Find the sum of 1/3+1/8

Answer:

2/3

Step-by-step explanation:

Take each side of ABCD and divide it on each side of LMNO

AB/LM = 4/6=2/3

AD/LO =2/3

DC/ON = 4/6 =2/3

BC/MN = 2/3

Answer:

15/8

Step-by-step explanation:

Applying

tanθ = Opposite(O)/Adjacent(A)

tanθ = O/A............ Equation 1

From the diagram,

To get the opposite(O), we apply pythagoras theorem

a² = b²+c²

Where c = opposite

17² = 8²+c²

289 = 64+c²

c² = 289-64

c² = 225

c = √225

c = 15

Substitute into equation 1

Therefore,

tanθ = 15/8

Hence the exact value of tanθ is 15/8

The magnitude and angle of the complex number e^j2x/e^-jy are sqrt(e^(j4x) + e^(-j2y)) and 2.3562, respectively.

To determine the magnitude and angle of the given complex numbers, we need to use the following formulas:

Magnitude: |z| = sqrt(x^2 + y^2)

Angle: theta = tan^-1(y/x)

(a) 2e^-5jx

In this case, x = 2 and y = -5j

Magnitude: |z| = sqrt(2^2 + (-5j)^2) = sqrt(4 + 25j^2) = sqrt(29)

Angle: theta = tan^-1((-5j)/2) = -1.1903

Therefore, the magnitude and angle of the complex number 2e^-5jx are sqrt(29) and -1.1903, respectively.

(b) e^x + 1

In this case, x = e^x and y = 1

Magnitude: |z| = sqrt((e^x)^2 + 1^2) = sqrt(e^(2x) + 1)

Angle: theta = tan^-1(1/e^x) = 0.7854

Therefore, the magnitude and angle of the complex number e^x + 1 are sqrt(e^(2x) + 1) and 0.7854, respectively.

(c) e^j2x/e^-jy

In this case, x = e^j2x and y = e^-jy

Magnitude: |z| = sqrt((e^j2x)^2 + (e^-jy)^2) = sqrt(e^(j4x) + e^(-j2y))

Angle: theta = tan^-1((e^-jy)/(e^j2x)) = 2.3562

Therefore, the magnitude and angle of the complex number e^j2x/e^-jy are sqrt(e^(j4x) + e^(-j2y)) and 2.3562, respectively.

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If both p and 2p+1 are prime, then 2p+1 is a safe prime and p is a Sophie Germain prime.

Sophie Germain was a French mathematician who used these primes to investigate Fermat's Last Theorem, a famous mathematical conjecture that was finally proved in 1994 by Andrew Wiles. A safe prime is a prime number of the form 2p+1, where p is also a prime number, and it is called "safe" because it has some cryptographic properties that make it useful in certain encryption schemes.                                                                                                                                          In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions.

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Answer:

Step-by-step explanation:

\( \frac{2}{7} (x - 2) = 4x\)

\( = > \frac{2}{7} x - \frac{4}{7} = 4x\)

\( = > \frac{2}{7} x - 4x = \frac{4}{7} \)

\( = > \frac{2x - 28x}{7} = \frac{4}{7} \)

\( = > \frac{ - 26}{7} x = \frac{4}{7} \)

\( = > x = \frac{4}{7} \times \frac{7}{ - 26} \)

\( = > x = \frac{4}{ - 26} \)

\( = > x = \frac{ - 2}{13} (ans)\)

Answer:

x = -2/13

Step-by-step explanation:

\(\dfrac{2}{7}(x-2) = 4x\\\\Multiply \ both \ sides \ by \ 7 \\\\\\7*\dfrac{2}{7}(x-2)=4x*7\\\\\\2(x -2)= 28x\\Divide \ both \ sides \ by \ 2\\\\\dfrac{2(x-2)}{2}=\dfrac{28x}{2}\\\\\\x - 2 = 14x\\\\\\\)

Subtract 'x' from both sides

-2 = 14x - x

-2 = 13x

Divide both sides by 13

-2/13 = x

x = -2/13

Answer:

There are 6

Step-by-step explanation:

There are two within each circle.

