A type I error would occur when having done an experiment, the researcher rejects the null hypothesis when there is enough evidence that it is actually either less or equal to 13mins

A type II error would occur when the researcher fails to reject the null hypothesis when there is enough evidence that it is actually more than 13mins.

Answer:

[tex]r(t)=-ti-7tj-6tk[/tex]

Step-by-step explanation:

Given the points P(0,0,0) and Q(1,7,6).

We are to determine a function r(t) for the line passing through P and Q.

To do this, we express it in the form:

[tex]r(t)=r_0+tD,$ where:\\ r_0$ is the starting point and D is the direction vector.[/tex]

[tex]D=P-D=<0,0,0> -<1,7,6>=<-1,-7,-6)[/tex]

Therefore:

[tex]r(t)=<0,0,0>+t<-1,-7,-6>\\=<-t,-7t,-6t>\\$Therefore, the function for the line passing through P and Q is:$\\r(t)=-ti-7tj-6tk[/tex]

Answer:

no 4 is not perfect cube and no 2 is perfect cube

Answer:

3. 2916

2. 1728

Step-by-step explanation:

1: 2197 = 13³

2: 512 = 8³

3: 2916 = 2² × 3² × 61

4: 343= 7³

==============

1: 1525 = 5² × 61

2: 1728 = 12³

3: 1458 = 2 × 9³

4: 3993= 3 × 11³

Answer:

30 feet

Step-by-step explanation:

We can use ratios to answer this question:

8 foot shadow: 20 feet high

Therefore if we multiply both sides by 1.5

12 foot shadow: 30 feet high

Answer: your answer should be 103

Answer:

Step-by-step explanation:

103

Answer:

a) See step by step explanation

b) See annex

c) t(s) = 3,4255

d) p- value  = 0,00146   or   0,15 %

e) See step by step explanation

Step-by-step explanation:

As n < 30 we use a t-student distribution

Population mean  μ₀ = 10,5

Sample size   n = 23

Degree of freedom      n - 1   =  22

Sample mean    μ  =  11,5

Sample standard deviation   s = 1,4

Confidence Interval  95 %

a) Null Hypothesis                     H₀             μ  =   μ₀

   Alternative Hypothesis         Hₐ              μ  >  μ₀

As CI  = 95 %      α = 5%    or   α = 0,05

We are solving a one tail-test  

With  df  =  22   and     α  = 0,05 in t-table we find t(c) = 1,7171

c)  t(s)  =  (   μ  -  μ₀ ) / s / √n

    t(s)  = ( 11,5 - 10,5 ) / 1,4 / √23

    t(s)  =   1 * 4,7958 / 1,4

    t(s)  =  3,4255

We compare t(s)  and t(c)

t(s) > t(c)   and t(s) is in the rejection region

Then we reject the null hypothesis.

d) P-value for    t(s) = 3,4255  is from t-table   equal to:

We find        for  df = 22    α = 0,001    and   α = 0,005

values of t                            

t                  3,505              2, 819           Δt   =  0,686

α                  0,001               0,005           Δα  =  0,004

with these values we interpolate by rule of three

0,686                          ⇒   0,004

(3,505 - 3,4255)       ⇒       x

x = 0,000463

and  P-value  =  0,00146    or  0,15 %

e) The p-value indicates  we are far away to consider the accptance of H₀

Answer:

1/2

Step-by-step explanation:

The numbers that are odd on the spinner are 1, 3, and 5.

3 numbers out of 6.

3/6 = 1/2

P(odd)= 1/2