negative two minus seventeen plus twelve minus negative four

The quotient of 3/4 and 5/6, expressed in its simplest form, is 9/10 .To find the quotient of fractions, we need to divide the numerator of one fraction by the denominator of the other fraction.

To simplify the process, we can convert the division into multiplication by taking the reciprocal of the second fraction. The reciprocal of a fraction is obtained by interchanging the numerator and the denominator. So, the reciprocal of 5/6 is 6/5.

Now, we can multiply the fractions:

3/4 * 6/5 = (3*6)/(4*5) = 18/20

However, we need to simplify the fraction to its simplest form. To do this, we find the greatest common divisor (GCD) of the numerator and denominator, which is the largest number that divides both without leaving a remainder. In this case, the GCD of 18 and 20 is 2.

By dividing both the numerator and denominator of 18/20 by 2, we get the simplest form of the fraction:

18/20 ÷ 2/2 = 9/10

The quotient of 3/4 and 5/6, expressed in its simplest form, is 9/10.

It's important to note that simplifying fractions involves dividing both the numerator and denominator by their greatest common divisor. This ensures that the fraction is in its simplest form, where the numerator and denominator have no common factors other than 1.

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Answer:

81.05/20 is the better deal and the unit rate is $4.05

Step-by-step explanation:

hopefully this helps :)

Answer:

the second deal is better. the unit rate is 4.05/gal

Step-by-step explanation:

106/25=4.24

81/20=4.05

The order of the runners from fastest to slowest is:

Math friend

Red Sox pair (first member)

Golden State Warrior pair

Red Sox pair (second member)

Math friend

Patriot pair (first member)

Patriot pair (second member)

Last runner wearing a Patriots shirt

Based on the given information, we can deduce the order of the runners from fastest to slowest.

Since the last runner wore a Patriots shirt, we know that the Patriot pair is not the first pair to finish. This eliminates the possibility of the Patriots pair finishing in the first and second positions.

From the clues given:

(a) 1 runner between the Math friends

(b) 2 runners between the Red Sox pair

(c) 3 runners between the Golden State Warrior pair

(d) 4 runners between the Patriot pair

We can determine the following order:

Math friends (M)

Red Sox pair (R)

Golden State Warrior pair (G)

Patriot pair (P)

To satisfy the given conditions:

(a) There is 1 runner between the Math friends, which means one runner (M) must be between the two members of the Math friends.

(b) There are 2 runners between the Red Sox pair, which implies that one member of the Red Sox pair (R) must finish before the other member, with two runners (M and G) between them.

(c) There are 3 runners between the Golden State Warrior pair, indicating that the two members of the Golden State Warrior pair (G) must finish before the third member, with three runners (M, R, and P) between them.

(d) There are 4 runners between the Patriot pair, so both members of the Patriot pair (P) must finish after the other pairs, with four runners (M, R, G, and the last runner) between them.

Therefore, the order of the runners from fastest to slowest is:

Math friend

Red Sox pair (first member)

Golden State Warrior pair

Red Sox pair (second member)

Math friend

Patriot pair (first member)

Patriot pair (second member)

Last runner wearing a Patriots shirt

This order satisfies the given conditions and ensures that the last runner wore a Patriots shirt.

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The fraction is equal to 3/7

the sum of numerator and denominator is equal to 100

Let the numerator = x

Since, Numerator + Denominator = 100

x + Denominator = 100

Denominator = 100 - x

Thus, the fraction is in the form of;

Since it is given that the fraction is equal to 3/7

So,

Simplify the expression for x;

So, the numerator is 30

Since, Denominator = 100 - x

Substitute x = 30

Denominator = 100 - x

Denominator = 100 - 30

Denominator = 70

Thus, we have numerato = 30 denominator = 70

So, the resulting fraction is given as;

Answer: 30/70

Answer:

The answer will be 3

Step-by-step explanation:

The simplified complex expression of (10 - 6i)/(6 + 5i) is (30 + 14i)/61

From the question, we have the following parameters that can be used in our computation:

(10 - 6i)/(6 + 5i)

Using the above as a guide, we have the following:

Start by rationalizing the expression

So, we have the following representation

(10 - 6i)/(6 + 5i) = (10 - 6i)/(6 + 5i) * (6 - 5i)/(6 - 5i)

Evaluate the products of the numerator

This gives

(10 - 6i)/(6 + 5i) = (60 -30 + 50i - 36i)/(6 + 5i) * 1/(6 - 5i)

Evaluate the products of the denominator

This gives

(10 - 6i)/(6 + 5i) = (60 -30 + 50i - 36i)/(30 +25)

Evaluate the like terms

(10 - 6i)/(6 + 5i) = (30 + 14i)/61

So, we have

(10 - 6i)/(6 + 5i) = (30 + 14i)/61

Hence, the solution is (30 + 14i)/61

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Answer:

b. 20

Step-by-step explanation:

divide 118 by 6 and round to 20

Answer:

20 you will get me when you round it

Suppose X = the time that elapses between the bell and the end of the lecture and suppose the pdf of X is f(x)= kox, then the pdf of X is f(x) = (1/2)x, for 0 ≤ x ≤ 2.

Given that X represents the time elapsed between the bell and the end of the lecture, and the probability density function (pdf) of X is f(x) = kx, we can analyze the situation within the context of probability distributions.

Since the professor always finishes within 2 minutes after the bell, the range of X is between 0 and 2 minutes (0 ≤ x ≤ 2). To find the value of k, we need to ensure that the pdf integrates to 1 over this range, as required by probability density functions:

∫(from 0 to 2) kx dx = 1

After integrating, we get:

(k/2) * x² |(from 0 to 2) = 1

Evaluating at the limits:

(4k/2) - (0) = 1

Solving for k:

k = 1/2

Therefore, the pdf of X is f(x) = (1/2)x, for 0 ≤ x ≤ 2.

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Answer:

Step-by-step explanation:

Adjacent means right next to. Sometimes that could mean connect to. So what angles are right next to <XOY

The simplified expression is -4x + 44/3.

An exponent is a numerical value that indicates how many times a number, variable, or expression is to be multiplied by itself. It is usually written as a superscript to the right of the base, such as in the expression 3², where 3 is the base and 2 is the exponent.

The exponent indicates that 3 is to be multiplied by itself 2 times, resulting in a value of 9. Exponents are used in many areas of mathematics, including algebra, calculus, and geometry, and are an important concept for understanding mathematical operations and functions.

To simplify the expression, we need to follow the order of operations and combine like terms where possible:

2/3(3x - 1) + 4x + 3² - 10x + 5

First, simplify the expression inside the parentheses:

2/3(3x - 1) = 2x - 2/3

Next, simplify the squared term:

3² = 9

Now, combine the like terms:

2x - 2/3 + 4x - 10x + 9 + 5 = -4x + 14 + 2/3

Finally, we can rewrite the expression with the fractional coefficient as a mixed number:

-4x + 14 + 2/3 = -4x + 44/3

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Two equal-size vectors at right angles to each other have a resultant that is equal to \(\sqrt{2}\) times the magnitude of each individual vector.

The magnitude of the resultant vector of two equal-size vectors at right angles to each other can be determined using the Pythagorean theorem.

Let's assume the magnitude of each vector is represented by "a".

According to the Pythagorean theorem, the magnitude of the resultant vector, denoted as "R", can be calculated as:

R =\(\sqrt{a^2 + a^2}\)

R = (\(\sqrt{2a^{2} )}\)

R = \(\sqrt{2}\) a

Therefore, the magnitude of the resultant vector is equal to \(\sqrt{2}\) times the magnitude of each individual vector.

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Answer:

$800

Step-by-step explanation:

2,400/3 = 800

Answer:

Step-by-step explanation:

35.5

The general indefinite integral is: (x^2.4)÷2.4 + 2 × x^3.5 + C.

To find the indefinite integral of (x^1.4 + 7x^2.5) dx, you'll need to perform integration on each term separately and add a constant of integration (C).

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The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.

Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:

Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.

We can write as below:

Maximum capacity per person=1884/12=157lb.

And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586

Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.

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I believe that y is equal to -5.

y=-5

Answer: 2 5/6 I think.

Wait no. I just did the math and it would be 2 1/2

3/4 a number b divided by 5 is 15b/4

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction).

3/4 a number b:

=3b/4

Divided by 5:

=3b/4/5

We have to multiply numerator with the dominator by 5 to remove the double fraction:

=3b*5/4

=15b/4

3/4 a number b divided by 5 is 15b/4

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The forward Fourier Transform formula for a signal is X(jω) = F{x(t)}. The inverse Fourier Transform formula is x(t) = F^(-1){X(jω)}. The two formulas are related by the Fourier Transform property called duality or symmetry.

1. The forward Fourier Transform formula is given by:

  X(jω) = ∫[x(t) * e^(-jωt)] dt

  This formula calculates the complex spectrum X(jω) of a signal x(t) by integrating the product of the signal and a complex exponential function.

2. The inverse Fourier Transform formula is given by:

  x(t) = (1/2π) ∫[X(jω) * e^(jωt)] dω

  This formula reconstructs the original signal x(t) from its complex spectrum X(jω) by integrating the product of the spectrum and a complex exponential function.

