an airplane has an airspeed of 530 kilometers per hour bearing N45 degrees E. The wind velocity is 30 kilometers per hour in the direction N30 degrees W. Find the resultant vector representing the path of the plane relative to the ground. What is the ground speed of the plane? What is its direction?

Answer:

x=1

Step-by-step explanation:

4x=4

(Linear equation)

Solved:-

Transpose 4 from LHS to RHS:

[tex] \rm = > x = \tt \cfrac{4}{4} [/tex]

[tex] \rm = > x = \tt1 [/tex]

Answer:

13

Step-by-step explanation:

a parallelogram has sides that are parallel to the opposite side. This means that y + 7 is going to be parallel to 20.

Two opposing sides of a parallelogram are parallel and equal

You know that the length of both of the sides is equivalent because the other set of opposing lines is also parallel (you can think of it as cutting off the line segment of y+7 and 20 at the same length. )

this means that we can set up the equation to find y as:

y + 7 = 20

then, you can proceed to find y by isolating it:

y + 7 = 20 ; so therefore

y + 7    =    20

   - 7           -7

y           =     13

y = 13

So, the value of y is 13

Answer:

[tex]\text{The quotient is}~ x^2 +2x +5 \\\\\text{The remainder is}~ -3[/tex]

Step-by-step explanation:

Answer:

y= -1/5x+5

STEP BY STEP EXPLAINATION:

m = slope = -1/5

c = y-intercept = 5

equation of a straight line:

y=mx+c

so.

y= -1/5x+5

The patient would be administered 4 tablets per dose.

In mathematics, solving word problems involves a careful understanding of the content of the problem. This will enable the use of appropriate variables and data representation.

From the given information:

From the standard conversion rate, we know that:

Here, to determine the number of dose to be administered, we have:

(x) /dose = 1000 mg/250 mg

x = 4 dose.

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Answer:

Its A

Step-by-step explanation:

Answer:

68.27%

Step-by-step explanation:

By the Empirical Rule, as 65% and 75% are both one standard deviation apart from the mean of 70%, then this represents 68.27% of the data.

The probability that exactly 800 chips are acceptable is less than 0.000001

The given parameters are:

The binomial probability is represented as:

[tex]P(x) = ^nC_x * p^x * (1- p)^{n - x}[/tex]

So, we have:

[tex]P(300) = ^{3000}C_{800} * (72\%)^{800} * (1- 72\%)^{3000 - 800}[/tex]

The data values are large.

So, we use a statistical calculator to evaluate the expression

Using the calculator, we have:

P(300) < 0.000001

Hence, the probability that exactly 800 chips are acceptable is very small i.e. less than 0.000001

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Answer:

4 x y ^2

Step-by-step explanation:

4 x y^2    would be the GFC

The parameters of an Exponential Distribution is D. a > 0

This refers to the distribution of probability with respects to time taken in a Poisson point process.

Hence, we can see that from the previous knowledge of exponential distributions, it is stated that λ > 0 is the parameter of the distribution, and is supported on the interval [0, ∞).

Therefore, option D is correct.

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Answer:

B

Step-by-step explanation:

We can either use sine or cosine, I choose cosine but sine works the same. cos(angle) = adj/hyp. adj = cos(angle) x hyp. adj = cos(30)8, cos(30) = √3/2. √3/2 x 8 = 4√3

Answer:

4 times

Step-by-step explanation:

If the smaller container only holds 2 liters, you would have to divide 8 by 2 which is 4.

Answer:

4 times

Step-by-step explanation:

Its 4 times cause 8/2=4

x²+3x

= x×x+3×x

= x(x+3)

Answer:

33,75 clients(huh?)

Step-by-step explanation:

75 / 100 = 0,75(1% of all clients)

0,75 * 45 = 33,75(number of business clients)

The function f(x) = 2x -14 is a polynomial function

The equation of the function is given as:

f(x) = 2x -14

A polynomial is represented as:

f(x) =ax^n + bx^(n - 1)....... + c

Where n is at least 1.

The function f(x) = 2x -14 is a polynomial with a degree of 1

Hence, the function f(x) = 2x -14 is a polynomial function

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Answer:

h'(z) = 2

Step-by-step explanation:

(b) First, let's expand everything so our equation is easier to look at.
h(z) = (3-4)(8-2z+3)
         (-1)(-2z+11)
         2z-11

Now, let's find the derivative:
h'(z) = 2

Answer:

4,186.67 in³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)(3.14)(10 in)³

V = (4/3)(3.14)(1,000 in³)

V = 4,186.666667 in³

The mean and standard deviation for the number of boys in the 950 babies are 475 and 15.41, respectively

From the complete question, we have:

P(boy)= 0.5

Sample size = 950

The mean is then calculated as:

[tex]\bar x = np[/tex]

This gives

[tex]\bar x = 950 * 0.5[/tex]

Evaluate

[tex]\bar x = 475[/tex]

The standard deviation is calculated as:

[tex]\sigma = \sqrt{np(1 - p)[/tex]

This gives

[tex]\sigma = \sqrt{950 * 0.5(1 - 0.5)[/tex]

Evaluate

[tex]\sigma = 15.41[/tex]

Hence, the mean and standard deviation for the number of boys in the 950 babies are 475 and 15.41, respectively

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Answer:

47.1408

Step-by-step explanation:

They gave us the percentage of a number and wants us to find the whole

to do that we will use the following equation:

46.116*100/4.5 = 47.1408 is the number we are looking for.