Answer: 18.84 radians

Step-by-step explanation:

The two equivalent ratios of 15 / 60 are 30/120 and  45 / 180.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

The given fraction or ratio is 15 / 60. The equivalent ratio to the 15 / 60 will be written as:-

15 / 60 = 15 x 2 / 60 x 2

15 / 60 = 30 / 120

Multiply the numerator and the denominator by the same number.

15 / 60 = 15 x 3 / 60 x 3

15 / 60 = 45 / 180

Therefore, the two equivalent ratios of 15 / 60 are 30/120 and  45 / 180.

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Answer: 12

Step-by-step explanation:

1) 25%of50=$12.5. 50-12.5=37.5

2)20%of21=$4.2. 21-4.2=16.8

3)5%of12=$0.6.    12-0.6=11.4

HOPE THIS HELPED!!!

Answer:

1. $37.50

2.$16.80

3. 0.41

Step-by-step explanation:

Answer:

The second flare travels higher, 256 feet, and remains in the air longer, 8 seconds, than the first flare

Step-by-step explanation:

The given parameters are;

The height of the first flare = 196 feet

The duration the first flare spends in the air = 7 seconds

The function representing the height of the second flair is f(t) = -16t(t - 8)

Where;

t = The time since the passenger shot the second flare

The time the flair stays i the air is given by the time it takes for the height, f(t),  to be 0 as follows;

f(t) = 0 = -16t(t - 8)

-16t(t - 8) = 0

t = 0, or t = 8

The time the second flare stays in the air = 8 seconds

The maximum height reached by the second flair is given by the finding the maximum point of the curve of the function as follows;

d(f(t))/dt = 0 = d(-16t(t - 8))/dt = -32t + 128 at the maximum point (the coefficient of t² is negative in the quadratic equation)

-32t + 128 = 0

128 = 32t

32t = 128

t = 128/32 = 4

t = 4 at maximum height and f(4) = -16 × 4 × (4 - 8) = 256 feet

The maximum height reached by the second flare f(4) = -16 × 4 × (4 - 8) = 256 feet.

Therefore, the second flare travels higher, 256 feet, and remains in the air longer, 8 seconds, than the first flare, with maximum height of 196 feet, and time in the air of 7 seconds.

Euclid receives 20 shares of common stock as a nontaxable stock dividend.The basis of the common stock remains the same as in scenario a, which is $96.15 per share.

To calculate the per share basis, we divide the original purchase cost by the total number of shares (including the dividend shares).  In scenario b, Euclid receives a nontaxable preferred stock dividend of 20 shares. The preferred stock has a fair market value of $5,000, and the common stock, on which the preferred is distributed, has a fair market value of $75,000.

The tax consequences involve determining the new basis of the preferred stock and the common stock after the dividend. a. To find the per share basis of Euclid's common stock after receiving the stock dividend, we divide the original purchase cost by the total number of shares. The original purchase cost was $50,000 for 500 shares, which means the per share basis was $50,000/500 = $100. After receiving 20 additional shares as a dividend, the total number of shares becomes 500 + 20 = 520.

Therefore, the new per share basis is $50,000/520 = $96.15. b. In this scenario, Euclid receives a preferred stock dividend of 20 shares. The preferred stock has a fair market value of $5,000, and the common stock has a fair market value of $75,000. To determine the new basis of the preferred stock, we consider its fair market value.

Since the preferred stock dividend is nontaxable, its basis is equal to the fair market value, which is $5,000.

