SOMEONE PLEASE HELP WITH THIS EQUATION

The person is approximately 7.73 miles from home.

To solve this problem, we can use the Pythagorean theorem and trigonometry. Let us assume that the person starts from the origin (0, 0) and walks 5 miles west, which takes her to the point (-5, 0) on the x-axis.

If we assume that the starting point is (0, 0) and we assign a coordinate system, then the point reached after walking 5 miles west can be represented as (-5, 0). Similarly, the point reached after walking 6 miles southwest can be represented as (-3, -6).Then, she walks 6 miles southwest, which forms a 45-degree angle with the x-axis. We can represent this vector as (6 cos 45°, -6 sin 45°) = (3√2, -3√2).

To find the total distance from home, we need to add the magnitude of these two vectors using the Pythagorean theorem:

d =[tex]\sqrt((-5)^2 + (-3\sqrt2)^2)[/tex]≈ 7.73 miles

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Answer:

  4

Step-by-step explanation:

You want the sum of digits of the largest number that divides 1305, 4665, and 6905 with the same remainder.

We can look at 4665/1305 ≈ 3.57 and 6905/1305 ≈ 5.29 for a clue as to the divisor of interest. These quotients tell us that one possibility is the value that would give quotients of 4 and 6 after the remainder is subtracted from each of the numbers.

For 1305 and 4665, if r is the remainder, we require ...

  4(1305 -r) = 4665 -r

  5220 -4665 = 4r -r

  555/3 = r = 185

If 185 is the remainder in this scenario, then 1305 -185 = 1120 is the divisor. Checking the remainder with 6905, we find ...

  6905/1120 = 6 r 185

The sum of digits of this divisor is 1 + 1 + 2 + 0 = 4.

The sum of the digits in N is 4.

The percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.

The percentage of profit on a $1200 investment that results in a $350 profit can be calculated using the formula:

Percentage of profit = (Profit / Investment) x 100

In this case, the profit is $350 and the investment is $1200. Plugging these values into the formula:

PercThe percentage of profit on a $1200 investment that results in a $350 profit can be calculated using the formula:

Percentage of profit = (Profit / Investment) x 100

In this case, the profit is $350 and the investment is $1200. Plugging these values into the formula:

Percentage of profit = (350 / 1200) x 100

Calculating this expression gives us:

Percentage of profit = 0.2917 x 100 = 29.17%

Therefore, the percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.

To calculate the percentage of profit, we divide the profit by the investment and then multiply by 100 to express it as a percentage. In this case, the profit is $350 and the investment is $1200. Dividing $350 by $1200 gives us 0.2917. Multiplying this by 100 gives us 29.17%. This means that the profit of $350 represents 29.17% of the initial investment of $1200.entage of profit = (350 / 1200) x 100

Calculating this expression gives us:

Percentage of profit = 0.2917 x 100 = 29.17%

Therefore, the percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.

To calculate the percentage of profit, we divide the profit by the investment and then multiply by 100 to express it as a percentage. In this case, the profit is $350 and the investment is $1200. Dividing $350 by $1200 gives us 0.2917.

Multiplying this by 100 gives us 29.17%. This means that the profit of $350 represents 29.17% of the initial investment of $1200.

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Answer: 88.94

Step-by-step explanation:

First, l found what was 8.125 out of 110 which is 8.94

then added 8.125 and 8.94 which got 118.94

But Angela gave the retailer an $30 coupon so l subtracted 30 from 118.94 which got me 88.94

The product of two irrational numbers can be either rational or irrational, depending on the specific irrational numbers being multiplied. It is not always rational, nor is it never rational.

The product of two irrational numbers can be either rational or irrational, depending on the specific irrational numbers being multiplied. It is not always rational, nor is it never rational.

Consider the square root of 2 (√2) and the square root of 3 (√3), both of which are irrational numbers. When you multiply √2 and √3, you get √6, which is also an irrational number. In this case, the product of two irrational numbers is irrational.

