Create an equivalent expression for 18^-7. 18^5. -18² 18² 1/18^-2 1/18²​

So our final solutions on the given interval are theta = 153.4 degrees and theta = 333.4 degrees.

An equation is a mathematical statement that uses an equal sign (=) to show that two expressions are equal. It typically contains variables, constants, and mathematical operations. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true. Equations are commonly used in various fields of mathematics, as well as in physics, chemistry, engineering, and many other scientific disciplines.

Here,

To solve the equation tan(theta) = -1/2, we first need to find the angle whose tangent is -1/2. We can do this by using the inverse tangent function (also known as arctan or tan^-1) on a calculator or by using the reference angles for tangent.

Using a calculator, we get theta = -26.6 degrees or theta = 153.4 degrees.

To find all solutions on the given interval 0(degrees) < theta < 360 degrees, we need to add 360 degrees to each solution that is less than 0 degrees and subtract 360 degrees from each solution that is greater than 360 degrees.

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Answer:

x = 1 / 2 ( or ) 0.5

Step-by-step explanation:

4x - y = 5

Substitute the value of y = - 3 in the given equation,

4x - ( - 3 ) = 5

4x + 3 = 5

4x = 5 - 3

4x = 2

x = 2 / 4

x = 1 / 2 ( in terms of fraction )

                  ( or )

x = 0.5 ( in terms of decimal )

Note : -

- ( - 3 ) can be written as - 1 x ( - 3 ).

When a negative number is multiplied with another negative number, the result will be positive number.

Hence,

- ( - 3 ) = + 3

Step-by-step explanation:

you can just put in some values to check.

I actually used p =2 and q=3

the It will be

2^3-1 + 3^2-1 = 1 (mod 2×3)

2^2 +3^1 = 1 (mod 6)

4+3= 1 (mod6)

7= 1 (mod6)

which is true.

therefore p^(q-1) + q^( p-1) = 1 ( mod pq) is true

To show that p^(q-1) + q^(p-1) = 1 (mod pq), we can use Fermat's Little Theorem, which states that if p is a prime number and a is an integer not divisible by p, then a^(p-1) = 1 (mod p). Using this theorem, we can first show that p^(q-1) = 1 (mod q), since q is a prime number and p is not divisible by q. Similarly, we can show that q^(p-1) = 1 (mod p), since p is a prime number and q is not divisible by p.

Therefore, we can write:

p^(q-1) + q^(p-1) = 1 (mod q)
p^(q-1) + q^(p-1) = 1 (mod p)

By the Chinese Remainder Theorem, we can combine these two equations to obtain:

p^(q-1) + q^(p-1) = 1 (mod pq)

Thus, we have shown that p^(q-1) + q^(p-1) = 1 (mod pq).
We'll use Fermat's Little Theorem to show that p^(q-1) + q^(p-1) = 1 (mod pq).

Fermat's Little Theorem states that if p is a prime number and a is an integer not divisible by p, then:
a^(p-1) ≡ 1 (mod p)

Step 1: Apply Fermat's Little Theorem for p and q:
Since p and q are prime numbers, we have:
p^(q-1) ≡ 1 (mod q) and q^(p-1) ≡ 1 (mod p)

Step 2: Add the two congruences:
p^(q-1) + q^(p-1) ≡ 1 + 1 (mod lcm(p, q))

Step 3: Simplify the congruence:
Since p and q are prime, lcm(p, q) = pq, so we get:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

In your question, you've mentioned that the result should be 1 (mod pq), but based on Fermat's Little Theorem, the correct result is actually:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

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The random variable "the number of cups of coffee sold in a cafeteria during lunch" is discrete.

This is because the variable can only take on integer values, such as 0, 1, 2, 3, and so on. It is not possible to sell a fraction of a cup of coffee, which is what would make it a continuous variable.

A discrete random variable has a finite or countably infinite number of possible outcomes, and each outcome has a non-zero probability.

In contrast, a continuous random variable can take on any value within a certain range, and the probabilities are described by a probability density function.

In this case, since the number of cups of coffee sold can only take on whole number values, it is a discrete random variable.

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Answer:

$598.8

Step-by-step explanation:

499*1.2

598.8

Answer:

Pancho will earn $25.50 interest.

Step-by-step explanation:

interest= prt (principal x rate x time)

i= prt = 850(.015)(2)

i= 25.5

(.015 comes from dividing the percentage 1.5 by 100)

a) To find the percentage of pregnancies that should last between 26 and 275 days, we can calculate the area under the normal curve between these two values.

Using the standard normal distribution, we need to standardize the values by subtracting the mean and dividing by the standard deviation.