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Answer:

Time required to save 1000$ is 100 hours

Step-by-step explanation:

Money wasted = 1000$

savings = 10.00$ per hour

using unitary method

if i am saving 10.00 $ per hour then let in t hours i save 1000$

⇒ 10.00 x t = 1000

dividing above equation by 10 we get,

⇒ t = 100 hours

Therefore, Time required to save 1000$ is 100 hours

Step-by-step explanation:

Given that,

The diameter of the merry-go-round, d = 14 feet

Time taken, t = 6 seconds

Radius, r = 7 feet

The linear speed of the merry-go-round is given by :

\(v=\dfrac{2\pi r}{t}\\\\v=\dfrac{2\pi \times 7}{6}\\\\=7.33\ m/s\)

Also,

\(v=r\omega\)

Where

\(\omega\) is the angular speed

So,

\(\omega=\dfrac{v}{r}\\\\\omega=\dfrac{7.33}{7}\\\\=1.04\ rad/s\)

Hence, his linear and angular speeds are 7.33 m/s and 1.04 rad/s.

The probability that a randomly selected tire will have a life of at least 47,500 miles is 6.68%, which corresponds to answer choice c: .0668.

Probability is a mathematical concept that measures the likelihood or chance of an event occurring.It is a number between 0 and 1, with 0 designating an impossibility and 1 indicating a certainty. The probability of an event is calculated as the number of favorable outcomes divided by the number of possible outcomes.

The probability that a randomly selected tire will have a life of at least 47,500 miles can be found using a normal distribution and the z-score formula.

The z-score is calculated as follows:

z = (47,500 - 40,000) / 5,000 = 3.5

Using a standard normal table or calculator, we can find the cumulative probability associated with a z-score of 3.5. The probability that a randomly selected tire will have a life of at least 47,500 miles is:

P(X >= 47,500) = 1 - P(X < 47,500) = 1 - .9993 = .0007

Therefore, the answer is: c. .0668

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\(\frac{10^8}{10^6} = 10^{8-6} = 10^2 = 100\)

The rule used is

\(\frac{a^b}{a^c} = a^{b-c}\)

Subtract the exponents when dividing exponentials like this of the same base.

Answer: x = 2 hours y= 7 hours = 9 hours a week, 80$ a week

Step-by-step explanation:

5$x2=10$   10$x7=70$ 70$ + 10$ = 80 $.

hopefully, maybe that helps for the first question.

Answer:

The answer is C. 6ft 2

Step-by-step explanation:

The area of the rectangle having the dimension 3 feet by 2 feet is 6 square feet. Then the correct option is C.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.

A rectangle is 3 feet wide and 2 feet high.

Then the area of the rectangle will be

Area = Length × Width

Area = 3 × 2

Area = 6 ft²

The area of the rectangle is 6 square feet.

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Answer:

y=−9x and y=−4

Step-by-step explanation:

Answer:

part a:when it was 20 feranheight -50 we had a good rate selling hot chocolate but as it got hotter we decrease our sale

part b the y intercept will probably be 24 if it would had been keep going

Step-by-step explanation:

Answer:

Part A: It seems like the colder it was in his city, the more cups of chocolate he sold that day.

Part B:The line of best fit is y ≈-0.122x+20.944; r ≈ -0.372

Step-by-step explanation:

I added a snapshot of my work on a regression calculator

Answer:5 1/2

Step-by-step explanation:I took the test

We can determine coordinates if point t is between points u and v by checking if u < t < v or v < t < u.

To determine if point t is between points u and v, we need to compare their coordinates. If u < v, then point t is between points u and v if and only if u < t < v. On the other hand, if v < u, then point t is between points u and v if and only if v < t < u.

Whether or not point t is between points u and v depends on the relationship between the coordinates of u and v. If u < v, t must fall between them, and if v < u, t must also fall between them.

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The equation 3x = 6.4 can be solved for x by dividing both sides of the equation by 3: 3x/3 = 6.4/3; x = 2.13

So, for 3x and 6.4x to be equal, x must be equal to 2.13. This means that you need to multiply the number 6.4 by 2.13 to equal 3. The equation 3x = 6.4 represents the relationship between two variables, x and 3x. We are trying to find the value of x that would make 3x equal to 6.4. To do this, we divide both sides of the equation by 3. Dividing both sides of an equation by the same number does not change the relationship between the variables; it only scales down the variable's value by the same factor.

