At noon, ship A is 150 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 PM?

Answer:

$32 704

Step-by-step explanation:

(102.2÷100) × 32 000 = $32 704

Answer:

I will answer in English.

We can prove that the angle APS is a triangle rectangle.

Remember that for a triangle rectangle of catheti A and B, and hypotenuse H, the Pythagorean's theorem says that:

A^2 + B^2 = H^2

In this case, we can assume that the hypotenuse is the longer side, AS, and the other two sides are the catheti.

Then we have:

H = 5x + 10

A = 3x + 6

B = 4x + 8

Now let's write the equation from the theorem, and let's see if its true.

A^2 + B^2 = H^2

( 3x + 6 )^2 + (4x + 8)^2 = (5x + 10)^2

So we can start with:

( 3x + 6 )^2 + (4x + 8)^2

And try to "transform" this into:

(5x + 10)^2

First, let's expand it:

((3x)^2 + 2*(3x)*6 + 6^2) + ( (4x)^2 + 2*(4x)*8 + 8^2)

9x^2 + 24x + 36 + 16x^2 + 64x + 64

25x^2 + 40x + 100

Now we can complete squares on the left side, by writing:

(5x)^2 + 2*10*(5x) + 10^2

(5x + 10)^2

Then we saw that the equation is true for every value of x, then we just prove that the triangle fulfills the theorem, thus, the triangle is a triangle rectangle.

Answer:

There is a 60.00 percent probability of a particular outcome and 40.00 percent probability of another outcome.

Answer:

[tex]-2[/tex]

Step-by-step explanation:

Just substitute -3 for all instances of x.

[tex](-3)^{2} + 4(-3) + 1\\\\[/tex]

[tex]9 - 12 + 1[/tex]

[tex]-2[/tex]

Answer:

She had 8 doubles.

Step-by-step explanation:

This question is solved by a system of equations.

I am going to say that:

x is the number of singles.

y is the number of doubles

z is the number of triples.

46 hits

This means that [tex]x + y + z = 46[/tex]

46 hits totaled 66 bases

This means that:

[tex]x + 2y + 3z = 66[/tex]

4 times as many singles as doubles

This means that [tex]x = 4y[/tex]

So

[tex]x + 2y + 3z = 66[/tex]

[tex]4y + 2y + 3z = 66[/tex]

[tex]6y + 3z = 66[/tex]

And

[tex]x + y + z = 46[/tex]

[tex]4y + y + z = 46[/tex]

[tex]5y + z = 46 \rightarrow z = 46 - 5y[/tex]

Then

[tex]6y + 3z = 66[/tex]

[tex]6y + 3(46 - 5y) = 66[/tex]

[tex]6y + 138 - 15y = 66[/tex]

[tex]9y = 72[/tex]

[tex]y = \frac{72}{9}[/tex]

[tex]y = 8[/tex]

She had 8 doubles.

Answer:

1 (2) f(x) = 1 (3) 1< f(x) < 2 (4) f(x) greater than or equal to 2

Step-by-step explanation:

We know AM ≥ GM

(cos2x+sec2x )/2 ≥ √(cos2x sec2x)

(cos2x+sec2x ) ≥ 2√(cos2x (1/cos2x)

f(x) ≥ 2

Hence option (4) is the answer.

Step-by-step explanation:

[tex]\dfrac{dy}{dx} = \dfrac{2x}{y(x^2 + 1)}[/tex]

Rearranging the terms, we get

[tex]ydy = \dfrac{2xdx}{x^2 + 1}[/tex]

We then integrate the expression above to get

[tex]\displaystyle \int ydy = \int \dfrac{2xdx}{x^2 + 1}[/tex]

[tex]\displaystyle \frac{1}{2}y^2 = \ln |x^2 +1| + k[/tex]

or

[tex]y = \sqrt{2\ln |x^2 + 1|} + k[/tex]

where I is the constant of integration.

Answer:

A, C and D are not polynomials

Step-by-step explanation:

A because the variable has a negative power.

C because the variable is in the denominator

D because the variable has a root.

When a variable has a root, it's power is 1/2 which does not count as an ideal polynomial. You might be wondering then that why E is a polynomial?

E is a polynomial because because the root is not on the variable but on the constant.

B and E are polynomials while A,C and D are not.

Please mark me as brainliest.

