can yall please help

Answer:

  124.2 miles

  ∠310.1°

Step-by-step explanation:

You want to know the bearing and distance to the airport from a plane that is 95 miles east and 80 miles south of it.

The Pythagorean theorem or the distance formula can be used to find the distance to the airport.

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((95 -0)² +(-80 -0)²) = √(9025 +6400) = √15425

  d ≈ 124.197 . . . . miles

The plane is about 124.2 miles from the airport.

The reference angle with respect to the +y axis can be found using the tangent relation.

  Tan = Opposite/Adjacent

  tan(α) = 95/80 = 19/16

  α = arctan(19/16) ≈ 49.9° . . . . . . CCW from +y axis

The bearing angle is measured clockwise from the +y axis (north), so is ...

  bearing = 360° -49.9° = 310.1°

The bearing to the airport is 310.1°.

__

Additional comment

Some navigators would refer to the bearing as N 49.9° W.

Less commonly, it might be referred to as W 40.1° N. Usually, N and S are the reference directions, with the modification being E or W from there. The less common usage might be chosen if an angle less than 45° is wanted.

The bearing is often reported to the nearest degree, without any degree symbol, as N50W.

The equation of the line perpendicular to y = - (1 / 2) · x - 2 and that passes through the point (x, y) = (- 3, - 5) is y = 2 · x + 1.

In this problem we must determine the equation of a line perpendicular to another line, provided that the equation of a line and a point of intersection are given. According to analytical geometry, two lines are perpendicular if and only if the product of the two slopes equals - 1.

The equations of the line are defined by functions of the form:

y = m · x + b

Where:

And the slope relationship between two perpendicular line:

m · m' = - 1

Where:

First, derive the equation of the line in slope-intercept form:

x + 2 · y = - 4

2 · y = - x - 4

y = - (1 / 2) · x - 2

Second, calculate the slope of the perpendicular line by the slope relationship:

m' = - 1 / (- 1 / 2)

m' = 2

Third, find the y-intercept of the perpendicular line by the equation of line, the slope and the coordinates of the given point:

b = y - m · x

b = - 5 - 2 · (- 3)

b = - 5 + 6

b = 1

Then, obtain the equation of the line in slope-intercept form:

y = 2 · x + 1

The equation of the line is y = 2 · x + 1.

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Answer:

see explanation

Step-by-step explanation:

there is a common difference between consecutive terms in the sequence, that is

8 - 13 = 3 - 8 = - 2 - 3 = - 7 - (- 2) = - 5

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 13 and d = - 5 , then

[tex]a_{n}[/tex] = 13 - 5(n - 1) = 13 - 5n + 5 = 18 - 5n

then

a₁₀₀ = 18 - 5(100) = 18 - 500 = - 482

Answer: You make a system of inequality to spend at least $20. The word "at least" means you can spend equal to $20 or higher than $20. Or you can write it as,

⇒ what you buy should be ≥ 20

Input the price to the inequality above

⇒ what you buy should be ≥ 20

⇒ paperback price + hardcover price ≥ 20

⇒ 10x + 17y ≥ 20

Because the number of paperback books and the number of hardcover books can't be negative, make new inequality forms

⇒ x ≥ 0

⇒ y ≥ 0

So this is the summary

10x + 17y ≥ 20

x ≥ 0

y ≥ 0

Step-by-step explanation:

For the given triangle ΔABC the value of (x + y) would be 7 cm.

What is an equilateral triangle?

An equilateral triangle is a triangle with the same length on all three sides. An equilateral triangle is also equiangular in Euclidean geometry; that is, all three internal angles are congruent to each other and are each 60°.

Given data:

Length of AB = (3x + 2) cm.

Length of AC = 11 cm.

Length of BC = (2y + 3) cm.

The property of an equilateral triangle says that all sides of an equilateral triangle are equal.

then we can write,

                  AB = AC

               3x + 2 = 11

                3x = 11 - 2

                3x = 9

                x = 9/3

                x = 3 cm

Also, BC = AC

        2y + 3 = 11

        2y = 11 - 3

        2y = 8

          y = 8/2

          y = 4 cm

So the value of (x + y) = 3 +4

                                    = 7 cm.