For 26 days:

Z = (26 - 262) / 18 = -12.222

For 275 days:

Z = (275 - 262) / 18 = 0.722

Now, we can find the corresponding probabilities using a standard normal table or a calculator.

The probability of a pregnancy lasting less than 26 days is P(Z < -12.222) which is essentially 0.

The probability of a pregnancy lasting less than 275 days is P(Z < 0.722) = 0.766.

To find the percentage between 26 and 275 days, we subtract the probability of less than 26 days from the probability of less than 275 days:

Percentage = 0.766 - 0 = 0.766 = 76.6%

Therefore, approximately 76.6% of pregnancies should last between 26 and 275 days.

b) To find the number of days for the longest 30% of all pregnancies, we need to find the corresponding Z-score for the upper 30% of the standard normal distribution.

Z(0.30) = 0.524 (approximately)

Now, we can reverse the standardization process to find the corresponding number of days:

X = Z * σ + μ

X = 0.524 * 18 + 262

X ≈ 271.43

Therefore, the longest 30% of all pregnancies should last at least approximately 271.43 days.

c) According to the Central Limit Theorem, the distribution of the sample mean will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Mean (μ) of the sample mean (y) = Mean of the population = 262 days

Standard deviation (σ) of the sample mean (y) = Standard deviation of the population / √n

σ(y) = 18 / √80 ≈ 2.015

Therefore, the mean of the distribution of the sample mean is 262 days and the standard deviation is approximately 2.015 days.

d) To find the probability that the mean duration of the patients' pregnancies will be less than 200 days, we can standardize the value using the sample mean and standard deviation:

Z = (200 - 262) / (18 / √80) ≈ -7.150

Using a standard normal table or a calculator, we find that P(Z < -7.150) is essentially 0.

Therefore, the probability of the mean duration of the patients' pregnancies being less than 200 days is very close to 0.

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Answer:

55.00

Step-by-step explanation:

basically I subtracted 84.25 from 75.49 and I got 8.76. So I too kthat answer and subtracted 8.76 from 63.76. So the answer is 55.00

The cancellation law for matrices states that if AB = AC, and A is an invertible matrix, then B = C. However, if A is not invertible, the cancellation law does not necessarily hold.

a)To determine the conditions on A, B, and C that guarantee the cancellation law, we must consider the rank of A.

If A has full rank (i.e., rank(A) = n), then the cancellation law holds. This is because a matrix with full rank has a trivial null space, and therefore, if AB = AC, we can left-multiply both sides by A-¹ to obtain B = C.

If A does not have full rank, then the cancellation law may not hold. In particular, if rank(A) < n, then there exist non-zero vectors x and y such that Ax = 0 and A(y+x) = Ay,

which implies that B(y+x) = C(y+x) and hence, B ≠ C.

Therefore, the condition for the cancellation law to hold is that the matrix A has full rank.

b)An example of matrices A,B and C for which the cancellation law does not hold is

A = [1 1 1  1 1 1  1 1 1]

B = [100  010  001]

C = [010  001  100]

We can verify that AB = AC, but B ≠ C.

AB = [1 1 1  1 1 1  1 1 1] [100 010 001] = [1 1 1  1 1 1  1 1 1]

AC = [1 1 1  1 1 1  1 1 1] [010 001 100] = [1 1 1  1 1 1  1 1 1]

However, B = [1 0 0  0 1 0  0 0 1] and C = [0 1 0  0 0 1  1 0 0] are not equal. Therefore, the cancellation law does not hold for these matrices.

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Answer:

-1/2

Step-by-step explanation:

Answer:

..

Step-by-step explanation:

It is not always possible to arrange a dance where each man dances with a different woman that he knows in the given scenario of n men and n women, with each man knowing exactly k women and each woman knowing exactly k men. The feasibility depends on the values of n and k, and in some cases, it may not be possible to satisfy this condition.

Let's consider the scenario where there are n men and n women. Each man knows exactly k women, and each woman knows exactly k men. In order for each man to dance with a different woman he knows, we need to ensure that there are enough women available for each man.

If we have n men and n women, and each man knows exactly k women, then the total number of women known to all men is n * k. For each man to have a different woman to dance with, we need at least n different women available.

However, if n * k is less than n, it means there are not enough women available to satisfy this condition, and it would be impossible to arrange a dance where each man dances with a different woman that he knows.

In some cases, it may be possible to arrange such a dance if n * k is equal to or greater than n, ensuring there are enough women for each man. However, the condition of mutual acquaintances does not guarantee a feasible arrangement in all scenarios. The feasibility depends on the specific values of n and k.

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The possibility that experimental results are due to chance, or some factor other than the experimental variable, is measured by the Probability Value.

