Recall the following corollary to Fermat’s Little Theorem: If p is a prime, then a p ≡ a(mod p) for any integer a.
a. Use this result to prove the following lemma: If p and q are distinct primes with a^p ≡ a(mod q) and a^q ≡ a(mod p), then a^pq ≡ a(mod pq).
b. Use the result in part a. to establish that 2^340 ≡ 1(mod 341). Hence, the converse of Fermat’s Little Theorem is false

Answer:

207 cubic centimeters

Step-by-step explanation:

Given

volume of cone  = 9 cubic centimeters

Since the cone and cylinder above have the same radius, r, and height, h, then r = h

volume of the cone = 1/3πr²h

69 =  1/3πr²h

πr²h = 69*3

πr²h = 207cubic cm

Since the volume of the cylinder =  πr²h

Hence volume of the cylinder is 207 cubic centimeters

Answer:

not enough information

Step-by-stepexplanation:

Answer:

64 combination attempts

Step-by-step explanation:

Since each dial in the lock is numbered from 1-8 then there are 8 possibilities for each dial. Out of the three dials, only 2 actually need to be correct in order for the lock to open therefore, we simply raise the number of possibilities for each dial to the power of 2 which should give us the total number of tries we need in order to guarantee that it opens. Assuming that you are making the combinations in numerical order 1-1-1, 1-1-2, 1-1-3, etc.

8^2 = 64 combination attempts

Answer:

3000 here hope this helps you out

Answer:

Parameter OF Δ JKL = 138 unit

Step-by-step explanation:

Given:

JN = 8x - 35

NK = 7y - 9

OK = 2y + 11

OL = 32 - [2y + 11]

JM = 5x - 8

Find:

Parameter OF Δ JKL

Computation:

We know that tangent from same points are always equal

So,

ML = OL

JM = JN

5x - 8 = 8x - 35

8x - 5x = 35 - 8

3x = 27

x = 9

So,

JN = 8x - 35

JN = 8(9) - 35

JN = 37 unit

JM = 5x - 8

JM = 5(9) - 8

JM = 37 unit

NK = OK

7y - 9 = 2y + 11

5y = 20

y = 4

NK = 7y - 9

NK = 7(4) - 9

NK = 19 unit

OK = 2y + 11

OK = 2(4) + 11

Ok = 19 unit

OL = 32 - [2(y) + 11]

OL = 32 - [2(4) + 11]

OL = 13 unit

So,

LM = OL = 13 unit

Parameter OF Δ JKL = JN + NK +  OK + OL + LM + JM

Parameter OF Δ JKL = 37 + 19 + 19 + 13 + 13 + 37

Parameter OF Δ JKL = 138 unit

Answer:

Step-by-step explanation:

g

Answer:

Since Ben would have $362, he won't be able to buy the stereo as he needs to have an amount greater than or equal to 365.

Step-by-step explanation:

First, you need to determine the amount that Ben would have after saving $15 for the next 10 weeks:

$15*10=$150

Now, the inequality indicates that the amount left to save plus 212 should be greater than or equal to 365, so you have to add up 212 plus the amount Ben will save in the next 10 weeks to be able to determine if he would be able to buy the stereo:

150+$212=$362

Since Ben would have $362, he won't be able to buy the stereo as he needs to have an amount greater than or equal to 365.

Answer:

add 5 to both sides, divide by 2, take square root, subtract 3/4

Step-by-step explanation:

I think you maybe do the reverse order of operations, which is SADMEP (subtract/add, then divide/multiply, then take care of exponents and square roots, then do that same order for whatever's in parenthesis.)

Answer:

14

Step-by-step explanation:

First you figure out what the value of x is, and then you must add the numbers in the Participates in Sports column to get 14

Answer:

-2x² + x - 7

Step-by-step explanation:

(6x² - 9x + 7) + (-8x² + 10x - 14)

6x² - 9x + 7 - 8x² + 10x - 14

6x² - 8x² - 9x + 10x + 7 - 14

-2x² + x - 7

Answer:

4 revolutions per second

Step-by-step explanation:

60 revs / 15 secs = 4 revs/sec

Answer:

4 revolutions per second

Step-by-step explanation:

60/15 = 4

We evaluate S_n by substituting x = 0.4 into the nth partial sum and obtain our approximation for the integral.

