At noon, ship A is 120 km west of ship B. Ship A is sailing east at 20 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM?

Answer:

Option C

Step-by-step explanation:

The chi square test of independence is used to determine if there is a significant association between two categorical variables from a population.

It tests the claim that the row and column variables are independent of each other.

The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1) (c-1) where r is the number of rows and c is the number of columns.

Answer:

99% confidence interval for the mean of college students

A) 112.48 < μ < 117.52

Step-by-step explanation:

step(i):-

Given sample size 'n' =150

mean of the sample = 115

Standard deviation of the sample = 10

99% confidence interval for the mean of college students are determined by

[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

Degrees of freedom

ν = n-1 = 150-1 =149

t₁₄₉,₀.₀₁ =  2.8494

99% confidence interval for the mean of college students are determined by

[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]

on calculation , we get

(115 - 2.326 , 115 +2.326 )

(112.67 , 117.326)  

we just have to use the Pythagoras theorem and then calculate the value of x and y.

Answer:

width = 4.5 m

length = 14 m

Step-by-step explanation:

okay so first you right down that L = 5 + 2w

then as you know that Area = length * width so you replace the length with 5 + 2w

so it's A = (5 +2w) * w = 63

then 2 w^2 + 5w - 63 =0

so we solve for w which equals 4.5 after that you solve for length : 5+ 2*4.5 = 14

Answer:

0.07

Step-by-step explanation:

The number of sophmores is 2+25+3 = 30.

Of these sophmores, 2 drive to school.

So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.

Answer:

[tex]\large \boxed{0.07}[/tex]

Step-by-step explanation:

The usual question is, "What is the probability of A, given B?"

They are asking, "What is the probability that you are driving to school if you are a sophomore (rather than taking the bus or walking)?"

We must first complete your frequency table by calculating the totals for each row and column.

The table shows that there are 30 students, two of whom drive to school.

[tex]P = \dfrac{2}{30}= \mathbf{0.07}\\\\\text{The conditional probability is $\large \boxed{\mathbf{0.07}}$}[/tex]

Answer:

100%

Step-by-step explanation:

Start with x.

x = x/1

Increase the numerator by 60% to 1.6x.

Decrease the numerator by 20% to 0.8.

The new fraction is

1.6x/0.8

Do the division.

1.6x/0.8 = 2x

The fraction increased from x to 2x. It became double of what it was. From x to 2x, the increase is x. Since x was the original number x is 100%.

The increase is 100%.

Answer:

33%

Step-by-step explanation:

let fraction be x/y

numerator increased by 60%

=x+60%ofx

=8x

denominator increased by 20%

=y+20%of y

so the increased fraction is 4x/3y

let the fraction is increased by a%

then

x/y +a%of (x/y)=4x/3y

or, a%of(x/y)=x/3y

[tex]a\% = \frac{x}{3y} \times \frac{y}{x} [/tex]

therefore a=33

anda%=33%

Answer:

16 ounces = 1 pound

Step-by-step explanation:

You would just do 18/16 = 1.125 pounds. There are always 16 ounces in a pound, so it always works like this

Answer:

B

Step-by-step explanation:

A is not a function because the same x value is repeated twice with different y values. The same goes for C and D so the answer is C.

Answer:

B.

Step-by-step explanation:

Well a relation is a set of points and a function is a relation where every x value corresponds to only 1 y value.

So lets see which x values in these relations have only 1 y value.

A. Well a isn’t a function because the number 3 which is a x value had two y values which are -1 and 4.

B. This relation is a function because there are no similar x values.

C. This is not a function because the x value 4 has two y values which are 4 and -3.

D. This is not a function because the number 1 has 2 and 3 as y values.

━━━━━━━☆☆━━━━━━━

▹ Answer

0.25 = 1/4 because 25/100 = 1/4

▹ Step-by-Step Explanation

0.25 to a fraction → 25/100

25/100 = 1/4

Therefore, this statement is true. (0.25 = 1/4 because 25/100 = 1/4)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

a. 0.34885

b. 0.04651

c. 0.02404

d. 36

e. 14.7, say 15 trials

Step-by-step explanation:

Q17070205

Note:  

1. In order to be applicable to established probability distributions, each roll is considered a Bernouilli trial, i.e. has only two outcomes, success or failure, and are all independent of each other.

2. use R to find the probability values from the respective distributions.

a) the chance that the first 6 appears before the tenth roll

This means that a six appears exactly once between the first and the nineth roll.