However, there are cases where the product of two irrational numbers can be rational. For example, consider √2 and its reciprocal (1/√2), both of which are irrational. When you multiply these two numbers, you get 1, which is a rational number. So, in this case, the product of two irrational numbers is rational.

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Answer:

True

EXPLANATIONDETAIL STEPS:

(A)Determine whether y = 5 is a function: Click for video explanations: True

(B)Determine whether x = -2 is a function: Click for video explanations: False

(7)Determine whether y = 2x-5 is a function: Click for video explanations: True

(D)Determine whether 2y = x-4 is a function: Click for video explanations: True

(A)Determine whether

=

is a function: Click for video explanations: True

(B)Determine whether

=

is a function: Click for video explanations: False

(7)Determine whether

=

is a function: Click for video explanations: True

(D)Determine whether

=

is a function: Click for video explanations: True

The answer is:

↬ f(x + 2) = 2x + 11

Work/explanation:

To evaluate the function, plug in x + 2 for x:

[tex]\boxed{\large\begin{gathered}\sf{f(x)=2x+7}\\\\\bf{distribute}\\sf{f(x+2)=2(x+2)+7}\\\\\bf{simplify}\\\sf{f(x+2)=2x+4+7}\\\\\sf{f(x+2)=2x+11}\end{gathered}}[/tex]

Answer:

Here's an example:

convert 2.5 into a mixed number.

Make the denominator less than the original.

The easy way for this is to do 25/10

when you put it through a calculator it ends up being 2.5

(essentially the mixed number and the decimal are the SAME numbers.)

Hope this clarified. :)

To convert a decimal to a mixed number, follow these steps:

Step 1: Identify the whole number part of the decimal. This is the part of the decimal before the decimal point.

Step 2: Identify the decimal part. This is the part of the decimal after the decimal point.

Step 3: Express the decimal part as a fraction by using the place value of the last digit.

Step 4: Simplify the fraction, if possible, by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.

Step 5: Combine the whole number part, the fraction, and simplify if necessary.

Here's an example:

Let's say we have the decimal 2.75.

Step 1: The whole number part is 2.

Step 2: The decimal part is 0.75.

Step 3: To express 0.75 as a fraction, we write it as 75/100. Since 75 and 100 have a common factor of 25, we can simplify it to 3/4.

Step 4: The fraction 3/4 is already in its simplest form.

Step 5: Combining the whole number part and the fraction, we have 2 3/4.

So, the decimal 2.75 can be written as the mixed number 2 3/4.

Remember to always simplify the fraction part if possible.

Answer:

A: the probability that a 1 is received is 0.56.

B:  the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

Step-by-step explanation:

To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.

a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.

Let's denote:

P(1 sent) = 0.6 (probability a 1 is sent)

P(0→1) = 0.2 (probability a 0 is flipped to 1)

P(1 received) = ?

P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)

= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)

= 0.6 * (1 - 0.2) + 0.4 * 0.2

= 0.6 * 0.8 + 0.4 * 0.2

= 0.48 + 0.08

= 0.56

Therefore, the probability that a 1 is received is 0.56.

b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.

Let's denote:

P(0 sent) = ?

P(1 received) = 0.56

We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).

Using Bayes' theorem:

P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)

P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08

P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56

Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):

P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56

Simplifying:

P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56

= 0.08 * (1 - P(0 sent)) * (1 / 0.56)

= 0.08 * (1 - P(0 sent)) * (25/14)

= (2/25) * (1 - P(0 sent))

Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?

The values of L and M in the triangle displayed are 55 and 60 respectively.

The value of angle L can be obtained thus :

125 + L = 180 (sum of angles in a triangle)

L = 180 - 125 = 55°

B.

The value of L can be calculated thus:

55 + (2x - 10) + 65 = 180 (sum of internal angles of a triangle)

120 + 2x - 10 = 180

110+2x = 180

2x = 180-110

x = 35

M = 2(35) -10 = 60°

Therefore, L = 55 and M = 60.