To approximate the definite integral ∫(0 to 0.4)

[tex] {e}^{-x^3} [/tex]

dx with an error less than

[tex] {10}^{ - 4} [/tex]

we can use a Taylor series expansion for

[tex]{e}^{-x^3} [/tex]

The Taylor series expansion of

[tex]{e}^{-x^3} [/tex]

centered at x = 0 is:

[tex] {e}^{-x^3} = 1 - x^3 + (x^3)^2/2! - (x^3)^3/3! + ...[/tex]

By integrating this series term by term, we can approximate the integral. Let's denote the nth partial sum of the series as S_n.

To estimate the number of terms needed for the desired accuracy, we can use the error estimate formula for alternating series:

|Error| ≤ |a_(n+1)|, where a_(n+1) is the absolute value of the first omitted term.

In this case, |a_(n+1)| =

[tex]|(x^3)^{n+1} /(n+1)!| ≤ {0.4}^{(3(n+1)} /(n+1)!

[/tex]

By setting

[tex]{0.4}^{(3(n+1))} /(n+1)! < 10^(-4)[/tex]

and solving for n, we can determine the number of terms required.

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Answer:

The area inside the running track is 248.5 m².

Step-by-step explanation:

The area inside the running track is given by the sum of the area of a rectangle and the area of a semicircle:

[tex] A_{t} = A_{r} + 2A_{c} [/tex]                

[tex] A_{t} = x*(2r) + 2*(\frac{\pi r^{2}}{2}) [/tex]      

Where:

x: is one side of the rectangle = 30 m            

r: is the radius = half of the other side of the rectangle = 7/2 m = 3.5 m

Hence, the total area is:

[tex] A_{t} = 30*7 + \pi (3.5)^{2} = 248.5 m^{2} [/tex]                            

Therefore, the area inside the running track is 248.5 m².

I hope it helps you!                                                    

Answer:

4.56

Step-by-step explanation:

The slope (m) of the line given in the graph is -0.332.

In the given graph coordinates of the line are given, that is (2,0) and (-4, 2).

Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

Now, the slope of the line=m=0-2/2-(-4)=-2/6=-0.33333

-0.33333≈-0.332

Therefore, the slope (m) of the line given in the graph is -0.332.

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Answer:

∠x = 59°

Step-by-step explanation:

∠ECD = 52°   because they are alternate angles and will be equal

∠x = 180° - 52° - 69° = 59°  because the sum of the interior angles of a triangle = 180°

The probability P(X=0) is equal to 0.24.

In the given probability distribution, we are provided with the probabilities associated with each value of the random variable X. To find P(X=0), we need to identify the probability assigned to the value 0.

Looking at the table, we see that the probability P(X=0) is given as 0.24. Therefore, the correct answer is option b. 0.24.

The probability distribution assigns probabilities to specific values of the random variable X. In this case, the value 0 has a probability of 0.24. This indicates that there is a 0.24 chance of observing the value 0 when the random variable X is sampled from this distribution.

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If your car gets 29 miles per gallon, the cost to drive 300 miles when gasoline costs $3.20 per gallon is approximately $33.10.

One way to determine the cost of driving 300 miles is to divide the number of miles by the miles per gallon (MPG) and then multiply by the cost of gasoline per gallon.

Divide 300 miles by 29 MPG to get the total number of gallons of gasoline needed:

300 ÷ 29 ≈ 10.34 gallons

Round up to the nearest whole number to get 11 gallons

Multiply the number of gallons by the cost per gallon of gasoline:

$3.20/gallon x 11 gallons = $35.20

Therefore, it will cost $35.20 to drive 300 miles when gasoline costs $3.20 per gallon with a car that gets 29 miles per gallon.

We know that 1 US gallon equals 3.785411784 liters. Therefore, the car travels 29 x 3.785411784 = 109.724897 liters in 1 US gallon.

So, the cost of traveling 300 miles will be 300/29 = 10.34482759 gallons.

So, the cost of traveling 300 miles will be $3.2 x 10.34482759 = $33.10344828. Therefore, the cost of traveling 300 miles will be $33.10 approximately.

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Answer:

answer : b

Step-by-step explanation:

hello :

calculate : f (x)=-7(x+4)²-1

f(x) = -7(x²+16+8x) -1  use  identity : (a+b)² = a²+b²+2ab

f(x) = -7x²-112 -56x -1

f(x) = -7x²-56x -113  

Answer:

By the end of the week there will be 49,152 zombies in Panama City Beach.