Probability value, also called P-value, is defined as:

Under the premise that the null hypothesis is true, the p-value is the likelihood that test findings will be at least as extreme as the result actually observed.

Now,

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Answer:

Simplify the expression.

X+10x+1

Answer:

X+10x+1

Step-by-step explanation:

this would be your answer

Vertex is at (3,−1) ; y-intercept is at (0,8) and x-intercepts are at (2,0) and (4, 0)

We know the equation of parabola in vertex form is y = a(x - h)² + k where vertex is at (h,k). Here y = x² - 6x + 8 = (x - 3)² - 9 + 8 = (x - 3)² - 1 ∴ Vertex is at (3,-1) we find y-intercept by putting x = 0 in the equation. So y = 0 - 0 + 8 = 8 and x-intercept by putting y=0 in the equation. So x² - 6x + 8 = 0 or (x - 4)(x - 2) = 0 or x = 4; x = 2 graph{x^2-6x+8 [-20, 20, -10, 10]}

Answer:

62.5 miles per hour

Step-by-step explanation:

Answer:62.5 miles an hour

Step-by-step explanation: You would divide 250 by 4.

The expected value of x is e(√(x)) = e(√(2)) ≈ 1.6487.

The number of possible outcomes when tossing an unbiased coin four independent times is 2^4 = 16, and the probability of obtaining x heads is given by the binomial distribution:

P(x) = (4 choose x) * (1/2)^4 = (4!/(x!(4-x)!) * 1/16

Thus, the expected value of x is:

E(x) = Σ[xP(x)] from x=0 to x=4

= 0*(1/16) + 1*(4/16) + 2*(6/16) + 3*(4/16) + 4*(1/16)

= 2

So, e(√(x)) = e(√(2)) ≈ 1.6487.

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The conclusion that is appropriate at a 5% level of significance is this:C. There are statistically significant differences in the mean time to recurrence of depression symptoms for patients in the three treatment groups. this suggests that there is a treatment effect.

The correct conclusion is that the result obtained from the analysis is statistically significant, so the null hypothesis can be rejected. This also means that there are 1 in 20 chances of obtaining an error.

So, for a study checking the relationship between the mean time to recurrence of depression symptoms, the 5% level of significance would demonstrate a relationship.

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Answer:

C

Step-by-step explanation:

Answer:

2x + y = - 5

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 2 and (a, b) = (- 1, - 3 ) , thus

y - (- 3) = - 2(x - (- 1)), that is

y + 3 = - 2(x + 1) ← distribute

y + 3 = - 2x - 2 ( add 2x to both sides )

2x + y + 3 = - 2 ( subtract 3 from both sides )

2x + y = - 5

Answer:

the answer is -2/7 i hope this helps n srry if it dont help

Step-by-step explanation:

The two polygons triangle RST = triangle VWU are similar by the scale factor of 6/5. Option C is the correct answer.

Shapes in various dimensions can be scaled using the Scale Factor. In geometry, we study many geometrical forms that exist in both two- and three-dimensions. The scale factor is a way to compare figures with similar appearances but differing scales or measurements. Consider two circles that resemble one another but may have different radii.

The scale factor is given by:

Scale factor = length of segment of figure A / Length of segment of figure B

SF = 12/10 = 6/5

For the second segment:

SF = 18/15 = 6/5

Also, the angle WUF = angle TRS.

Hence, the two polygons triangle RST = triangle VWU are similar by the scale factor of 6/5. Option C is the correct answer.

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Answer:

I think it would be option 1

Step-by-step explanation:

Hope this is right and helpful

Answer:

what was your question?

Answer:

B. Right

C. Scalene

Step-by-step explanation:

The square shows that it's right angled

and the sides are different.

The number of the largest series and 3 times the smallest is 234 would be = 58 and 60.

An integer is a whole number, regardless of sign, that goes from 0 to infinity or to minus infinity.

Let's suppose the first integer is x then the second will be x + 2

Sum of the larger and 3 times the smaller is 234

(x + 2) + 3x = 234

4x + 2 = 234

4x = 232

x = 58 so x + 2 = 60

Therefore, both consecutive even integers such that the sum of the larger and 3 times the smaller is 234 is 58 and 60.

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Answer:

-1

Step-by-step explanation:

-4(y-2)=12

-4y+8=12

-4y=4

y= -1

Answer:

2×4=8

3×4=12

12÷2=6

8+6=14

Step-by-step explanation:

Answer:

17m

Step-by-step explanation: Cut the triangle in half and place it over the other triangle creating a square. We know that one side is 3m so since all the sides of a square are equal 3 times 3 equals to 9. For the rectangle 2 times 4 is 8. So finally 8 plus 9 equals to 17. The area of the composite figure is 17m.