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Step-by-step explanation:

We can use the equation h(t) = -4.9t^2 + vt + h0, where h0 is the initial height of the rock, v is the initial velocity and t is time in seconds, to solve the problem.

h0 = 43 meters (the top of the cliff)

v = 11 meters per second (upwards direction)

To find the time when the rock is 10 meters from ground level, we set h(t) = 10 meters and solve for t:

10 = -4.9t^2 + 11t + 43

0 = -4.9t^2 + 11t + 33

Solving this quadratic equation, we get t = 4.04 seconds or t = 1.37 seconds.

Since the rock is thrown upwards, it will be 10 meters from ground level twice - once on the way up and once on the way down. We can discard the negative time answer as that would correspond to when the rock is thrown from the ground.

Therefore, the rock will be 10 meters from ground level after 4.04 seconds (on the way down).

Answer:

-5/4

Step-by-step explanation:

Let [tex](x_1,y_1)=(-4,4)[/tex] and [tex](x_2,y_2)=(0,-1)[/tex]. The slope of the line would be:

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{0-(-4)}=\frac{-5}{4}=-\frac{5}{4}[/tex]

Answer: -5/4

Step-by-step explanation:

To find the slope between two points, you can use the formula:

Slope = (y2 - y1)/(x2 - x1)

Using the points (0, -1) and (-4, 4), we can substitute the coordinates into the formula:

slope = (4 - (-1))/(-4 - 0)

slope = (4 + 1)/(-4)

slope = 5/-4

Therefore, the slope between the two points is -5/4.

The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).

To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.

Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).

Using the midpoint formula, we can set up the following equations:

(x1 + x2) / 2 = -4

(y1 + y2) / 2 = 2

Substituting the coordinates of point A (-7, 3), we have:

(-7 + x2) / 2 = -4

(3 + y2) / 2 = 2

Simplifying the equations:

-7 + x2 = -8

3 + y2 = 4

Solving for x2 and y2:

x2 = -8 + 7 = -1

y2 = 4 - 3 = 1

Therefore, the coordinates of point B are (-1, 1).

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The difference in size between the two guys is approximately -0.3108 inches, which implies that the first guy is bigger than the second guy.

To calculate the difference in size between two people, one measuring in inches and the other measuring in centimeters, we must first convert all measurements to a common unit.

Guy measures 3 inches + 1/4 inch. We can convert 1/4 inch to a decimal fraction by dividing 1 by 4, which gives us 0.25 inches. So your measurement in inches would be 3 + 0.25 = 3.25 inches.

The other guy measures 9.045 cm. To convert centimeters to inches, we use the following relationship: 1 cm = 0.3937 inches. Multiplying the measurement in centimeters by 0.3937, we get the measurement in inches: 9.045 cm * 0.3937 = 3.5608 inches (approximately).

Now we can calculate the size difference between them. We subtract the measurement of the second chavo (3.5608 inches) from the measurement of the first chavo (3.25 inches):

3.25 inches - 3.5608 inches = -0.3108 inches.

The resulting difference is -0.3108 inches. This means that the second chavo is smaller in size than the first. Since the difference is negative, it indicates that the first chavo is bigger than the second.

In summary, the difference in size between the two guys is approximately -0.3108 inches, which implies that the first guy is bigger than the second guy.

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Answer:

  19 or 26

Step-by-step explanation:

You want the value of 3n² -8n -9, given that n(n -3) = 10.

We recognize that 10 = 5·2 and that these factors differ by 3. This means n(n -3) = 10 is equivalent to saying n ∈ {-2, 5}.

The value of 3n² -8n -9 will be one of ...

  (3n -8)n -9 = (3(-2) -8)(-2) -9 = (-14)(-2) -9 = 19 . . . . for n = -2

or

  (3(5) -8)(5) -9 = (7)(5) -9 = 26 . . . . . . . for n = 5

The expression 3n² -8n -9 will be either 19 or 26.

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Answer: [tex](-\infty, 0) \cup (0, \infty)[/tex]

Step-by-step explanation:

The graph of [tex]\frac{\sin x}{x}[/tex] is continuous for all real [tex]x[/tex] except [tex]x=0[/tex], and multiplying this by [tex]1/3[/tex] does not change this.