Answer:

x=2

Step-by-step explanation:

axis of symmetry is

x-2=0

or

x=2

Answer:

Graph B. On a coordinate plane, a vertical dashed line at (2, 0) is parallel to the y-axis.

Answer:

436.6

Step-by-step explanation:

3700×0.118=436.6

The value of the next term in the geometric sequence is 16

From the graph, we have the following highlights:

The means that:

Next term = Current term * 2

From the graph, we have:

Current term = 8

So, the equation becomes

Next term = 8 * 2

Evaluate

Next term = 16

Hence, the value of the next term in the geometric sequence is 16

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[tex]20^{\tfrac 52}\\\\=(20^5)^{\tfrac 12}\\\\=\left(20^4 \cdot 20 \right)^{\tfrac 12}\\\\=20^{\tfrac 42} \cdot 20^{\tfrac 12}\\\\=20^2 \sqrt{20}\\\\=400\sqrt{4 \times 5}\\\\=400 \times 2\sqrt 5\\\\=800\sqrt 5[/tex]

Answer:

[tex]800\sqrt{5}[/tex]

Step-by-step explanation:

Given: [tex]\large (20)^\text{$ \dfrac{5}{2} $}[/tex]

Properties of Exponents:

Rational Exponent Property: [tex]\large x^\text{$ \dfrac{m}{n} $} = \large \text{$ \sqrt[n]{x^m} $}[/tex]

Product of Powers Property:

1. Convert into a radical:

[tex]\sqrt[2]{20^5} \implies \sqrt{20^5}[/tex]

2. Simplify the expression:

[tex]\sqrt{20^2\times20^2\times20^1}\\\\\implies \sqrt{20^4\times20}\\\\\implies 20^2\sqrt{20}\\\\\implies 20^2\sqrt{4\times5}\\\\\implies 20^2\times2\sqrt{5}[/tex]

3. Evaluate the power:

[tex]20\times20\times2\sqrt{5}\\\\\implies 400\times2\sqrt{5}[/tex]

4. Multiply:

[tex](400\times2)\sqrt{5}\\\\\implies800\sqrt{5}[/tex]

Answer:

Perimeter=150cm

Step-by-step explanation:

25cm×6=150cm

The angle (off of a north-south line) at which a navy carrier needs to travel to sail straight to the submarine is 53.843°.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite the 90° angle.

The Navy carrier, Mercy, is sailing in the Pacific Ocean. The ship is in the sea, 4,365 miles south of a city. On radar, they notice a submarine is 7,390 miles away from them and north-west of their current position.

Therefore, the angle at which the Carrier needs to move to reach the submarine is,

Cosθ = 4365/7390

θ = Cos⁻¹ (0.59)

θ = 53.843°

Hence, the angle (off of a north-south line) at which a navy carrier needs to travel to sail straight to the submarine is 53.843°.

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The mean, median, and midrange of the given that are 66, 66 and 66 respectively.

Option D) Mean = 66, median = 66, midrange = 66 is the correct answer.

Mean is the sum total of the number divided by number of terms

Median is the middle number when arranged in ascending or descending order.

Midrange is the average of the sum of the maximum number and the minimum number.

Given that;

First, we arrange in ascending order.

60, 62. 64, 66, 68, 70, 72

Mean = ( 60 + 62 + 64 + 66 + 68 + 70 + 72 ) / 7

Mean = 462 / 7

Mean = 66

Median = 66

66 is the middle number.

Range = ( Max + Min ) / 2

Range = ( 72 + 60 ) / 2

Range = 132 / 2

Range = 66

Therefore, the mean, median, and midrange of the given that are 66, 66 and 66 respectively.

Option D) Mean = 66, median = 66, midrange = 66 is the correct answer.

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Answer:

55.2 is the mean

Explanation:

Given data set:  {113, 14, 23, 12, 114}

Mean = sum of the terms/number of terms

Mean = (113 + 14 + 23 + 12 + 114)/5

          = (276)/5

          = 55.2

Answer:

Mean = 55.2

Step-by-step explanation:

Given data set:   113, 14, 23, 12, 114

To find the mean of a data set, divide the sum of all data values by the total number of data values:

[tex]\large \begin{aligned}\sf Mean & = \sf\dfrac{sum\:of\:all\:data\:values}{total\:number\:of\:data\:values} \\\\\implies \sf Mean & = \sf \dfrac{113 + 14 + 23 + 12 + 114}{5}\\\\& = \sf \dfrac{276}{5}\\\\& = \sf 55.2\end{aligned}[/tex]