Step-by-step explanation:

Since the Zombie Apocalypse has come to Panama City Beach, starting when 3 Spring Breakers become zombie after an encounter with a deadly fish, and since waking up the next day, each Spring Breaker can infect 4 more people per day before needing a rest , and each of these zombies can, in turn, infect an additional 4 people per day, to determine how many crazy Spring Break Zombies will be roaming the beach at the end of the week the following exponential function has to be solved:

3 x 4 ^ 7 = X

3 x 16,384 = X

49.152 = X

Therefore, by the end of the week there will be 49,152 zombies in Panama City Beach.

The number of crazy Spring Break Zombies will be roaming the beach at the end of the week 7 are 49,152 and the equation for the situation is,

[tex]x=3\times(4)^7\\[/tex]

Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.

The exponential function with dependent variable y and independent variable x can be written as,

[tex]y=ba^x+c[/tex]

Here, a, b and c are the real numbers.

The Zombie Apocalypse has come to Panama City Beach. It starts when 3 Spring Breakers become zombie after an encounter with a deadly fish.

In the next morning, each Spring Breaker can infect 4 more people per day before needing a rest. Each of these zombies can, in turn, infect an additional 4 people per day.

As total number of weeks are 7. Thus, for this situation, the exponential function for the variable x can be given as,

[tex]x=3\times(4)^7\\[/tex]

Now to find the number of crazy Spring Break Zombies will be roaming the beach at the end of the week 7, simplify the above equation as,

[tex]x=3\times(4)^7\\\\x=3\times16384\\x=49152[/tex]

Hence, the number of crazy Spring Break Zombies will be roaming the beach at the end of the week 7 are 49,152 and the equation for the situation is,

[tex]x=3\times(4)^7\\[/tex]

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Answer:

I believe that the answer is '3a^2-4a+2

The formula for the kth payment Pₖ is Pₖ = (1/10 * PV) + (PV * r).

To find a formula for the kth payment Pₖ, we can start by calculating the monthly interest rate and the total number of payments.

Given that the loan is payable in 10 years, we have a total of 10 payments. The loan amount PV is 500,000 pesos, and the effective annual interest rate r is 18%.

First, let's calculate the monthly interest rate:

Monthly interest rate = (1 + r)^(1/12) - 1

Substituting the values, we have:

Monthly interest rate = (1 + 0.18)^(1/12) - 1 ≈ 1.4337% or 0.014337

Now, let's find the kth payment Pₖ. Since the borrower pays 50,000 pesos in principal at the end of each year, which is 1/10 of the loan amount, we can modify the formula to:

Pₖ = (1/10 * PV) + (PV * r)

Substituting the given values, we have:

Pₖ = (1/10 * 500,000) + (500,000 * 0.014337)

Simplifying, we get:

Pₖ ≈ 50,000 + 7,168.5 ≈ 57,168.5 pesos

This formula gives the kth payment Pₖ for any specific year during the loan term.

Now, let's construct an amortization schedule for this loan:

Year | Payment | Principal | Interest | Balance

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

1    | 57,168.5 | 50,000   | 7,168.5  | 450,000

2    | 57,168.5 | 50,000   | 7,168.5  | 400,000

3    | 57,168.5 | 50,000   | 7,168.5  | 350,000

...

10   | 57,168.5 | 50,000   | 7,168.5  | 0

In each year, the principal payment remains constant at 50,000 pesos, and the interest payment gradually decreases as the outstanding balance decreases. The balance reaches zero after 10 years, indicating that the loan has been fully paid off.

Please note that the actual schedule may vary slightly due to rounding errors and the specific date of the first payment.

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Answer:

√{100×4)=√20²=±20 is your answer

P-value is less than the level of significance α = 0.05, we reject the null hypothesis and conclude that the mean time to assemble at the end of a 3-week training period is less for the new training procedure.

a. Performing the test using the classical approach α=0.05

Hypothesis test:

Null hypothesis H₀: The mean time for the new procedure = the mean time for the standard procedure

Alternative hypothesis H₁: The mean time for the new procedure < the mean time for the standard procedure (one-tailed test)

Level of significance α = 0.05

Since population standard deviations are unknown, we will use the t-test to conduct the hypothesis test.

Below is the calculation of the t-test.(For detailed calculation of t-test, please refer to the image attached)

Using a t-distribution table with df = 14 (n1 + n2 - 2), the critical value for a one-tailed test at α = 0.05 is -1.761.

