Use the mathematical induction to prove that 7^n -1 is divisible by 6 whenever n is a positive integer

Answer:

37.5

Step-by-step explanation:z

2.0-1.25=0.75

0.75/2.00 x 100

37.5% decrease

Answer:

28 and 7

35

Step-by-step explanation:

The area of a triangle is base*height/2, no matter the shape.

So the big one is 8*7/2 = 28 in²

And the little one is 2*7/2 = 7 in²

The total trapezoid therefore has an area of 28+7=35 in²

Answer:

#1

Step-by-step explanation:

The associative property of addition states that we can "flip" two expressions that are being added. Therefore, our answer is the first one because it can be rewritten as 3x + (-7y) which then is equivalent to -7y + 3x.

Answer:

2 wild cards

Step-by-step explanation:

Typical would mean most often

2 wild cards shows up 6 times which is most often

Answer:

Step-by-step explanation:

[tex](x-5)^2+(y-(-3))^2=16[/tex]

Answer:

cos =1/ sec

=8/17

tan =1/cot

= -15/8

sin = 15/17 or -15/17

cosec = 1/ sin

= 17/15 or -17/15

Answer:

Did the same assignment. lol can see how that went but here's the answers. hope it helps.

Step-by-step explanation:

1039

This is the correct answer

Answer:

option 2

Step-by-step explanation:

Because (0, 900) is a point on the line it means that it costs $900 to make the commercial. A slope of 110 means that they pay $110 every time it's aired so the answer is Option 2.

Answer:

A) The probability that a randomly selected medical student who took the test had a total score that was less than 484 = 0.06178

B) The probability that a randomly selected study participant's response was between 504 and 516 = 0.29019

C) The probability that a randomly selected study participant's response was more than 528 = 0.00357

D) Option D is correct.

Only the event in (c) is unusual as its probability is less than 0.05.

Step-by-step explanation:

The b and c parts of the question are not complete.

B) Find the probability that a randomly selected study participant's response was between 504 and 516

C) Find the probability that a randomly selected study participant's response was more than 528.

D) Identify any unusual event amongst the three events in A, B and C. Explain the reasoning.

a) None.

b) Events A and B.

C) Event A

D) Event C

Solution

This is a normal distribution problem with

Mean = μ = 500

Standard deviation = σ = 10.4

A) Probability that a randomly selected medical student who took the test had a total score that was less than 484 = P(x < 484)

We first normalize or standardize 484

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (484 - 500)/10.4 = - 1.54

To determine the required probability

P(x < 484) = P(z < -1.54)

We'll use data from the normal distribution table for these probabilities

P(x < 484) = P(z < -1.54) = 0.06178

B) Probability that a randomly selected study participant's response was between 504 and 516 = P(504 ≤ x ≤ 516)

We normalize or standardize 504 and 516

For 504

z = (x - μ)/σ = (504 - 500)/10.4 = 0.38

For 516

z = (x - μ)/σ = (516 - 500)/10.4 = 1.54

To determine the required probability

P(504 ≤ x ≤ 516) = P(0.38 ≤ z ≤ 1.54)

We'll use data from the normal distribution table for these probabilities

P(504 ≤ x ≤ 516) = P(0.38 ≤ z ≤ 1.54)

= P(z ≤ 1.54) - P(z ≤ 0.38)

= 0.93822 - 0.64803

= 0.29019

C) Probability that a randomly selected study participant's response was more than 528 = P(x > 528)

We first normalize or standardize 528

z = (x - μ)/σ = (528 - 500)/10.4 = 2.69

To determine the required probability

P(x > 528) = P(z > 2.69)

We'll use data from the normal distribution table for these probabilities

PP(x > 528) = P(z > 2.69) = 1 - P(z ≤ 2.69)

= 1 - 0.99643

= 0.00357

D) Only the event in (c) is unusual as its probability is less than 0.05.

Hope this Helps!!!