Hence, For the given triangle ΔABC the value of (x + y) would be 7 cm.

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Answer:

-3

Step-by-step explanation:

You can use  to find the slope of a line going through  and .

I like to line up the points and subtract vertically. Then put 2nd difference over 1st difference.

(6,h)

minus

(7,-10)

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

-1     h-(-10)

This also said to be equal to -7:

Multiply -1 on both sides:

Subtract 10 on both sides:

[texh=-3[/tex]

So if h=-3 then the slope of the line going through (6,h) and (7,-10) is -7.

Let's test it:

(6,-3)

minus

(7,-10)

----------

-1  7

So the slope is 7/-1=-7. This is the intended goal.

The check is good.

Nick got a total of $33.25 for his part of work.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have Nick and Pam are paid $52.25 for their work. Nick worked 3.5 Hours, and Pam worked two hours. They split the money according to the amount of time each of them worked.

Assume that Nick recieved $[x]. Then, Pam will get - (52.25 - x). For direct proportionality -

y₁/x₁ = y₂/x₂

We can write -

x/3.5 = (52.25 - x)/2

2x = 3.5(52.25 - x)

2x = 182.875 - 3.5x

x = 33.25

Therefore, Nick got a total of $33.25 for his part of work.

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Step-by-step explanation:

   a-b=10--(1)

Same side interiors(vertical) have sum 180°

   a+b=180--(2)

From both equations

2a=190

   a=95

And

  a-b=10

   b=95-10

   b=85

We can conclude that train A is moving faster than train B

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following problem -

The distance y (in miles) that train A travels in [x] amount of time is represented by the equality y = 78x. The graph shows the distance that train B travels.

Train A is moving with speed s[A] = 78 miles/hour {As slope of the equation is 78}. The train B will move with speed given by -

s[B] = (132 - 66)/(2 - 1) = 66 miles/hour

Therefore, we can conclude that train A is moving faster than train B

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[In the complete question it is asking to find which train is moving faster]

Yes, the difference in mean mpg between 4 and 8 cylinder cars statistically significant because the calculated value of t statistic is higher than the critical t value.

What is t statistic and critical value of t?

T statistic is ratio of a parameter's estimated value to its standard error when it deviates from its hypothesized value.

Critical t value is a cut-off point in t distribution

In question, the calculated t statistic is 8.1023 and critical t value one tail is 1.7139 and critical t value two tail is 2.0686. So, the value of calculated t statistic is higher than critical t value one tail or two tail. Therefore, we can reject the null hypothesis.

Thus, yes, the difference in mean mpg between 4 and 8 cylinder cars statistically significant because the calculated value of t statistic is higher than the critical t value.

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The statement that best describes the relationship that is displayed by the scatter plot is: D. As the distance of the attempt increases, the kickers tend to have a lower success rate for their field goals.

A scatter plot is used to show the relationship between two variables that are different, whereby the trendline formed by each data point determines whether the relationship between the two variables is negative or positive.

If the trendline slopes upwards, it is positive, if it slopes downwards, it is negative.

If it is negative, it means as one variable increases, the other one decreases. On the other hand, if it is positive, it implies that as one variable increases, the other variables decreases.

The scatter plot given shows that the relationship between the distance of the attempt and success rate is negative. This implies that, as the distance of the attempt increases, the success rate decreases.

Therefore, the accurate description is: D. As the distance of the attempt increases, the kickers tend to have a lower success rate for their field goals.

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Answer:

D. as the distance of the attempt increases, the kickers tend to have a lower success rate for their field goals.

Step-by-step explanation:

The probability that Roger Federer wins at least 2 Grand Slam titles is 60.82%

Given data:

To calculate the probability that Roger wins at least 2 Grand Slam titles out of the 20 competitions during the 5-year period, we can use the binomial distribution.

The binomial distribution calculates the probability of obtaining a certain number of successes (in this case, Roger winning a Grand Slam) in a fixed number of independent trials (the 20 competitions), given the probability of success in a single trial (0.1).