Answer:

3

Step-by-step explanation:

Answer:

1 : 4

Step-by-step explanation:

2 feet is 24 inches so we are finding the ratio between

6 and 24

Simplify

1 : 4

Answer:

50,000 : 0.01

multiply by 100...

5000000 : 1

 1:5,000,000

Step-by-step explanation:

Answer:

8x-7y=6

or, -7y=-8x+6

or, y=8x/7-6/7

so the slope is 8/7

8x-y=-8

or, -y=-8x-8

or, y=8x+8

So the slope is 8

Both has different slope and they don't satisfy the property of being perpendicular to each others, so they're neither parallel nor perpendicular.

Answered by GAUTHMATH

Answer:

The original graph was shifted 2 units to the left and 5 units down.

Step-by-step explanation:

y = |x|

From this, we go to: y = |x - 2|.

When we want to shift a function f(x) a units to the left, we find f(x - a). So first, the graph was shifted 2 units to the left.

y = |x - 2|.

From this, we go to: y = |x - 2| - 5.

Shifting a function f(x) down b units is the same as finding f(x) - b, so the second transformation was shifting the graph 5 units down.

Answer:

An equation in the slope-intercept form is:

y = a*x + b

Where a is the slope, and b is the y-intercept.

a)

Here we have a slope of 6 and a y-intercept of -3

Then the equation is:

y = 6*x - 3

Now we want to graph this.

To graph it, we first need to find two points (x, y) that belong to this equation, then we can graph the points, and connect them with a line.

To find the points, we evaluate in two different values of x.

x = 0

y = 6*0 - 3 = -3

Then we have the point (0, -3)

x = 1

y = 6*1 - 3 = 3

Then we have the point (1, 3)

The graph of this line can be seen in the image below (the red one)

b) Similar to before, here the slope is -3/5, then the equation is something like:

y = (-3/5)*x + b

Now we also know that the line passes through the point (-10, 8)

This means that when x = -10, we must have y = 8

Replacing these two in the equation we get:

8 = (-3/5)*-10 + b

8 = 6 + b

8 - 6 = 2 = b

Then this equation is:

y = (-3/5)*X + 2

The graph can be found in the same way as before, the graph of this function can also be seen in the image below (the green one)

Answer:

Metro and Medec

METRO

Post-merger Financial Position, using the pooling of interest method:

Pre-merger Financial Positions:

                           Metro (RM ‘000)

Assets  

Current assets                          120

Fixed assets                             830

Total assets                             950

Liabilities and Equities  

Current liabilities                      40

Long term debt                      200

Common stock (RM1 par)      480

Capital surplus                       120

Retained earnings                  110

Total liabilities and equity    950

Earnings available to

common stockholders            230

Common Dividends                  150

Addition to Retained Earnings  80

Step-by-step explanation:

Pre-merger Financial Positions:

                           Metro (RM ‘000)    Medec(RM ‘000)

Assets  

Current assets                          50                     70

Fixed assets                           650                    180

Total assets                            700                   250

Liabilities and Equities  

Current liabilities                      30                     10

Long term debt                       140                    60

Common stock (RM1 par)      400                    80

Capital surplus                         50                    70

Retained earnings                   80                    30

Total liabilities and equity     700                 250

Earnings available to

common stockholders            100                  130

Common Dividends                  50                  100

Addition to Retained Earnings 50                   30

Exchange ratio = 1:2

Answer:

Answer:Amy used 4 41-cent stamps and 8 6-cent stamps.

Step-by-step explanation:

Let x represent the number of 41-cent stamps that Amy used. Let y represent the number of 6-cent stamps that Amy used.

41 cents = 41/100 = $0.41

6 cents = 6/100 = $0.06

She uses 41-cent stamps and 6-cent stamps to pay $2.12 in postage. It means that

0.41x + 0.06y = 2.12

Multiplying through by 100, it becomes

41x + 6y = 212

6y = 212 -41x

We would test for corresponding values of x and y that satisfies the equation and they must be whole numbers.

If x = 3,

6y = 212 - 41 × 3 = 89

y = 89/6 = 14.8333

If x = 4,

6y = 212 - 41 × 4 = 48

y = 48/6 = 8

Answer:Amy used 4 41-cent stamps and 8 6-cent stamps.

Step-by-step explanation:

Let x represent the number of 41-cent stamps that Amy used. Let y represent the number of 6-cent stamps that Amy used.

41 cents = 41/100 = $0.41

6 cents = 6/100 = $0.06

She uses 41-cent stamps and 6-cent stamps to pay $2.12 in postage. It means that

0.41x + 0.06y = 2.12

Multiplying through by 100, it becomes

41x + 6y = 212

6y = 212 -41x

We would test for corresponding values of x and y that satisfies the equation and they must be whole numbers.

If x = 3,

6y = 212 - 41 × 3 = 89

y = 89/6 = 14.8333

If x = 4,

6y = 212 - 41 × 4 = 48

y = 48/6 = 8

Answer:

3/8

Step-by-step explanation:

the total number of possible results is 4×4=16.

out of these 16 only the results

1 2

1 3

1 4

2 2

2 3

3 2

are desired results. these are 6.

so the probability of a desired result is 6/16 = 3/8

Answer:

The value of the standard error for the point estimate is of 0.0392.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In a randomly selected sample of 100 students at a University, 81 of them had access to a computer at home.

This means that [tex]n = 100, p = \frac{81}{100} = 0.81[/tex]

Give the value of the standard error for the point estimate.

This is s. So

[tex]s = \sqrt{\frac{0.81*0.19}{100}} = 0.0392[/tex]

The value of the standard error for the point estimate is of 0.0392.

Answer:

C. 6.8 in

Step-by-step explanation:

hope it helps please correct me If I am wrong

Answer:

0.0498

Step-by-step explanation:

In this question,

x~exponential

we have

mean = 1/λ = 8

from here we cross multiply, when we do

such that

λ = 1/8

probability of x functioning in 8 months

= e^-λx

= e^-1/8x12

= e^-1.5

= 0.2231

i got this value through the use of a scientific calculator

then the probability that these two are greater than 12

= 0.2231²

= 0.04977

= approximately 0.0498

therefore the probability that both components are functioning in 12 months is 0.0498

Answer:

The rewritten expression is [tex](u - 8)(3u^2 - 2)[/tex]

Step-by-step explanation:

We are given the following expression:

[tex]3u^2(u - 8) - 2(u - 8)[/tex]

Factoring out (u-8)

Place (u-8) to the front, and then divide each term by (u-8). So

[tex]3u^2(u - 8) - 2(u - 8) = (u - 8)\left[\frac{3u^2(u - 8)}{u - 8} - \frac{2(u-8)}{u - 8}\right] = (u - 8)(3u^2 - 2)[/tex]

The rewritten expression is [tex](u - 8)(3u^2 - 2)[/tex]

Answer:

Step-by-step explanation:

First you have to know two definitions. Well, you only have to know one for this problem, but you should probably learn the 2nd just to be thorough.

Definition 1: Complementary angles are two angles whose sum is 90 degrees.

Definition 2: Supplementary angles are two angles whose sum is 180 degrees.

For this problem, we'll work with the definition that says two complementary angles have a sum of 90 degrees.

Soooo, here are the facts from your problem: if one angle is 15 degree more than 2 times the other.find the measure of two angles.

Let's let the larger angle equal this: 15 + 2(x) (<--See how it is 15 degrees MORE than 2 times the other?)

Let's let the smaller angle equal: x

SO now our total equation is:

15 + 2(x) + x = 90

3x + 15 = 90 (combined like terms)

3x = 75 (subtracted 15 from both sides)

x = 25 (divided both sides by 3)

Now we know that one angle is 25. The other angle must add to 25 to make 90 degrees, so 90 - 25 = 65.

Therefore, your two angles are 25 and 65 degrees.

Does this check out? Let's see...

First: 25 + 65 = 90 Therefore, this checks out.

Second: The angle that is 65 degrees must be 15 degrees more than twice the other. So, let's take twice the other...... 25 * 2 = 50. And, let's add 15....50 + 15 = 65. Therefore YES, the 2nd angle is 15 more than 2 times the angle that was 25 degrees.

I hope this is helpful. :-)

9514 1404 393

Answer:

Step-by-step explanation:

The third angle can be found from the sum of angles in a triangle.

  A + B + C = 180°

  C = 180° -62° -97°

  C = 21°

__

The remaining side lengths can be found using the Law of Sines.

  a/sin(A) = b/sin(B)

  a = sin(62°)(15/sin(97°)) ≈ 13.34

Similarly, ...

  c/sin(C) = b/sin(B)

  c = sin(21°)(15/sin(97°)) ≈ 5.42

The remaining side lengths are approximately ...

  a ≈ 13.3

  c ≈ 5.4

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

When given the following equation;

[tex]\frac{x+3}{3x-2}-\frac{x-3}{3x+2}=\frac{44}{9x^2-4}[/tex]

One has to solve for the variable (x). Remember, when working with fractions, one must have a common denominator in order to perform operations. Since the denominators on the left side of the equation are unlike, one must change them so that they are like denominators. Multiply each fraction by the other fraction's denominator on the respective side. Remember to multiply both the numerator and denominator by the value to ensure that the equation remains true.

[tex]=\frac{x+3}{3x-2}*(\frac{3x+2}{3x+2})-\frac{x-3}{3x+2}*(\frac{3x-2}{3x-2})=\frac{44}{9x^2-4}[/tex]

Simplify,

[tex]=\frac{(x+3)(3x+2)}{(3x-2)(3x+2)}-\frac{(x-3)(3x-2)}{(3x+2)(3x-2)}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6}{9x^2-4}-\frac{3x^2-11x+6}{9x^2-4}=\frac{44}{9x^2-4}[/tex]

Distribute the negative sign to simplify the left side of the equation;

[tex]=\frac{3x^2+11x+6}{9x^2-4}-\frac{3x^2-11x+6}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6-(3x^2-11x+6)}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{3x^2+11x+6-3x^2+11x-6}{9x^2-4}=\frac{44}{9x^2-4}\\\\=\frac{22x}{9x^2-4}{=\frac{44}{9x^2-4}[/tex]

Since the denominators on opposite sides of the equation are like, one can now ignore the denominators,

[tex]=22x=44[/tex]

Inverse operations,

[tex]=22x=44[/tex]

   ÷[tex]2[/tex]       ÷[tex]2[/tex]

     [tex]x=2[/tex]

Answer:

x ≤ -12

Step-by-step explanation:

To get x by itself you simply multiply both sides by 4, since 1/4 * 4 = 1.

Answer:

The mean is to the right of the median

Step-by-step explanation:

Given

Skewed right distribution

Required

Relationship between the mean and the median

The question would be better answered if there are options available. Since there are none, I will provide a general answer/explanation.

For a distribution that is right skewed, the mean is always on the right side of the median.

Answer:

a) it is a discrete random variable

b) It is a continuous random variable

c) It is not a random variable

d) It is a discrete random variable

e)  It is a discrete random variable

f) It is a continuous random variable

Step-by-step explanation:

Explanation,

Continuous Random Variable  

A continuous variable is one that can take on an uncountable set of values.

It may take any values within an interval.

It can take infinite values within an interval.

They are obtained by measuring rather than counting.

Discrete Random Variable  

These can only take a discrete value and cannot be expressed in the form of decimals.

They are obtained by counting rather than measuring.

a). it is a discrete random variable  ⇒ as a number of people is a discrete count, which takes values such as 0 or 1 or 2.

b). The exact time it takes to evaluate 27+72 ⇒ Since, Time is measured and thus it is a continuous random variable.

c). The gender of college students ⇒ Gender is categorical data. It is neither continuous nor discrete.

d).  The number of hits to a website in a day ⇒ Since the number of people cannot be expressed as decimals, thus it is a discrete random variable

e). The number of bald eagles in a country ⇒ Since the number of people cannot be expressed as decimals, thus it is a discrete random variable

f).  The distance a baseball travels in the air after being hit  ⇒ Distance is measured and thus it is a continuous random variable.

Answer:

2

Step-by-step explanation:

8*8 is 64

Since it looks like the empty box is an exponent, and there are 2 8s being multiplied, the answer is 2

Answer:

50 text messages would have to be sent or received in order for the plans to cost the same each month.

Step-by-step explanation:

x = number of text messages sent

0.2x+40=50

0.2x = 10

5(0.2x) = 5(10)

x = 50

Therefore, 50 text messages would have to be sent or received in order for the plans to cost the same each month.

Answer:

The statements are logically equivalent.

The 6th column is:

F T F F

The 7th column is:

F T F F

Step-by-step explanation:

The 6th column is just the opposite of the 5th column

The 7th column is T only if both the 1st and 4th are T