Convert 60 miles pr hour to yards pr minute

Hello,

a) We know the binomial coefficients are all integers, so

[tex]\dfrac{p!}{k!(p-k)!}[/tex]

is an integer.

And we can notice that the numerator p! is divisible by p.

If we take [tex]1\leq k\leq (p-1)[/tex]

It means that k! does not contain p, and we can say the same for (p-k)!

So, we have no p at the denominator so the binomial coefficient is divisible by p, meaning this is 0 modulo p.

b) We can write that

[tex]\displaystyle (x+y)^p=\sum_{i=0}^{p} \ {\dfrac{p!}{i!(p-i)!}x^{p-i}y^i[/tex]

We use the result from question a) and the binomial coefficients are 0 modulo p for i=1,2 , ... p-1 so there are only two terms left and then,

[tex](x+y)^p=x^p+y^p \text{ modulo p}[/tex]

c) Let's prove it by induction.

step 1 - for x = 0

This is trivial to notice that

[tex]0^p=0 \text{ modulo p}[/tex]

Step 2 - we assume that this is true for k

meaning [tex]k^p=k \text{ modulo p}[/tex]

and we need to prove that this is true for the k+1

We use the results of b)

[tex](k+1)^p=k^p+1^p=k^p+1 \text{ modulo p}[/tex]

and we use the induction hypothesis to say

[tex](k+1)^p=k^p+1^p=k^p+1=k+1 \text{ modulo p}[/tex]

And it means that this is true for k+1

Step 3 - conclusion

We have just proved by induction the Fermat's little theorem.

p a prime number, for for all x integers

[tex]\Large \boxed{\sf \bf x^p=x \textbf{ modulo p}}[/tex]

Thank you

Answer:

la distancia del punto de observación A al incendio = 5.5 millas

la distancia del punto de observación B al incendio = 3.8 millas

Step-by-step explanation:

La expresión esquemática de la pregunta se puede ver en la imagen adjunta a continuación :

Del siguiente diagrama;

Usando la sine regla:

[tex]\dfrac{sin \ F}{f} = \dfrac{sin \ A }{a}[/tex]

[tex]\dfrac{sIn \ 79}{6} = \dfrac{sin \ 63}{a}[/tex]

a sin 79 = 6 sin 63

[tex]a =\dfrac{6 \times sin \ 63}{sin \ 79}[/tex]

[tex]a =\dfrac{6 \times 0.8910}{0.9816}[/tex]

a = 5.446 millas

la distancia del punto de observación A al incendio = 5.5 millas (a la décima más cercana)

[tex]\dfrac{sin \ F}{f} = \dfrac{sin \ B}{b}[/tex]

[tex]\dfrac{sin \ 79}{6} = \dfrac{sin \ 38}{b}[/tex]

b sin 79 = 6 sin 38

[tex]b = \dfrac{6 \times sin \ 38}{sin \ 79}[/tex]

[tex]b = \dfrac{6 \times0.6157 }{0.9816}[/tex]

b = 3.7635 millas

la distancia del punto de observación B al incendio = 3.8 millas (a la décima más cercana)

Answer:

none

Step-by-step explanation:

110 + 60 = 170

but 170 is obviously not 180 sooo none will be 60 degrees

Answer:

The round off values are- 3.14, 6.12, and 4.57 respectively.

Step-by-step explanation:

The given value to which we have to round off is a. 3.14159 b. 6.12356 c. 4.56787

In order to round off the number we must keep in mind that there should be three digits in total and we will increase the value by one if the right-hand side value is more than 5.  

Thus round off figure of 3.14159 is 3.14.

The round off figure of 6.12356 is 6.12.

The round off figure of 4.56787 is 4.57.

Answer:

4, 15, 6, 18.

Step-by-step explanation:

Try the others by yourself and if you have any questions ask me in the comments

Answer:

Step-by-step explanation:

True

Answer:

∠ B = 54°

Step-by-step explanation:

Supplementary angles sum to 180°.