We need to calculate the probability of Roger winning 2, 3, 4, ..., up to 20 Grand Slam titles and then sum those probabilities to find the overall probability of winning at least 2 titles.

Using a binomial probability formula, the probability of getting exactly k successes in n trials is given by:

[tex]P(X = k) = C(n, k) * p^k * (1 - p)^{(n - k)}[/tex]

Where:

C(n, k) is the binomial coefficient (n choose k)

p is the probability of success in a single trial (0.1)

n is the number of trials (20)

To find the probability of winning at least 2 Grand Slam titles, we calculate the probabilities for k = 2, 3, 4, ..., 20, and sum them up:

P(X ≥  2) = P(X = 2) + P(X = 3) + ... + P(X = 20)

P(X ≥  2) = Σ(P(X = k)) from k = 2 to 20

Calculating each individual probability P(X = k) and summing them up can be tedious. However, use complementary probability to simplify the calculation:

P(X ≥  2) = 1 - P(X = 0) - P(X = 1)

[tex]P(X = 0) = C(20, 0) * 0.1^0 * (1 - 0.1)^{(20 - 0) }[/tex]

[tex]=(1 - 0.1)^{20}[/tex]

= 0.12157

[tex]P(X = 1) = C(20, 1) * 0.1^1 * (1 - 0.1)^{(20 - 1) }[/tex]

[tex]= 20 * 0.1 * (1 - 0.1)^{19 }[/tex]

= 0.27017

P(X ≥  2) = 1 - 0.1074 - 0.2684

P(X ≥ 2 ) = 0.60826 (approximately)

Hence, the probability that Roger Federer wins at least 2 Grand Slam titles out of the 20 competitions is approximately 0.60826, or 60.82%.

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The probability that they will run out of raw material is 0.78 or 78% if the order quantity is 150 gallons.

We have following information,

the demand for the polymer is distributed normally .

Mean (μ) = 250 gallons and Standard deviations (σ) = 125 gallons

Selling price of poymer = $25 per gallons

cost price of raw material for polymer= $ 10 per gallons

Salvage value = $(-5)/ gallon

Now, Using the formula for normally distributed sample,

Z = ( X - μ ) /σ

where , X---> sample mean

μ ----> population mean

σ----> standard deviations

Z -----> Z-value

from question it is clear X = 150

putting all the values of variables in above formula we get, Z = ( 150-250)/125 = -100/125

= - 0.8

(-0.8) value of z = 0.21 = 21% , the value of z is measure from normal distribution table.

They will run out of raw material if demands exceds this quantity or

Probability ( out of stock ) = 1 - 0.21 = 0.79 = 79%

So, the probability that they will run out of raw material is 0.78 or 78% if the order quantity is 150 gallons.

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#Complete Question :

Goop Inc needs to order a raw material to make a special polymer. The demand for the polymer is forecasted to be Normally distributed with a mean of 250 gallons and a standard deviation of 125 gallons. Goop sells the polymer for $25 per gallon. Goop's purchases raw material for $10 per gallon and Goop mrust spend $5 per gallon to dispose off all unused raw material due to government regulations. (One gallon of raw material yields one gallon of polymer.) That is to say, the salvage value is $(-5)/gallon. If demand is more than Goop can make, then Goop sells only what they made and the rest of demand is lost. ?

1. Suppose Good purchases 150 gallons of raw material. What is the probability that they will run out of raw material? ?

Answer:

I think is 50m.