Using binomial distribution, p=1/6, n=9, x=1

dbinom(1,9,1/6) = 0.34885

b) the chance that the third 6 appears on the tenth roll

This means exactly two six's appear between the first and 9th rolls, and the tenth roll is a six.

Again, we have a binomial distribution of p=1/6, n=9, x=2

p1 = dbinom(2,9,1/6) = 0.27908

The probability of the tenth roll being a 6 is, evidently, p2 = 1/6.

Thus the probability of both happening, by the multiplication rule, assuming independence  

P(third on the tenth roll) = p1*p2 = 0.04651

c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.

Again, using binomial distribution, probability of 3-6's in the first 10 rolls,

p1 = dbinom(3,10,1/6) = 0.15504

Probability of 3-6's in the NEXT 10 rolls

p1 = dbinom(3,10,1/6) = 0.15504

Probability of both happening  (multiplication rule, assuming both events are independent)

= p1 *  p1 = 0.02404

d) the expected number of rolls until six 6's appear

Using the negative binomial distribution, the expected number of failures before n=6 successes, with probability p = 1/6

=  n(1-p)/p

Total number of rolls by adding n  

= n(1-p)/p + n = n(1-p+p)/p = n/p = 6/(1/6) = 36

e) the expected number of rolls until all six faces appear

P1 = 6/6 because the firs trial (roll) can be any face with probability 1

P2 = 6/5 because the second trial for a different face has probability 5/6, so requires 6/5 trials

P3 = 6/4 ...

P4 = 6/3

P5 = 6/2

P6 = 6/1

So the total mean (expected) number of trials is 6/6+6/5+6/4+6/3+6/2+6/1 = 14.7, say 15 trials

Answer:

D

Step-by-step explanation:

Solution:-

The standard sinusoidal waveform defined over the domain [ 0 , 2π ] is given as:

                                   f ( x ) = sin ( w*x ± k ) ± b

Where,

                 w: The frequency of the cycle

                 k: The phase difference

                 b: The vertical shift of center line from origin

We are given that the function completes 2 cycles over the domain of [ 0 , 2π ]. The number of cycles of a sinusoidal wave is given by the frequency parameter ( w ).

We will plug in w = 2. No information is given regarding the phase difference ( k ) and the position of waveform from the origin. So we can set these parameters to zero. k = b = 0.

The resulting sinusoidal waveform can be expressed as:

                           f ( x ) = sin ( 2x )  ... Answer

Answer:

x < 11.5

Step-by-step explanation:

2x + 9 < 32

(2x + 9) - 9  < 32 - 9

2x < 23

2x/2 < 23/2

x < 11.5

Answer:

x < 11 1/2

Step-by-step explanation:

2x+9<32

Subtract 9 from each side

2x+9-9 < 32-9

2x<23

Divide by 2

2x/2 <23/2

x < 11 1/2

X is any number less than 11 1/2

Answer:

Increasing: [tex](0, 750)[/tex]

Decreasing: [tex](750, \infty)[/tex]

Step-by-step explanation:

Critical points:

The critical points of a function f(x) are the values of x for which:

[tex]f'(x) = 0[/tex]

For any value of x, if f'(x) > 0, the function is increasing. Otherwise, if f'(x) < 0, the function is decreasing.

The critical points help us find these intervals.

In this question:

[tex]P(x) = -0.004x^{2} + 6x - 5000[/tex]

So

[tex]P'(x) = -0.008x + 6[/tex]

Critical point:

[tex]P'(x) = 0[/tex]

[tex]-0.008x + 6 = 0[/tex]

[tex]0.008x = 6[/tex]

[tex]x = \frac{6}{0.008}[/tex]

[tex]x = 750[/tex]

We have two intervals:

(0, 750) and [tex](750, \infty)[/tex]

(0, 750)

Will find P'(x) when x = 1

[tex]P'(x) = -0.008x + 6 = -0.008*1 + 6 = 5.992[/tex]

Positive, so increasing.

Interval [tex](750, \infty)[/tex]

Will find P'(x) when x = 800

[tex]P'(x) = -0.008x + 6 = -0.008*800 + 6 = -0.4[/tex]

Negative, then decreasing.

Answer:

Increasing: [tex](0, 750)[/tex]

Decreasing: [tex](750, \infty)[/tex]

Answer:

Step-by-step explanation:

Surface Area of the rectangular box = 2(LW+LH+WH)

L is the length of the box

W is the width of the box

H is the height of the box

let dL, dW and dH be the possible error in the dimensions L, W and H respectively.