So, by dividing both sides of the equation by 3, we get:

3x/3 = 6.4/3

x = 2.13

Finally, to make 6.4x equal to 3, we need to divide 6.4 by 2.13: 6.4 / 2.13 = 3. So, we need to multiply 6.4 by 2.13 to equal 3.

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Let p be the probability of an adult over 50 wearing glasses for driving. Since we don't know the value of p, we can't use the binomial distribution directly. However, we can use the normal approximation to the binomial distribution since n is large (assuming n * p >= 10 and n * (1-p) >= 10).

Let X be the number of adults over 50 wearing glasses for driving in a random sample of n adults. Then X ~ Binomial(n, p) can be approximated by a normal distribution with mean µ = n * p and standard deviation σ = sqrt(n * p * (1-p)).

We want to find the probability that at least six adults over 50 in a random sample of n wear glasses for driving. This is equivalent to finding P(X >= 6) = 1 - P(X < 6) using the normal approximation.

To apply the normal approximation, we need to standardize the random variable X:

Z = (X - µ) / σ

Using continuity correction:

P(X >= 6) = P(X > 5.5)

Z = (5.5 - n * p) / sqrt(n * p * (1-p))

We can use the standard normal distribution table or calculator to find the probability:

P(Z >= (5.5 - n * p) / sqrt(n * p * (1-p)))

Since we don't know the value of p, we can use a conservative estimate of p = 0.5 (assuming 50% of adults over 50 wear glasses for driving). Then:

P(Z >= (5.5 - n * 0.5) / sqrt(n * 0.5 * (1-0.5)))

For example, if we sample n = 100 adults over 50, the probability of at least six wearing glasses is:

P(Z >= (5.5 - 100 * 0.5) / sqrt(100 * 0.5 * (1-0.5)))

= P(Z >= 0.5)

Using a standard normal distribution table or calculator, P(Z >= 0.5) = 0.3085.

Therefore, the probability of at least six adults over 50 wearing glasses for driving in a random sample of 100 is approximately 0.3085 or 30.85%.

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The value of (a) is (−133 mod 23 261 mod 23) mod 23 equals 20 and the value of (b) is (457 mod 23 ⋅ 182 mod 23) mod 23 equals 16.

a) To calculate (−133 mod 23 261 mod 23) mod 23, we start by evaluating the innermost parentheses.

−133 mod 23 equals -10, because -133 divided by 23 gives a quotient of -5 with a remainder of -10.

Similarly, 261 mod 23 equals 7, because 261 divided by 23 gives a quotient of 11 with a remainder of 7.

Now, we substitute these values into the expression:

(-10 mod 23 7 mod 23) mod 23.

Next, we evaluate the outermost parentheses:

-10 mod 23 equals -10, and 7 mod 23 equals 7.

Finally, we substitute these values back into the expression:

(-10 mod 23 7 mod 23) mod 23 equals (-10 7) mod 23.

Calculating the subtraction first, we get -3 mod 23.

To ensure the result is positive, we add 23 to -3, giving us 20 mod 23.

Therefore, (−133 mod 23 261 mod 23) mod 23 equals 20.

b) To find (457 mod 23 ⋅ 182 mod 23) mod 23, we begin by evaluating the innermost parentheses.

457 mod 23 equals 4, as 457 divided by 23 gives a quotient of 19 with a remainder of 4.

Similarly, 182 mod 23 equals 4, because 182 divided by 23 gives a quotient of 7 with a remainder of 4.

Now, we substitute these values into the expression:

(4 ⋅ 4) mod 23.

Multiplying 4 by 4 gives us 16.

Finally, we substitute this value back into the expression:

(4 ⋅ 4) mod 23 equals 16 mod 23.

Therefore, (457 mod 23 ⋅ 182 mod 23) mod 23 equals 16.

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Answer:

The data shows a linear association between the variables.

The data shows a negative association between the variables.