Step-by-step explanation:

Answer:

y = m x + b       equation for a straight line

when x = 4     y = 5

5 = m * 4 + b

m = (5 - b) / 4      solving for m

when x = -3      y = -1

-1 = (5 - b) / 4 * -3 + b = -3 * (5 - b) / 4 + 4 b / 4

-1 = (-15 + 3 b + 4 b) / 4

11 = 7 b      b = 11 / 7

Since m = (5 - b) / 4

m = (5 - 11/7) / 4  = 6/7

We then have y = 6 x / 7 + 11 / 7

Or 7 y = 6 x + 11

Check:

when (4 , 5)     35 = 24 + 11 = 35

The equation of the line in the given form Ax + By = C is 3x + 4y = 40

The given parameters from the question are given as

Point = (8, 4)

Slope = -3/4

Start by representing the equation in the slope intercept form

This is calculated as

y = m(x - X) + Y

Where

m, Slope = -3/4

(X, Y), Point = (8, 4)

So, we have

y = -3/4(x - 8) + 4

Multiply through by 4

4y = -3(x - 8) + 16

Evaluate the like terms

4y = -3x + 24 + 16

This gives

3x + 4y = 24 + 16

Evaluate

3x + 4y = 40

Hence, the equation is 3x + 4y = 40

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Answer:

X = 2, Y = 0

Step-by-step explanation:

Add the two equations together to cancel out -4y and +4y

leaving you with:

8x = 16

8x = 16

divide both sides of the equation by 8 to get x on its own (8x/8 = x, 16/8 =2)

leaving you with:

x = 2

substitute the value of x back into the equation to calculate y (it can be either equation, top or bottom):

8(2) - 4 y = 16

8 x 2 = 16

leaving you with:

16 - 4y = 16

subtract 16 from both sides to get 4y on its own

leaving you with:

-4y = 0

so y = 0, and x = 2

The original amount of nuts, x, in the recipe is 103

The equation for the original amount is 2x + 2x = 412

An algebraic expression can be defined as an expression made up of terms, factors, constants, coefficients, and variables.

These expressions are also known to be made up of mathematical operations such as;

From the information given, we have that;

Beverly doubles the amount of nuts and peanut butter chips

Total number = 412

This is represented as;

2x + 2x = 412

collect like terms

4x = 412

Make 'x' the subject of formula

x = 412/ 4

x = 103

Hence, the value is 103

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The equation of the absolute value function graph is: y = |x - 3| + 5.

The equation, y = a|x – h| + k, represents the equation of an absolute value function in the vertex form, where:

We are given the following from the graph:

Vertex (h, k) = (3, 5)

Plug in the values of h and k into the equation, y = a|x – h| + k:

y = a|x - 3| + 5

A point on the graph is (5, 7). Find the value of a by substituting (x, y) = (5, 7) into y = a|x - 3| + 5:

7 = a|5 - 3| + 5

7 = a|2| + 5

7 = 2a + 5

7 - 5 = 2a

2 = 2a

2/2 = 2a/2

1 = a

a = 1

Write the equation of the absolute function graph by substituting a = 1 into y = a|x - 3| + 5:

y = |x - 3| + 5

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The original price of the shirt before the discount will be $25.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

You're looking for another shirt and find one that is discounted to $16.25. According to the sign, it is a 35% markdown.

Then the original price of the shirt before the discount will be given as,

⇒ $16.25 / (1 - 0.35)

⇒ $16.25 / 0.65

⇒ $25

The original price of the shirt before the discount will be $25.

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Answer:

x = 9/5 y - 4/5

Step-by-step explanation:

Make x the subject:

9y - 5x =4

Subtract 9y from each side

9y-9y - 5x =-9y+4

-5x = -9y +4

Divide each side by -5

-5x/-5 = -9y/-5 + 4/-5

x = 9/5 y - 4/5

Answer:

x = (9/5)y - (4/5)

Step-by-step explanation:

Given equation,

→ 9y - 5x = 4

Solving for the required value of x,

→ 9y - 5x = 4

→ -5x = -9y + 4

→ x = (-9y + 4)/-5

→ [ x = (9/5)y - (4/5) ]

Hence, value of x = (9/5)y - (4/5).

Answer:

[tex]\sf \dfrac{-1}{2}[/tex]

Step-by-step explanation:

Find the slope:

(-9 , -5)   ⇒ x₁ = -9  ; y₁ = -5

(-1 , -9)   ⇒ x₂ = -1   ; y₂ = -9

[tex]\sf \boxed{Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

           [tex]\sf = \dfrac{-9-[-5]}{-1-[-9]}\\\\\\=\dfrac{-9+5}{-1+9}\\\\\\=\dfrac{-4}{8}\\\\\\=\dfrac{-1}{2}[/tex]

Answer:

Slope = -1/2

Step-by-step explanation:

Formula we use,

→ (y2 - y1)/(x2 - x1)

Now the value of slope is,

→ (-9 -(-5))/(-1 -(-9))

→ (-9 + 5)/(-1 + 9)

→ -4/8 = -1/2

Hence, the slope is -1/2.

The solution set for the inequality is.

-113 ≤ y ≤ 131

Here we have the following inequality:

|y - 9| ≤ 122

Any absolute value inequality can just be decomposed as follows:

|y - 9| ≤ 122

to:

-122 ≤  y - 9 ≤  122

Now we can solve this for y by adding 9 in all places:

-122 + 9 ≤ y - 9 + 9 ≤  122 + 9

-113 ≤ y ≤ 131

That is the solution set.

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Answer: 17 Dimes.

Step-by-step explanation:

Using the concepts of probability, we got that 0.4286 is the probability  that the battery life for an iPad Mini will be 10 hours or less  which is about 42.86%.

From the given information;

Let  X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :

[tex]f_X(x)[/tex] = [tex]\frac{1}{B-A}[/tex] where A<x<B

where A and B  are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

[tex]f_X(x)[/tex] = [1 / (12-8.5)]8.5<x<12

[tex]f_X(x)=[/tex](1/3.5)8.5<x<12

The  probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

F(10)=[tex](x-A)/(B-A)[/tex]

F(10)=(10-8.5)/(12-8.5)

F(10)=1.5/3.5

F(10)=0.4286

Hence, the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286

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(Complete question)

In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

The values of y and x is 117 degrees and 28 degrees.

Given:

o ll m

Let angle beside 63 is a.

63 + <a = 180

<a = 180 - 63

<a = 117 degrees.

y = 117 degrees (since alternate interior angles are equal)

y = 4x + 5(vertically opposite angles are equal)

117 - 5 = 4x

4x = 112

divide by 4 on both sides

x = 112/4

x = 28 degrees.

Therefore the values of y and x is 117 degrees and 28 degrees.

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Answer:

- 0.5 ≤ x ≤ 3.5

Step-by-step explanation:

since both ends of the interval are closed circles. This indicates that x can equal both - 0.5 and 3.5 and the values between , then

- 0.5 ≤ x ≤ 3.5

The inequality shown on the number line is -0.5 ≤ x ≤ 3.5.

Given is a number line where a value starts from -0.5 and end at 3.5, we need to write down the inequality shown on the number line,

To write down the inequality shown on the number line starting from -0.5 and ending at 3.5, we need to determine the range of values represented by the line segment.

The left endpoint of the line segment is -0.5, which means the value represented by that point is greater than or equal to -0.5.

We can express this as:

x ≥ -0.5

The right endpoint of the line segment is 3.5, which means the value represented by that point is less than or equal to 3.5.

We can express this as:

x ≤ 3.5

Combining these two inequalities, we have:

-0.5 ≤ x ≤ 3.5

This inequality represents all the values on the number line between -0.5 and 3.5, inclusive.

Hence the required inequality is -0.5 ≤ x ≤ 3.5.

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Tower B is 14.9 miles away from the fire.

What is the law of sines?

According to the law of sine, or sine law, the ratio of a triangle's side length to the sine of the opposing angle remains constant for all three sides. The sine rule is another name for it.

Here,

According to the law of sines

BC/sin A = AC/sin B = AB/sin C

∠A = 43°, ∠B = 31°, ∠C = 180° - ∠A - ∠B = 106°

AB = 21 miles

So, BC = (AB/SinC)×SinA

BC = 14.9 miles

Hence, Tower B is 14.9 miles away from the fire.

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Answer:

A)- 65

B)- 25

c)- 25

To find A- pay attention to the bottom..add 60+55 then subtract that from 180

yu get 65..now we know that 65+90= 155 subtract that from 180 you get 25. so now we have B..B and C are congruent meaning they are equals

hope this helps