Since there is a possible error of 0.2cm in each dimension, then dL = dW = dH = 0.2cm

The surface Area of the rectangular box using the differentials is expressed as shown;

S = 2{(LdW+WdL)+(LdH+HdL)+(WdH+HdW)]

Also given L = 96cm W = 58cm and H = 48cm, on substituting this given values and the differential error, we will have;

S = 2{(96*0.2+58*0.2) + (96*0.2+48*0.2)+(58*0.2+48*0.2)}

S = 2{19.2+11.6+19.2+9.6+11.6+9.6}

S = 2(80.8)

S = 161.6 cm²

Hence, the surface area of the box is 161.6 cm²

Step-by-step explanation:

given,

base( b) = 6cm

height (h)= 11cm

now, area of parallelogram (a)= b×h

or, a = 6cm ×11cm

therefore the area of parallelogram (p) is 66cm^2.

hope it helps...

Answer:

Dy/Dx=1/√ (2x+3)

Yeah it's correct

Step-by-step explanation:

Applying differential by chain differentiation method.

The differential of y = √(2x+3) with respect to x

y = √(2x+3)

Let y = √u

Y = u^½

U = 2x +3

The formula for chain differentiation is

Dy/Dx = Dy/Du *Du/Dx

So

Dy/Dx = Dy/Du *Du/Dx

Dy/Du= 1/2u^-½

Du/Dx = 2

Dy/Dx =( 1/2u^-½)2

Dy/Dx= u^-½

Dy/Dx=1/√ u

But u = 2x+3

Dy/Dx=1/√ (2x+3)

Answer:

k = -6

Step-by-step explanation:

hello

saying that (x-2) is a factor of [tex]x^2+x+k[/tex]

means that 2 is a zero of

[tex]x^2+x+k=0 \ so\\2^2+2+k=0\\<=> 4+2+k=0\\<=> 6+k =0\\<=> k = -6[/tex]

and we can verify as

[tex](x^2+x-6)=(x-2)(x+3)[/tex]

so it is all good

hope this helps

Answer:

When describing a property line drawn down the center of a creek bed

Answer: D

Step-by-step explanation:

According to the question, Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year

The initial population Po = 114000

Rate = 1.5% = 0.015

The declining population formula will be:

P = Po( 1 - R%)x^2

The decay formula

Since the population is decreasing, take away 0.015 from 1

1 - 0.015 = 0.985

Substitutes all the parameters into the formula

P(s) = 114000(0.985)x^2

P(s) = 114000× 0985x^2

The correct answer is written above.

Since option A does not have square of x, we can therefore conclude that the answer is D - non of the choices is correct.

Answer:

21=2w+2w+3    18=4w     w=4.5

Answer:

81.23 ft and 77.88 ft long

Step-by-step explanation:

The sum of the internal angles of a triangle is 180 degrees, the missing angle is:

[tex]a+b+c=180\\a+23+22=180\\a=135^o[/tex]

According to the Law of Sines:

[tex]\frac{A}{sin(a)}= \frac{B}{sin(b)}= \frac{C}{sin(c)}[/tex]

Let A be the side that is 147 feet long, the length of the other two sides are:

[tex]\frac{A}{sin(a)}= \frac{B}{sin(b)}\\B=\frac{sin(23)*147}{sin(135)}\\B=81.23\ ft\\\\\frac{A}{sin(a)}= \frac{C}{sin(c)}\\C=\frac{sin(22)*147}{sin(135)}\\C=77.88\ ft[/tex]

The other two sides are 81.23 ft and 77.88 ft long

Answer:

C and D

Step-by-step explanation:

khan acedemy

An equation is formed when two equal expressions. The solutions to the given equation are A, B, and C.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of the given equation v²=25/81 can be found as shown below.

v²=25/81

Taking the square root of both sides of the equation,

√(v²) = √(25/81)

v = √(25/81)

v = √(5² / 9²)

v = ± 5/9

Hence, the solutions of the given equation are A, B, and C.

Learn more about Equation here:

https://brainly.com/question/2263981

#SPJ2

Answer: 29,000.00

Step-by-step explanation:

Let the income=x.  22%=0.22.

So 6380/x=0.22

x=6380/0.22=29,000.00

Answer:

(7, 5.25) lies on the graph.

Step-by-step explanation:

We are given the following values

x = 4,   6,  8, 12 and corresponding y values are:

y = 3, 4.5, 6, 9

Let us consider two points (4, 6) and (6, 4.5) and try to find out the equation of line.

Equation of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:

[tex]y=mx+c[/tex]

where m is the slope.