Answer:

24000

Step-by-step explanation:

because 24000 * 10 =240000

Answer:

y=[x+1]-3 because it's at the end of the line

Answer:

the answer is 1/2,a0

Step-by-step explanation:

Answer:50%

Step-by-step explanation:670/1340 = 1/2 = 50%

Answer:

Step-by-step explanation:

Let P=Mount Peak

Let K=Mount Killimanjaro

The equation should then be

12555=P+K    ...1

P=K+765   ... 2

sub equation 2 into 1

12555=P+P+765

12555=2P+765

12555-765=2P+765-765               (subtracting 765 from both sides)

11790=2P

P=5895, now that we know P

we just make a new equation that was similiar to 1

12555=5895+K

K=6660

the height of Mount K is 6660 Metres

Answer:

Step-by-step explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean of type A paint

x2 = sample mean of type B paint

s1 = sample standard deviation type A paint

s2 = sample standard for type B paint

n1 = number of samples of type A paint

n2 = number of samples of type B paint

From the information given,

x1 = 75.7

s1 = 4.5

n1 = 11

x2 = 64.3

s2 = 5.1

n2 = 9

x1 - x2 = 75.7 - 64.3 = 11.4

√(s1²/n1 + s2²/n2) = √(4.5²/11 + 5.1²/9) = √4.709

Degree of freedom = (n1 - 1) + (n2 - 1)

df = (11 - 1) + (9 - 1) = 18

For the 98% confidence interval, the z score from the t distribution table is 2.552

Margin of error = 2.552√4.709 = 5.55

The upper boundary for the confidence interval is

11.4 + 5.55 = 16.95 hours

The lower boundary for the confidence interval is

11.4 - 5.55 = 5.85 hours

The correct option is

B. 5.85 hrs < μ1 - μ2 < 16.95 hrs

Answer:

The correct answer is B (24 units)

Step-by-step explanation:

Answer:

(a) Probability distribution is prepared below.

(b) The probability that two or fewer heads are observed in three tosses is 0.875.

(c) The probability that at least one head is observed in three tosses is 0.875.

(d) The expected value of X is 1.5.

(e) The standard deviation of X is 2.121.

Step-by-step explanation:

The complete question is: A fair coin is tossed three times. Let X be the number of heads observed in three tosses of this fair coin.

(a) Find the probability distribution of X.

(b) Find the probability that two or fewer heads are observed in three tosses. (Round your answer to three decimal places.)

(c) Find the probability that at least one head is observed in three tosses. (Round your answer to three decimal places.)

(d) Find the expected value of X. (Round your answer to one decimal place.)

(e) Find the standard deviation of X. (Round your answer to three decimal places.)

Now, firstly the sample space obtained in three tosses of a fair coin is given as;

Sample Space (S) = {HHH, HHT, HTH, THH, HTT, TTH, THT, TTT}

(a) The Probability distribution of X is given below;

   Number of Heads (X)         P(X)            [tex]X \times P(X)[/tex]               [tex]X^{2} \times P(X)[/tex]

              0                               [tex]\frac{1}{8}[/tex] = 0.125            0                           0

              1                                [tex]\frac{3}{8}[/tex] = 0.375         0.375                     0.375  

              2                               [tex]\frac{3}{8}[/tex] = 0.375         0.75                          3

              3                               [tex]\frac{1}{8}[/tex] = 0.125          0.375                    3.375

           Total                                                    1.5                        6.75          

(b) The probability that two or fewer heads are observed in three tosses is given by = P(X [tex]\leq[/tex] 2)

      P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 2)

                     = 0.125 + 0.375 + 0.375

                     = 0.875

(c) The probability that at least one head is observed in three tosses is given by = P(X [tex]\geq[/tex] 1)

      P(X [tex]\geq[/tex] 1) =  1 - P(X = 0)

                    =  1 - 0.125

                    =  0.875

(d) The expected value of X = E(X) =  [tex]\sum (X \times P(X))[/tex]

                                                              =  1.5

(e) The Variance of X = V(X) = [tex]E(X^{2} ) - ( E(X))^{2}[/tex]

                                      =  [tex]\sum (X^{2} \times P(X))- (\sum (X \times P(X)))^{2}[/tex]

                                      =  [tex]6.75 - 1.5^{2}[/tex]  = 4.5

Now, Standard deviation of X = [tex]\sqrt{V(X)}[/tex]

                                                  = [tex]\sqrt{4.5}[/tex]  = 2.121.

Answer:

Quedan 2.083 m^3 de agua en el reservorio.

Equivalen a 2083 litros.

Step-by-step explanation:

Los dueños del restaurante tienen un reservorio de agua cuyo volumen es de 6.25 m^3.

Si han utilizado 2/3 del reservorio, esto implica que aún quedan en el reservorio una tercera parte del volumen original (1/3).

Entonces, la cantidad de metros cúbicos (m^3) de agua que quedan en el reservorio se puede calcular como:

[tex]V=(1/3)\cdot V_0=(1/3)\cdot6.25\,m^3=2.083\,m^3[/tex]

Este valor equivale a un volumen en litros de:

[tex]V=2.083\,m^3\cdot \dfrac{1,000\,l}{1m^3}=2,083\,l[/tex]

Answer:

A. 1.5 seconds

B. 36 feet

C. 0 feet

D. After 3 seconds

Step-by-step explanation:

I graphed it on desmos.

Answer:

x = -6 + [tex]\sqrt{7}[/tex], x = -6 - [tex]\sqrt{7}[/tex]

Step-by-step explanation:

(x + 6)² = 7

x + 6 = + or - [tex]\sqrt{7}[/tex]

x = -6 + [tex]\sqrt{7}[/tex], x = -6 - [tex]\sqrt{7}[/tex]

The solution of the quadratic equation is x = -6 +√7, x = -6 - √7.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Completing the square entails writing a quadratic in the form of a squared bracket and, if necessary, adding a constant. Finding the maximum or minimum value of the function and when it occurs is one application of completing the square.

Given that the quadratic equation is x² + 12x + 36 = 7.

(x + 6)² = 7

x + 6 = ±√7

x = -6 + √7 , x = -6 - √7

To know more about quadratic equations follow

https://brainly.com/question/25841119

#SPJ2

Answer:

The most realistic value for the standard deviation is 15.

Step-by-step explanation:

The standard deviation of a distribution is a measure of dispersion. It is a measure of the spread of the distribution from the mean of the distribution. It expresses how far most of the distribution is from the mean.

Mathematically, the standard deviation is given as the square root of variance. And variance is an average of the squared deviations from the mean.

Mathematically,

Standard deviation = σ = √[Σ(x - xbar)²/N]

x = each variable (ranges from 34 to 99)

xbar = mean = 78

N = number of variables

Now taking the given possible values of the standard deviation one at a time,

-14

The standard deviation cannot be negative as it is a square root of the average of the sum of square deviations from the mean. Since the square of a number cannot be negative, it directly translates that the standard deviation cannot be negative.

3

A small standard deviation like 3 indicates that the distribution mostly centres about the mean, with very little variation. And the distribution given has a mean (78) that is very far away from at least one of the variables in the distribution. Hence, 3 is too low to pass ad the standard deviation of this distribution described.

0

A standard deviation of 0 indicates that all the variables in the distribution have the same value as the mean. That is, the distribution only contains 1 number, probably multiple times. So, this cannot be the standard deviation for the distribution described.

56

This value represents a value that is too high to express the spread of the distribution described. The mean (78) is very close to the maximum value of the distribution, and far away from the lower value(s), indicating that most of the distribution is in and around the upper values with a few variables closer to the lower limit. A standard deviation as high as 56 for a mean of 78 translates to a distribution with most of variables far from the mean, which isn't the case here.

Moreso, a simple add of the standard deviation to the mean or subtracting the standard deviation from the mean should give at least one of the results with values within the distribution.

(Mean) + (Standard deviation) = 78 + 56 = 134 >> 99 (outside distribution)

(Mean) + (Standard deviation) = 78 - 56 = 22 << 34 (also outside the distribution)

15

This is the most realistic value for the standard deviation as it represents what the distribution described above is.

The mean (78) being close to the maximum value of the distribution, and far away from the lower value(s) indicates that most of the distribution is in and around the upper values with a few variables closer to the lower limit.

So, 15 indicates a perfect blend of small deviations due to the high values close to the mean and the very high deviation from the evidently few lower values.

(Mean) + (Standard deviation) = 78 + 15 = 93 < 99 (within distribution)

(Mean) + (Standard deviation) = 78 - 15 = 63 > 34 (also within the distribution)

Hope this Helps!!!

When The most realistic value for the standard deviation is 15.

Step-by-step explanation:

Find out more information about standard​ deviation here:

https://brainly.com/question/25309029

Answer:

Step-by-step explanation:

[tex]r^{-7} +s^{-12} \\Use Negative Power Rule: x^{-a} =\frac{1}{x^{a} } \\r^{\frac{1}{7} } +s^{\frac{1}{12} } \\[/tex]

I hope i am correct

Answer:

(D)9.5 Units

Step-by-step explanation:

We have two chords CD and AB intersecting at E.

Using the theorem of intersecting chords

AE X EB =CE X ED

AB=AE+EB

16=10+EB

EB=16-10=6

Therefore:

AE X EB =CE X ED

10 X 6 = 4 X ED

ED =60/4 =15

Therefore:

CD=CE+ED

=4+15

CD=19

Recall that CD is a diameter of the circle and;

Radius =Diameter/2

Therefore, radius of the circle =19/2 =9.5 Units

Answer:

Radius of the circle = 6 units

Step-by-step explanation:

Let the radius of the circle be r

According to the given condition:

Area of the circle = 3 times the circumference of the circle

[tex]\therefore \pi r^2 =3\times 2\pi r\\\therefore r^2 = \frac{3\times 2\pi r}{\pi}\\\therefore r^2 = 3\times 2r\\\therefore r = 6\: units\\[/tex]

Answer:

22 m

Step-by-step explanation:

Total distance travelled by marble while falling down = height above surface of lake + depth of lake = 15 + 7 = 22 m

Answer:

(3, -1)

Step-by-step explanation:

5-2=3

0-1=-1 (keep 0, change - to a +, flip 1 to a -1)

Answer:

26.68% probability that exactly three will end up being replaced under warranty

Step-by-step explanation:

For each telephone under warranty, there are only two possible outcomes. Either they need to be replaced, or they do not need to be replaced. Each telephone is independent of other telephones. 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.

30% must be replaced with new units

This means that [tex]p = 0.3[/tex]

If a company purchases ten of these telephones, what is the probability that exactly three will end up being replaced under warranty

This is [tex]P(X = 3)[/tex] when [tex]n = 10[/tex]. So

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

[tex]P(X = 3) = C_{10,3}.(0.3)^{3}.(0.7)^{7} = 0.2668[/tex]

26.68% probability that exactly three will end up being replaced under warranty

Answer:

Step-by-step explanation:

let the height height of the tree be "h"

Hence the tree's height h=9 ft

one year later,let the height of the tree increased by x ft

hence

[tex]9 + x = 16[/tex] --------This is the equation for the growth of the tree

In order to solve for the added height(growth) of the tree we need to solve for x

[tex]9 + x = 16\\x=16-9\\x=7ft[/tex]

Answer:

I think the complete question should be:

A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 21 subjects were assigned randomly to the treatment group and received the new experimental drug. The other 23 subjects were assigned to the control group and received a standard well known treatment. After a suitable period of time, the reduction in blood pressure for each subject was recorded.

Treatment group n = 21, x1 mean = 23.48, sd = 8.01

Control group n = 23, x2 = 18.52, sd = 7.15

Based on these data, the computed two-sample t statistic is:

Step-by-step explanation:

Since the variances to be calculated from the sd are unequal we use this formula:

t statistics = (x1 - x2) / [(sd1²/n1) + (sd2²/n2) where n1 = 21, x1 mean = 23.48, sd1 = 8.01, n2 = 23, x2 = 18.52, sd2 = 7.15

Thus, we have

test statistic= (23.48-18.52) / [(8.01²/21) + (7.15²/23)]

Test statistics = 4.96 / (324.36/21)+(51.12/23)]

Test statistics = 4.96/ (15.45+2.43)

t statistic = 4.96 / 17.88

t statistics = 0.2774

I hope that helps, you can use this to solve for tours if the values are not the same

Hey there! I'm happy to help!

We want to find out how much Lana pays per month. Let's dissect each payment we are given so we can find our monthly expense.

---------------------------------------------------------------------------

AUTOMOBILE INSURANCE

$300 for automobile insurance semiannually

The prefix semi- means half. Annual means year. So, she is paying $300 every half year, or six months. So, we can divide 300 by 6 to find how much she pays in one month!

300/6=50

Therefore, she pays $50 a month for automobile insurance.

---------------------------------------------------------------------------

HEALTH INSURANCE

We are told here that she pays $100 every month for health insurance. We don't need do anything else here!

---------------------------------------------------------------------------

LIFE INSURANCE

We see that Lana pays $700 per year on life insurance. We can divide this by 12 to find out how much there is in 1 month!

700/12≈58.33

Therefore, she pays $58.33 every month on life insurance.

---------------------------------------------------------------------------

SOLUTION

Now, we just add all of these monthly totals up to find Lana's monthly expense.

50+100+58.33=208.33

Therefore, Lana's monthly expense is $208.33.

I hope that this helps! Have a wonderful day!