The test statistic (-2.029) is less than the critical value (-1.761), so we reject the null hypothesis and conclude that the mean time to assemble at the end of a 3-week training period is less for the new training procedure.

b.Performing the above test assuming population variances are equal

Hypothesis test

Null hypothesis H₀: The mean time for the new procedure = the mean time for the standard procedure

Alternative hypothesis H₁: The mean time for the new procedure < the mean time for the standard procedure (one-tailed test)Level of significance α = 0.05

Since population variances are assumed to be equal, we will use the pooled t-test to conduct the hypothesis test.

Below is the calculation of the pooled t-test.(For detailed calculation of pooled t-test, please refer to the image attached)

Using a t-distribution table with df = 16 (n₁ + n₂ - 2), the critical value for a one-tailed test at α = 0.05 is -1.746.

The test statistic (-2.029) is less than the critical value (-1.746), so we reject the null hypothesis and conclude that the mean time to assemble at the end of a 3-week training period is less for the new training procedure.

c. Performing the above test (#2) using the p-value approach.

Hypothesis test:

Null hypothesis H₀: The mean time for the new procedure = the mean time for the standard procedure

Alternative hypothesis H₁: The mean time for the new procedure < the mean time for the standard procedure (one-tailed test)

Level of significance α = 0.05

Since population variances are assumed to be equal, we will use the pooled t-test to conduct the hypothesis test.

The test statistic is -2.029, which corresponds to a p-value of 0.0328.

Since the p-value is less than the level of significance α = 0.05, we reject the null hypothesis and conclude that the mean time to assemble at the end of a 3-week training period is less for the new training procedure.

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Answer: $7,915.98

Step-by-step explanation: This is an exponentially decaying problem, so that means we use the formula ab^x.

The a value is the original price or the starting point, which is 15,000. The b value is the ratio in which it decreases or increases. It is decreasing, so we subtract 12 from 100, which is 88. The ratio should be in decimal form, so it is 0.88. Finally, the x should be the exponent, the amount of times it is getting multiplied by the ratio. So the equation would be 15,000(0.88)^5.

Then, we solve.

0.88 * 0.88 * 0.88 * 0.88 * 0.88 = 0.5277319168

Then 0.5277319168 * 15,000 = 7,915.978752.

Of course, we round to the nearest hundredth, which is 7,915.98. Hope this helped.

A coefficient is significantly different from zero at 5% level if the coefficient of a variable is twice as large as its estimated standard error. This is because, at the 5% level of significance, the critical value for the t-distribution, when a two-tailed test is used, is equal to 1.96. To be significantly different from zero, the calculated t-value has to be greater than 1.96 or less than -1.96.

Suppose the estimated standard error is SE and the coefficient of the variable is β. The standard error of β, denoted by SE(β), is equal to SE/√n, where n is the sample size. Thus, if the coefficient of the variable is twice as large as its estimated standard error, then β > 2SE.

And, the calculated t-value would be greater than (β/SE) > 2, which is greater than 1.96. Therefore, we can say that the coefficient is significantly different from zero at the 5% level.

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Answer:

its b

Step-by-step explanation:

have a great day <3

The growth rate of your credit card balance is approximately 0.0142.

Therefore, the correct option is B.

Given that you got a credit card, you purchased a stereo system for $200. your credit limit is $1000.

The monthly interest rate is 1.42%.

We need to determine the growth rate of your credit card balance,

To calculate the growth rate of your credit card balance, we need to consider the monthly interest rate and the initial purchase amount.

The monthly interest rate is 1.42%, which can be expressed as a decimal by dividing it by 100: 0.0142.

The initial purchase amount is $200.

Assuming no payments are made and no additional purchases are made, the credit card balance will increase each month due to the accrued interest.

To calculate the growth rate, we can divide the accrued interest by the initial purchase amount.

Accrued interest = Monthly interest rate x Initial purchase amount

= 0.0142 x $200

= $2.84

Growth rate = Accrued interest / Initial purchase amount

= $2.84 / $200

≈ 0.0142

Therefore, the growth rate of your credit card balance is approximately 0.0142, which corresponds to option B.

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Answer:

$220.5

Step-by-step explanation:

To answer this simply multiply the number of hours (25.2) times the hourly wage 8.75 and you'll get the answer

25.2 times 8.75 equals 220.5