Sum A and B  and equate to 180, that is

7x + 14 + 5x - 26 = 180, that is

12x - 12 = 180 ( add 12 to both sides )

12x = 192 ( divide both sides by 12 )

x = 16

Thus

∠ B = 5x - 26 = 5(16) - 26 = 80 - 26 = 54°

Answer:

x =0

Step-by-step explanation:

[tex]\left(6^2\right)^x=1\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\\left(6^2\right)^x=6^{2x}\\\\6^{2x}=1\\\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)\\\ln \left(6^{2x}\right)=\ln \left(1\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\\\ln \left(6^{2x}\right)=2x\ln \left(6\right)\\2x\ln \left(6\right)=\ln \left(1\right)\\[/tex]

[tex]\mathrm{Solve\:}\:2x\ln \left(6\right)=\ln \left(1\right):\\\quad x=0[/tex]

Answer:

If radius = 8 cm and we needed perimeter of complete circle then

circumference (or perimeter) = 2*PI * 8 = 50.2654824574  cm

or 50.27 cm (rounded)

Step-by-step explanation:

Step-by-step explanation:

The answer is not in the option.

The answer is 29/24.

Answer:

the sum of the this series is Sn = [n(n+1)] / 2

Answer:

This means in the first week the number sells of digital copies is 308, paperback sells was 385 copies and hardback sell was 77 copies

Step-by-step explanation:

Let the number of digital copies be x, the number of paperback copies be y and the number of hardback copies be z.

4 digital sales is equal to 5 paperback sales and 1 hardback sale.

5x = 4y, x = 4z, y = 5z

The company sells 308 more paperback copies of the book than hardback copies

y = 308 + z

But y = 5z

5z = 308 + z

4z = 308

z = 77

y = 5z = 5(77) = 385

x = 4z = 4(77) = 308

This means in the first week the number sells of digital copies is 308, paperback sells was 385 copies and hardback sell was 77 copies

Answer:

The equation for constant of proportionality is:

y = kx

K = Constant of proportionality

An example:

4y = 8x

=> 4y/4 = 8x/4

=> y = 2x

In the answer, y = 2x;   2 is the constant of proportionality

Answer:

it is ratio of the amount s y and x:k = y/x. put another way: y = Kx.

Example:- you are paid 20 rupaye an hour the constant of proportionality is 20

because pay = 20 hours worked

Answer:

x = 0.6

Step-by-step explanation:

3x - 1.1 = 0.7

3x = 1.8

x = 0.6

Answer:

x = .6

Step-by-step explanation:

3x – 1.1 = 0.7

Add 1.1 to each side

3x – 1.1+1.1 = 0.7+1.1

3x = 1.8

Divide each side by 3

3x/3 = 1.8/3

x = .6

Answer:

n = 5

Step-by-step explanation:

All of the other choices are true except for n = 5, which is a counterexample. [tex]4^{5}[/tex] = 1024, which is greater than the other side as the other side is:

and [tex]4^{2}[/tex] = 16, 16 + 250 = 266

1024 < 266 is definitely false.

Therefore, the counterexample is n = 5.

Answer:

0.49926

Step-by-step explanation:

We solve for this using z score formula

z-score is

z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation

The probability that defect length is at most 20 mm is calculated as:

x = 20mm, μ = 33 mm, σ = 7.9mm

z = 20 - 33/7.9

= -13/7.9

= -1.64557

Obtaining the Probability value from Z-Table:

Probability (At most 20mm) = P(x ≤ 20mm) P(z = -1.64557)

P(x ≤ 20) = 0.049926

Therefore, the probability that defect length is at most 20 mm is 0.049926

Answer:

The probability that defect length is at most 20 mm is 0.0495.

Step-by-step explanation:

We are given that the defect length of a corrosion defect in a pressurized steel pipe is normally distributed with a mean value of 33 mm and a standard deviation of 7.9 mm.