The solution to the polynomial division in quotient and remainder form is: (x + 2) + (-5x + 4)/(x² - 2x + 1)

The polynomials we want to divide are:

x³ - 8x + 6 by x² - 2x + 1 and as such we can write it as:

                x + 2

x² - 2x + 1|x³ - 8x + 6

             -  x³ - 2x² + x

                     2x² - 9x + 6

                  -  2x² - 4x + 2

                            -5x + 4

Thus, the solution expressed in quotient and remainder form is:

(x + 2) + (-5x + 4)/(x² - 2x + 1)

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The area of the segment is 9( π-2) units²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

A segment is the area occupied by a chord and an arc. A segment can be a major segment or minor segment.

Area of segment = area of sector - area of triangle

area of sector = 90/360 × πr²

= 1/4 × π × 36

= 9π

area of triangle = 1/2bh

= 1/2 × 6²

= 18

area of segment = 9π -18

= 9( π -2) units²

therefore the area of the segment is 9(π-2) units²

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con un conjunto de deshielo determinante igual a 4, es x = 2.

Para determinar el valor de x en la matriz x 2

5 7

dado que el conjunto de deshielo determinante es igual a 4, necesitamos utilizar la propiedad de que el determinante de una matriz 2x2 se puede calcular utilizando la siguiente formula:

determinante = (a × d) - (b × c)

Donde a, b, c, y d son los elementos de la matriz.

En este caso, tenemos la matriz:

x 2

5 7

Aplicando la formula del determinante, podemos establecer la siguiente ecuacion:

( x × 7 ) - ( 2 × 5 ) = 4

Simplificando la ecuacion, obtenemos:

7x - 10 = 4

A continuacion, vamos a resolver la ecuacion para encontrar el valor de x:

7x = 4 + 10

7x = 14

Dividiendo ambos lados de la ecuacion por 7, obtenemos:

x = 2

Por lo tanto, el valor de x en la matriz x 2

5 7

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The z-score for Brazil is given as follows:

Z = 0.87.

The z-score formula is defined as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]X = 6.24, \mu = 4.8, \sigma = 1.66[/tex]

Hence the z-score for Brazil is given as follows:

Z = (6.24 - 4.8)/1.66

Z = 0.87.

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(a) The average cost in 2011 is  $2247.64.

(b) A graph of the function g for the period 2006 to 2015 is: C. graph C.

(c) Assuming that the graph remains accurate, its shape suggest that: A. the average cost increases at a slower rate as time goes on.

Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:

g(x) = -1736.7 + 1661.6Inx

where:

x = 6 corresponds to the year 2006.

For the year 2011, the average cost (in dollars) is given by;

x = (2011 - 2006) + 6

x = 5 + 6

x = 11 years.

Next, we would substitute 11 for x in the function:

g(11) = -1736.7 + 1661.6In(11)

g(11) = $2247.64

Part b.

In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.

Part c.

Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.

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We can conclude that there are no ordered triples of positive integers (x, y, z) that satisfy the given equation and the condition x < y.

We are given that the product of three positive integers (x, y, z) is equal to four times their sum:

xyz = 4(x + y + z)

Rearranging the equation, we get:

xyz - 4x - 4y - 4z = 0

We can factor out a common factor of 4 from the terms on the right-hand side:

4(xy - x - y - z) = 0

Now, we have two cases to consider:

Case 1: xy - x - y - z = 0

In this case, we can rewrite the equation as:

x(y - 1) - (y + z) = 0

From this equation, we observe that (y + z) must be divisible by (y - 1). Since x < y, the minimum value of (y - 1) is 1, which means (y + z) should also be 1. However, since we are looking for positive integers, this case does not yield any solutions.