  The similarity between these two formulas is known as the Fourier Transform property of duality or symmetry. It states that the Fourier Transform pair (X(jω), x(t)) has a symmetric relationship in the frequency and time domains. The forward transform calculates the spectrum, while the inverse transform recovers the original signal. The duality property indicates that if the spectrum is known, the inverse transform can reconstruct the original signal, and vice versa.

3. To determine the Fourier Transform of the given signal x(t) = [-1, 1, 0, -1], we apply the defining integral:

  X(jω) = ∫[-1 * e^(-jωt1) + 1 * e^(-jωt2) + 0 * e^(-jωt3) - 1 * e^(-jωt4)] dt

  Here, t1, t2, t3, t4 represent the respective time instants for each element of the signal.

  Substituting the time values and performing the integration, we can obtain the Fourier Transform of x(t).

Note: Please note that without specific values for t1, t2, t3, and t4, we cannot provide the numerical result of the Fourier Transform for the given signal. The final answer will depend on these time instants.

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Yes, you can be certain that there are at least two guests who had the same number of handshakes. This is due to the Pigeonhole Principle.

As the party organizer, you shake hands with all 80 guests, which means you have 80 handshakes. The guests can have a minimum of 0 handshakes (if they don't shake hands with anyone except you) and a maximum of 79 handshakes (if they shake hands with everyone except themselves). There are 80 guests (excluding yourself), so there are 80 "pigeonholes" for the number of handshakes. The range of possible handshakes among the guests is from 0 to 79, which creates 80 possible outcomes or "pigeons."

According to the Pigeonhole Principle, if there are n pigeonholes and n+1 pigeons, at least one pigeonhole must contain at least two pigeons. In this case, there are 80 pigeonholes (guests) and 80 pigeons (possible handshakes). Therefore, at least two guests must have had the same number of handshakes.

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Answer:

120 Tickets

Step-by-step explanation:

Band rues charges $950 to play all night.

DJ phoria charges $350 plus $5 for each ticket sold.

(a)The graph is attached.

From the point of intersection of the two lines, the number of tickets for which the cost of the band and the DJ would be equal is 120 tickets.

(b)

Given the two linear equations

y=950

y=350+5x

Therefore:

950=350+5x

950-350=5x

5x=600

x=120

Therefore, the number of tickets at which the cost of the band and the DJ would be equal is 120, just as obtained above.

Answer:

B / 3 = 6 < 3

hope I helped.

Answer:

the total is 80 cm^2

Step-by-step explanation:

just because you should multiply by 2 40*2=80 cm^2

i hope this helps

have a great day

Since, The line of symmetry is drawn between them. That line makes both sides equal. So if area of one half is 40cm² the area of other half will be also 40cm²..

Now, their sum is:

\(40 + 40 = 80\)

Thus, The total area of the rhombus is 80cm²...~

Answer:

ST = 17 and WY = 32

Step-by-step explanation:

3

SV is a perpendicular bisector and divides Δ RST into 2 congruent triangles with

ST = SR , that is

7x - 4 = 3x + 8 ( subtract 3x from both sides )

4x - 4 = 8 ( add 4 to both sides )

4x = 12 ( divide both sides by 4 )

x = 3

Then

ST = 7x - 4 = 7(3) - 4 = 21 - 4 = 17

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

4

Δ WXY and Δ WXZ are congruent ( both have 3 congruent angles ), then

WZ = WY , that is

9x - 13 = 6x + 2 ( subtract 6x from both sides )

3x - 13 = 2 ( add 13 to both sides )

3x = 15 ( divide both sides by 3 )

x = 5

Then

WY = 6x + 2 = 6(5) + 2 = 30 + 2 = 32

Answer:

Triangle ABC is congruent to triangle DFE.

The Rational Roots Theorem identifies possible rational roots of a polynomial equation in terms of factors of its coefficients.

The Rational Roots Hypothesis, otherwise called the Judicious Zeros Hypothesis, is a numerical hypothesis that assists with recognizing conceivable objective foundations of a polynomial condition. In particular, that's what it expresses on the off chance that a polynomial condition with number coefficients has a sane root, that root should be of the structure p/q, where p is a variable of the consistent term and q is an element of the main coefficient.

For instance, in the event that a polynomial condition has the structure ax^3 + bx^2 + cx + d = 0, and the main coefficient an and the consistent term d are numbers, then, at that point, the conceivable sane foundations of the situation are the quantities of the structure p/q, where p is a component of d and q is a variable of a.

The Normal Roots Hypothesis is valuable in tackling polynomial conditions and deciding if they have reasonable roots.

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