Let X = the defect length of a corrosion defect in a pressurized steel pipe

The z-score probability distribution for the normal distribution is given by;

                             Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean defect length = 33 mm

           [tex]\sigma[/tex] = standard deviation = 7.9 mm

So, X ~ Normal([tex]\mu=33 \text{ mm}, \sigma^{2} = 7.9^{2} \text{ mm}[/tex])

Now, the probability that defect length is at most 20 mm is given by = P(X [tex]\leq[/tex] 20 mm)

        P(X [tex]\leq[/tex] 20 mm) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{20-33}{7.9}[/tex] ) = P(Z [tex]\leq[/tex] -1.65) = 1 - P(Z < 1.65)

                                                             = 1 - 0.9505 = 0.0495              

The above probability is calculated by looking at the value of x = 1.65 in the z table which has an area of 0.9505.

Answer:

the answer is b

Step-by-step explanation:

Answer:How many miles can a car be driven in 3 hours at 50 miles per hour? Under normal circumstances and the generally assumed conditions, the answer is of course (3 hours) * (50 miles / hour) = 150 miles.

3.5 hours

It will take you 3.5 hours to go 280 miles at 80 miles an hour.It travels at constant speed for the remaining time. Let x be the time traveled at the unknown constant speed. The total itme for the trip was 6 hours so: 6 = time traveled at 50 mph + time traveled at 60 mph + time traveled at x mph.

Step-by-step explanation:So you drive 25 miles / hour. then 25 miles/ 1 hour = 225 miles / nb of hours.2 minutes

However, traveling at 30 MPH for 1 mile (1 lap) takes 2 minutes, which means that your average will never be 60MPH.approximately 0.6818 miles per hour.

Answer:-6x^2+10x-5.

Step-by-step explanation: -6x^2-1−6x 2−1+x+9x+9                                                          -6x^2-1−6x 2−1+10x+9                                                                                                -6x^2-1-12−1+10x+9                                                                                                         -6x^2+10x-1-12-1+9                                                                                                                 6x^2+10x-5

The sum of the two expressions are -6x²+22x+9

In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.

Given here the expressions here as -6x²+1+6x ×2-1, x+9x+9

The sum is -6x²+1+6x ×2-1 +x+9x+9=-6x²+22x+9

Hence, The sum of the two expressions are -6x²+22x+9

Learn more about like and unlike terms here:

https://brainly.com/question/29078851

#SPJ2

Answer:

[tex]10^{11}[/tex]

Step-by-step explanation:

A statement is given i.e. "ten to the eighth divided by ten to the negative third."

It means that 10 to power 8 divided by 10 to the power -3.

Mathematically,

[tex]\dfrac{10^8}{10^{-3}}[/tex]

We know that, [tex]\dfrac{x^a}{x^b}=x^{a-b}[/tex]

Here, x = 10, a = 8 and b = -3

So,

[tex]\dfrac{10^8}{10^{-3}}=10^{8-(-3)}\\\\=10^{8+3}\\\\=10^{11}[/tex]

So, the answer is [tex]10^{11}[/tex]

Answer: [x/2 , 1]

Step-by-step explanation: Convert the inequality to interval notation.

The union consists of all of the elements that are contained in each interval. There is No Solution.

I hope this helps you out. If not, my apologizes.

-Leif Jonsi-

Answer: volume is 9 cubic units

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

Explanation:

Each cross section is a square with side length x, so the area of this cross section is x^2

We're integrating from x = 0 to x = 3

So we have

[tex]\displaystyle f(x) = x^2\\\\\\\displaystyle g(x) = \int x^2 dx = \frac{1}{3}x^3+C\\\\\\\displaystyle \int_{a}^{b} f(x) dx = g(b) - g(a)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = g(3) - g(0)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = \left(\frac{1}{3}(3)^3+C\right) - \left(\frac{1}{3}(0)^3+C\right)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = 9\\\\\\[/tex]

Answer: 32

Step-by-step explanation:

Answer: x = -2

x + 9 = 7, Move the constant to the right.

x =7 -9 now calculate that.

then you get x = -2

Hope that helps ya out :D

Answer:

x+9=7

So x= 7-9

( 9 became -9 because we brought it back to the other side to have the x alone and the digits alone )

So x= -2

Answer:

d = ±7i

Step-by-step explanation:

d^2 -1 = -50

Add 1 to each side

d^2 -1 = -50

d^2 = -49

Take the square root of each side

sqrt(d^2) = sqrt(-49)

d = sqrt(-1) sqrt(49)

d = i( ±7)

d = ±7i

Answer:

A.

Step-by-step explanation:

d^2-1= -50

First, add 1 to both sides.

d^2= -49

Take the square root of both sides:

d=√-49

Since i^2=-1

d=i√49

d= ±7i

Hope this helps!

Answer:

False

Step-by-step explanation:

|x+y| = |x| + |y|

To show this is false, all we have to do is find one example where it is false

Let x = -1 and y = 4

|-1+4| = |-1| + |4|

|3| = |1| + |4|

3 = 5

This is false so we have a set of integers where the statement is not true

Answer:

C

Step-by-step explanation:

So we have:

[tex]\frac{6^{\frac{3}{10}}}{6^\frac{1}{5}}[/tex]

To simplify, we can use the quotient rule of exponents, which says that if we have:

[tex]\frac{x^a}{x^b}[/tex]

Then this equals:

[tex]=x^{a-b}[/tex]

So, our equation will be:

[tex]\frac{6^{\frac{3}{10}}}{6^\frac{1}{5}}\\=6^{\frac{3}{10}-\frac{1}{5}}[/tex]

Subtract the exponents. Turn 1/5 into 2/10 by multiplying both layers be 2. Thus:

[tex]6^{\frac{3}{10}-\frac{1}{5}}\\=6^{\frac{3}{10}-\frac{2}{10}}[/tex]

Subtract in the exponent:

[tex]=6^{\frac{1}{10}}[/tex]

So, our answer is C :)

Answer:

[tex]Probability = \frac{845}{5832}[/tex]

Step-by-step explanation:

Given

Two standard dice

Required

Probability that the outcome will be greater than 8 for the first time on the third roll

First, we need to list out the sample space of both dice

[tex]S_1 = \{1,2,3,4,5,6\}[/tex]

[tex]S_2 = \{1,2,3,4,5,6\}[/tex]

Next, is to list out the sample when outcome of both dice are added together[tex]S = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}[/tex]

Next, is to get the probability that an outcome will be greater than 8

Represent this with P(E)

[tex]P(E) = \frac{Number\ of\ outcomes\ greater\ than\ 8}{Total}[/tex]

[tex]P(E) = \frac{10}{36}[/tex]

[tex]P(E) = \frac{5}{18}[/tex]

Next, is to get the probability that an outcome will noy be greater than 8

Represent this with P(E')

[tex]P(E) + P(E') = 1[/tex]

[tex]P(E') = 1 - P(E)[/tex]

[tex]P(E') = 1 - \frac{5}{18}[/tex]

[tex]P(E') = \frac{18 - 5}{18}[/tex]

[tex]P(E') = \frac{13}{18}[/tex]

Now, we can calculate the required probability;

Probability of a number greater than 8 first on the third attempt is:

Probability of outcome not greater than 8 on the first attempt * Probability of outcome not greater than 8 on the second attempt * Probability of outcome greater than 8 on the third attempt

Mathematically;

[tex]Probability = P(E') * P(E') * P(E)[/tex]

Substitute values for P(E) and P(E')

[tex]Probability = \frac{13}{18} * \frac{13}{18} * \frac{5}{18}[/tex]

[tex]Probability = \frac{13 * 13 * 5}{18 * 18 * 18}[/tex]

[tex]Probability = \frac{845}{5832}[/tex]

Answer:

f (x) = { 19 + 0.39(x - 300), x > 300

Step-by-step explanation:

Andrew has a cell phone plan that provides 300 free minutes each month for a flat rate of $19. For any minutes over 300, Andrew is charged $0.39 per minute. Let x be the number of minutes Andrew uses per month and f(x) be the charges based on Andrew's cell phone plan. If  then If  then first 300 minutes are free and each minute of next (x-300) minutes costs $0.39, therefore Hence, { 19 + 0.39(x - 300), x > 300

Hoped I helped