Case 2: xy - x - y - z = 4

In this case, we can rewrite the equation as:

x(y - 1) - (y + z) = 4

Similarly, we observe that (y + z) must be divisible by (y - 1), and now (y - 1) can take on a minimum value of 2. We can analyze different possibilities based on this:

If (y - 1) = 2, then (y + z) = 2. Since we are dealing with positive integers, the only possibility is y = 3 and z = -1, which does not satisfy the condition.

If (y - 1) = 3, then (y + z) = 3. The only possibility is y = 4 and z = -1, which also does not satisfy the condition.

If (y - 1) = 4, then (y + z) = 4. The only possibility is y = 5 and z = -1, which does not satisfy the condition.

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Answer:

11 : 1

Step-by-step explanation:

The probability of obtaining a head when a dime is flipped is 1/2, since there are two possible outcomes (heads or tails) and each is equally likely.

The probability of rolling any particular number on a fair six-sided die is 1/6, since there are six equally likely outcomes (the numbers 1 through 6).

To find the odds against obtaining a head and rolling any number on the die, we need to multiply the probabilities of the two events. This gives us

(1/2) x (1/6) = 1/12

So the probability of obtaining a head and rolling any number on the die is 1/12.

To find the odds against this event, we need to compare the probability of the event happening to the probability of it not happening. The probability of the event not happening is 1 - 1/12 = 11/12.

Therefore, the odds against obtaining a head and rolling any number on the die are:

11 : 1

Answer:

A acute angle is a angle that is less than 90*

Answer:

Hope this helps and have a nice day

Step-by-step explanation:

Let's denote the total number of boxes the hawker bought as "x".

The cost of each box is R18, so the total cost of buying "x" boxes is 18x.

He sold all but 5 boxes, so he sold (x - 5) boxes at R25 per box. The revenue from selling these boxes is 25 * (x - 5).

The profit is calculated by subtracting the cost from the revenue, so we have:

Profit = Revenue - Cost

155 = 25 * (x - 5) - 18x

Simplifying the equation:

155 = 25x - 125 - 18x

155 + 125 = 25x - 18x

280 = 7x

Dividing both sides by 7:

x = 280 / 7

x = 40

Therefore, the hawker bought 40 boxes of tomatoes.

Answer:

Let's denote:

- A as the event "student is accepted at FSU"

- B as the event "student is accepted at UF"

We have the following probabilities given:

- P(A) = 0.4 (probability of being accepted at FSU)

- P(B|A) = 0.6 (probability of being accepted at UF given acceptance at FSU)

- P(B'|A') = 0.9 (probability of not being accepted at UF given non-acceptance at FSU), where B' is the complement of B (not being accepted at UF) and A' is the complement of A (not being accepted at FSU).

We want to find P(A|B'), or the probability of being accepted at FSU given non-acceptance at UF.

To calculate this, we can use Bayes' Theorem, which states that:

P(A|B') = P(B'|A) * P(A) / P(B')

We can calculate P(B'|A), the probability of non-acceptance at UF given acceptance at FSU, by using the fact that the sum of probabilities of complementary events equals 1:

P(B'|A) = 1 - P(B|A) = 1 - 0.6 = 0.4

Next, we need to find P(B'), the total probability of non-acceptance at UF. We can use the law of total probability to calculate this:

P(B') = P(B'|A) * P(A) + P(B'|A') * P(A')

P(B') = 0.4 * 0.4 + 0.9 * 0.6 = 0.16 + 0.54 = 0.7

Finally, we can substitute these values into Bayes' theorem:

P(A|B') = P(B'|A) * P(A) / P(B') = 0.4 * 0.4 / 0.7 ≈ 0.229

Therefore, the probability that a student is accepted at FSU given that they are not accepted at UF is approximately 22.9%.

Answer:

We don't need to worry about the displaystyle- {3} −3 anyway, because we dcided in the first step that displaystyle {x}ge- {2} x ≥ −2. So the domain for this case is displaystyle {x}ge- {2}, {x}ne {3} x≥ −2,x≠ 3, which we can write as displaystyle {left [- {2}, {3}right)}cup {left ({3},inftyright)} [−2,3)∪(3,∞).

Step-by-step explanation: