A ship sails due north from point P to point Q,4km away.It then sails on a bearing of 090^0 to point R, 3kmfrom Q. i)llustrate the information in a diagram form. ii)calculate the length of PR.

Answer:

1420

Step-by-step explanation:

delta math

The required length of n is 1419.5 cm which is determined by the Law of Cosines.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

In triangle ΔLMN,

l = 810 cm, m = 620 cm and ∠N=166°.

We have to determine the length of n

The Law of Cosines as it relates all three sides of a triangle with an angle of a triangle.

n² = l² + m² − 2lm cos(N)

Substitute the values in the above formula and solve for n

n² = 810² + 620² − 2 × 810 × 620 × cos(166°)

n² = 810² + 620² − 104400 × cos(166°)

n = ±1419.5

n = 1419.5, and n = - 1419.5

Neglected the value of n = - 1419.5 because length should not be negative.

n = 1419.5 cm

Learn more about the triangles here:

https://brainly.com/question/17997149

#SPJ2

Answer:

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

Let the cost of the meal be x.

Adding a tip of 19%:

Answer:

Wyatt should multiply with 1.19.

Step-by-step explanation:

Forming the expression,

→ 1 + (19% of 1)

Now the required number is,

→ 1 + (19% of 1)

→ 1 + ((19/100) × 1)

→ 1 + (19/100)

→ 1 + 0.19 = 1.19

Hence, required number is 1.19.

Answer:

111

Step-by-step explanation:

The correct sample space for the gumballs in Julia's bag is {lemon-lime, watermelon, watermelon, grape, grape, grape} which makes option D correct.

The sample space for the gumballs in Julia's bag would be all the possible outcomes of selecting one gumball from the bag without replacement.

Since there are 1 lemon-lime, 2 watermelon, and 3 grape gumballs in the bag, the sample space would be expressed as:

sample space = {lemon-lime, watermelon, watermelon, grape, grape, grape}.

Therefore,we have 6 total outcomes in the sample space for the gumballs in Julia's bag.

Know more about sample space here:https://brainly.com/question/2117233

#SPJ1

Answer:

See below

Step-by-step explanation:

Pick two convenient integer coordinat e points to calculate the slope

(-1,1) AND  (1,0)

Slope = (y1-y2) / (x1-x2) = (1-0)/(-1-1) = -1/2

Slope-yaxis intercept form   y = mx + b

     y = -1/2 x +b    sub in either of the points to calculate  b = 1/2

y = -1/2 x   + 1/2    Done.

Answer:

The probability is \(P(X  \le 2 ) = 0.9072\)

The company will accept 90.72% of the shipment and will reject \((100 -90.72) =  9.2\%\) of the shipment , so many of the shipment are rejected

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  36

   The  proportion that did not meet the requirement is  \(p =  0.03\)

Generally the probability that the whole shipment is accepted is equivalent to the probability that there is at most 2 batteries that do not meet the requirement , this is mathematically represented as

     \(P(X  \le 2 ) = [ P(X =  0 ) +  P(X =  1 ) + P(X = 0)]\)

=>   \(P(X  \le 2 ) = [ [^{n}C_0 * (p)^{0} *(1-p)^{n-0} ] +  [^{n}C_1 * (p)^{1} *(1-p)^{n-1} ] +  [^{n}C_2 * (p)^{2} *(1-p)^{n-2} ]]\)

Here C stands for Combination (so we will be making the combination function in our  calculators )

So

=> \(P(X  \le 2 ) = [ [^{36}C_0 * (0.03)^{0} *(1-0.03)^{36-0} ] +  [^{36}C_1 * (0.03)^{1} *(1-0.03)^{36-1} ] +  [^{36}C_2 * (0.03)^{2} *(1-0.03)^{36-2} ]]\)

=> \(P(X  \le 2 ) = [ [1 * 1 * 0.3340  ] +  [36* 0.03 *0.3444 ] +  [630 * 0.0009 *(0.355 ]]\)

=>\(P(X  \le 2 ) = 0.9072\)

The company will accept 90.72% of the shipment and will reject \((100 -90.72) =  9.2\%\) of the shipment , so many of the shipment are rejected

The requried, local minimum and maxium for the given function is √2 and -√2.

We need to find the local maximum and local minimum of the function \(f(x) = 2x + 4x^{(-1)}.\)

First, we find the derivative of f(x):

\(f'(x) = 2 - 4x^{(-2)} = 2 - 4/x^2\)

Setting f'(x) = 0 to find the critical points:

\(2 - 4/x^2 = 0\)

Solving for x, we get:

x = ±√2

To determine whether these critical points are local maxima or minima, we need to examine the sign of the second derivative:

\(f''(x) = 8x^{(-3)}\)

When x = √2, f''(√2) = 8/(√2)³ = 8√2 > 0, so x = √2 is a local minimum.

When x = -√2, f''(-√2) = 8/(-√2)³ = -8√2 < 0, so x = -√2 is a local maximum.

Learn more about local maximum and minimum here:

https://brainly.com/question/28983838s

#SPJ1

24 pounds  of coffee worth $10 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

Given situation:

A coffee $10 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound

Now, Let x be the amount of coffee which is $10 per pound

So,

10x + 3(30) = 5(x+30)

10x + 30 = 5x+150

5x + 30 = 150

5x = 120

x = 24 pounds

Hence, 24 pounds  of coffee worth $10 a pound should be added to 30 pounds of coffee worth $3 a pound to get a mixture worth $5 a pound.

Learn more about Algebra here:

https://brainly.com/question/13715639

#SPJ1

Answer:

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle. In this case, the diameter is given as 14 cm, so we can substitute that into the formula:

C = π(14 cm)

Multiplying, we get:

C = 14π cm

So the circumference of the circle is 14π cm. The units are centimeters, since circumference is a length measurement.

Answer:

sin θ = \(\frac{\sqrt{6} }{3}\)

Step-by-step explanation:

Given that,

cos θ = \(\frac{\sqrt{3} }{3}\)

From the trigonometric functions,

cos θ = \(\frac{adjacent}{hypotenus}\)

⇒ adjacent = \(\sqrt{3}\), and the hypotenuse = 3

Let the opposite side be represented by x, applying the Pythagoras theorem we have;

\(/hyp/^{2}\) = \(/adj/^{2}\) + \(/opp/^{2}\)

\(/3/^{2}\) = \((\sqrt{3} )^{2}\) + \(x^{2}\)

9 = 3 + \(x^{2}\)

\(x^{2}\) = 9 - 3

   = 6

x = \(\sqrt{6}\)

Thus, opposite side = \(\sqrt{6}\)

So that,

sin θ = \(\frac{opposite}{hypotenuse}\)

        = \(\frac{\sqrt{6} }{3}\)

Therefore,

sin θ = \(\frac{\sqrt{6} }{3}\)

Answer:

8700kg

Step-by-step explanation:

b = mass of bricks

l = mass of lorry

b+l = total mass = 11600kg

b = 3l  ==>  l = b/3

substitute: b + b/3 = 11600

multiply every term by 3 to get rid of denominator: 3b + b = 34800

simplify and solve:  4b = 34800  ==>  b = 8700

check:  l = 8700/3 = 2900

2900 + 8700 = 11600?  YES

Answer:

12/60=12/60÷12/12

=1/5

12 minutes=1/5

Step-by-step explanation:

Answer:

1867

Step-by-step explanation:

What do you need it for?

The given equation is

When there's no y, the line is vertical. So, the graph would be

The amount of money that you would pay less for basic contact is $15 while the amount you will pay more for premium =$465.

From the given table in the diagram, the cost of calls made for 10 hours at Standard time=

$6 × 10 = $60

The amount of calls done for basic contact is 3 hours per month for $15 . Total cost per month = 3×15= $45

The amount of calls done for premium contact is 15 hours per month for $35 . Total cost per month = 15× 35=$525

Ordinarily, you per $60 for standard call hours. This means that,

$60 - 45 = $15 less for basic contact and

$525 - $60 = $465 more for premium.

Learn more about subtraction here:

https://brainly.com/question/4721701

#SPJ1

Answer:

An equation or an inequality that contains at least one variable is called an open sentence. When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality.

Answer:

Yes, w=5 is a solution for this inequality.

Step-by-step explanation:

w+11<22

If w=5, this is:

5+11<22

16<22, which is true. So w=5 works as a solution

Answer: 6/(6+2x) ; (-infinity, -3) U (-3, infinity)

Step-by-step explanation:

(a) This can be read as f(x) composed of g(x). Plug in the expression given for g(x) for every x value in f(x):

(6/x)/(6/x+2)

I gave the terms in the denominator the same denominator to combine the bottom two terms into one term. 6/x + 2 is equal to 6/x + 2x/x -->

(6 +2x)/x

Do the classic keep, change, flip. \(\frac{6}{x} * \frac{x}{6+2x}\)

This simplifies to: \(\frac{6}{6+2x}\)

(b) Domain is all real numbers except for what makes the denominator equal to 0.     6 + 2x = 0 when x = -3. Therefore it is all real numbers except -3.

The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.

We have,

Assuming that the probability of a child being born with the disease is independent of whether or not their siblings are born with the disease, we can use the multiplication rule of probability:

P(all 3 children have the disease)

= P(first child has the disease) x P(second child has the disease) x P(third child has the disease)

Since each child has a 57% chance of being born with the disease:

P(all 3 children have the disease)

= 0.57 x 0.57 x 0.57

Now,

P(all 3 children have the disease)

= 0.195

Therefore,

The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ1

Answer:

srry dude this isn't rly a quesiton

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

Read more on graphs:

https://brainly.com/question/19040584

#SPJ1

The equivalent expressions of the percentages are 0.08 * 94 and 8/100 * 94

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

8% of 94

To start with, we express 8% as decimal

So, we have the following representation

0.08 of 94

Express as product

0.08 * 94

Next, we express it as fraction

8/100 * 94

Hence, the expressions are 0.08 * 94 and 8/100 * 94

Read more anout percentage at

https://brainly.com/question/11360390

#SPJ1

The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.

The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.

For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.

Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

So we have derived p as the result using the Power of a Power Property.

In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.

For more such questions on square root

https://brainly.com/question/428672

#SPJ8

Answer:

9 days is neeeded for Nadia to reach her goal

Answer:

1711

Step-by-step explanation:

\(4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711\)

Make sure to follow order of operations!

The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

For moresuch questions on sequence visit:

https://brainly.com/question/30762797

#SPJ8

Answer:

-6

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

=-9+5-7+5

=(-9+5)-7+5

=-4-2

=-6

You owe someone 9pencils,and the person came for the pencils. You now have 5pencils, and you gave them out to the person .You will be left with 4 pencils to give the person since you have given him/her 5 of them.

You this same person owe another person 7pencils,So when you sum up the number of pencils you owe before the current one (-4+(-7))which is equivalent to -11.

The owners of the pencils then come for their pencils. You only have another 5 pencils and then you share it among them, you will be left with 6 pencils more to give out.

NB:Minus(-) means you owe and the plus(+) means add or you have.

The solution of the differential equation y'' + y = t with the initial conditions y(0)=1 and y'(0)=-2 is y(t)= 1-2t+te-t.

Equation is a mathematical statement that expresses the equality of two expressions. It shows the relationship between two or more variables and can be written using symbols, numbers, and operations. Equations are used to describe physical laws, to make calculations, and to solve problems. Examples of equations include the Pythagorean theorem, Newton's laws of motion, and linear equations.

We solve this differential equation using Laplace inverse, with the initial conditions y(0)=1 and y'(0)=-2. First, we take the Laplace transform of the equation:

L[y''+y]=L[t]

Using the properties of Laplace transform, we can write this as:

s2Y(s)-sy(0)-y'(0)+Y(s)= (1/s)

Substituting the initial conditions and rearranging terms, we have:

Y(s)= (1/s) + (2/s2) + (1/s2)

We can then invert the Laplace transform to get the solution of the original equation:

y(t)= 1-2t+te-t

Therefore, the solution of the differential equation y'' + y = t with the initial conditions y(0)=1 and y'(0)=-2 is y(t)= 1-2t+te-t.

To know more about equation click-
http://brainly.com/question/2972832
#SPJ1

Collin's gross salary, after the 7% raise, for each 2-week pay period, will be approximately $1,159.17.

To calculate Collin's gross salary after the 7% raise for each 2-week pay period, we need to find the raise amount and add it to his current gross salary.

Collin's current gross salary is $1,083.34.

To find the raise amount, we multiply his current gross salary by 7% (or 0.07):

Raise amount = $1,083.34 \(\times\) 0.07

= $75.8338 (rounded to two decimal places)

Now, we add the raise amount to his current gross salary to find the new gross salary:

New gross salary = $1,083.34 + $75.8338 = $1,159.1738 (rounded to two decimal places)

For similar question on gross salary.

https://brainly.com/question/28905653  

#SPJ8