(x,y) are the coordinates from where the line passes.

c is the y intercept.

Here,

[tex]x_{1} = 4\\x_{2} = 6\\y_{1} = 3\\y_{2} = 4.5[/tex]

Formula for slope is:

[tex]m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m = \dfrac{4.5-3}{6-4}\\\Rightarrow m = \dfrac{1.5}{2}\\\Rightarrow m = \dfrac{3}{4}[/tex]

Now, the equation of line becomes:

[tex]y=\dfrac{3}{4}x+c[/tex]

Putting the point (4,3) in the above equation to find c:

[tex]3=\dfrac{3}{4}\times 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0[/tex]

So, final equation of given function is:

[tex]y=\dfrac{3}{4}x[/tex]

OR

[tex]4y=3x[/tex]

As per the given options, the point (7, 5.25) satisfies the equation.

So correct answer is [tex](7, 5.25)[/tex].

Answer:

The series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

Step-by-step explanation:

We are given with the following series options below;

a. 3, 5, 7, 9

b. 2, 4, 5, 8

c. 4, 6, 8,10

d. 2, 3, 4, 5

And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].

For this, we will put the values of n in the above expression and then will see which series is obtained as a result.

So, the given expression is ; [tex]X_n=2n+1[/tex]

If we put n = 1, then;

[tex]X_1=(2\times 1)+1[/tex]

[tex]X_1 = 2+1 = 3[/tex]

If we put n = 2, then;

[tex]X_2=(2\times 2)+1[/tex]

[tex]X_2 = 4+1 = 5[/tex]

If we put n = 3, then;

[tex]X_3=(2\times 3)+1[/tex]

[tex]X_3 = 6+1 = 7[/tex]

If we put n = 4, then;

[tex]X_4=(2\times 4)+1[/tex]

[tex]X_4 = 8+1 = 9[/tex]

Hence, the series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

Answer:

Step-by-step explanation:

Least common denominator = a²b²

[tex]\frac{3}{a^{2}}+\frac{2}{ab^{2}}=\frac{3*b^{2}}{a^{2}*b^{2}}+\frac{2*a}{ab^{2}*a}\\\\=\frac{3b^{2}}{a^{2}b^{2}}+\frac{2a}{a^{2}b^{2}}\\\\=\frac{3b^{2}+2a}{a^{2}b^{2}}[/tex]

Answer:

Experimental Study

Step-by-step explanation:

In an experimental study, the researchers involve always produce and intervention (in this case they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10) and study the effects taking measurements.

These studies are usually randomized ie subjects are group by chance.

As opposed to observation studies, where the researchers only measures what was observed, seen or hear without any intervention on their parts.

Answer:

0.007

Step-by-step explanation:

We were told in the above question that a random sample of 51 households is monitored for one year to determine aluminum usage

Step 1

We would have to find the sample standard deviation.

We use the formula = σ/√n

σ = 12.2 pounds

n = number of house holds = 51

= 12.2/√51

Sample Standard deviation = 1.7083417025.

Step 2

We find the z score for when the sample mean is more than 61

z-score formula is z = (x-μ)/σ

where:

x = raw score = 61 pounds

μ = the population mean = 56.8 pounds

σ = the sample standard deviation = 1.7083417025

z = (x-μ)/σ

z = (61 - 56.8)/ 1.7083417025

z = 2.45852

Finding the Probability using the z score table

P(z = 2.45852) = 0.99302

P(x>61) = 1 - P(z = 2.45852) = 0.0069755

≈ 0.007

Therefore,the probability that the sample mean will be more than 61 pounds is 0.007

Answer:

See explanation

Step-by-step explanation:

To determine whether each of these functions is [tex]O(x^2)[/tex], we apply these theorems:

(a)Given the function: f(x)=100x+1000

The highest power of n is 1.

Therefore f(x) is O(x).

Since any O(x) function is always [tex]O(x^2)[/tex], 100x+1000 is [tex]O(x^2)[/tex].

[tex](b) f(x)=100x^ 2 + 1000[/tex]

The highest power of n is 2.

Therefore the function is [tex]O(x^2)[/tex].

Answer:

i think its 2000

Step-by-step explanation:

Answer:

7 + 5(x - 3) = 22

5(x - 3) = 15

x - 3 = 3

x = 6

Answer:

x = 6

Step-by-step explanation:

Step 1: Distribute 5

7 + 5x - 15 = 22

Step 2: Combine like terms

5x - 8 = 22

Step 3: Add 8 to both sides

5x = 30

Step 4: Divide both sides by 5

x = 6