A boy leaves station X on a bearing of 035' to station Y. which is 21km away. He then travels to another station Z on a bearing of 125 degrees . If Z is directly East of X, what is the distance from X to his present position?​

Answer:

3

Step-by-step explanation:

x 1，2，3，4

y-3，-5，-7，-9

[tex]y = - 3 - (x - 1) \times 2[/tex]

The linear function is given by y = 7x - 4

A linear function is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the y intercept

From the table, using the points (1, 3) and (4, 24):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-3=\frac{24-3}{4-1}(x-1)\\\\ y=7x-4[/tex]

The linear function is given by y = 7x - 4.

Find out more on linear function at: https://brainly.com/question/4025726

Answer:

480 gallons.

Step-by-step explanation:

Given that in a mixture of 240 gallons, the ratio of ethanol and gasoline is 3: 1, if the ratio is to be 1: 3, to find the quantity of gasoline that is to be added the following calculation must be performed:

240/4 x 3 = Ethanol

240/4 = Gasoline

180 = Ethanol

60 = Gasoline

0.25 = 180

1 = X

180 / 0.25 = X

720 = X

720 - 180 - 60 = X

480 = X

Therefore, 480 gallons of gasoline must be added if the ratio is to be 1: 3.

Answer: 12

Step-by-step explanation:

The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.

Answer:

[tex]h=\sqrt{16(4)}[/tex]

[tex]h=8[/tex]

[tex]ANSWER:E) 8[/tex]

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

~HOPE IT HELPS

~HAVE A GREAT DAY!!

Answer:

[tex] \frac{67}{30} \: \text{or} \:2 \frac{7}{30} [/tex]

Step-by-step explanation:

5/6 ÷ 1/3 - 2/3 (2/5)

Hope it helps you! ＼(^ᴥ^)／

Answer:

(a)

[tex]Q_1 = 14[/tex]

[tex]Median = 15[/tex]

[tex]Q_3 = 20[/tex]

(b) [tex]IQR = 6[/tex]

Step-by-step explanation:

Given

[tex]14\ 14\ 15\ 26\ 13\ 16\ 21\ 20\ 15\ 13[/tex]

[tex]n = 10[/tex]

Solving (a): Median and the quartiles

Start by sorting the data

[tex]Sorted: 13\ 13\ 14\ 14\ 15\ 15\ 16\ 20\ 21\ 26[/tex]

The median position is:

[tex]Median = \frac{n + 1}{2}[/tex]

[tex]Median = \frac{10 + 1}{2} = \frac{11}{2} = 5.5th[/tex]

This implies that the median is the average of the 5th and the 6th data;

So;

[tex]Median = \frac{15+15}{2} = \frac{30}{2} = 15[/tex]

Split the dataset into two halves to get the quartiles

[tex]Lower: 13\ 13\ 14\ 14\ 15\[/tex]

[tex]Upper: 15\ 16\ 20\ 21\ 26[/tex]

The quartiles are the middle items of each half.

So:

[tex]Lower: 13\ 13\ 14\ 14\ 15\[/tex]

[tex]Q_1 = 14[/tex] ---- 14 is the middle item

[tex]Upper: 15\ 16\ 20\ 21\ 26[/tex]

[tex]Q_3 = 20[/tex] ---- 20 is the middle item

Solving (b): The interquartile range (IQR)

This is calculated as:

[tex]IQR = Q_3 - Q_1[/tex]

[tex]IQR = 20 - 14[/tex]

[tex]IQR = 6[/tex]

Solving (c): Incomplete details

Answer:

A 1/2

Step-by-step explanation:

Ratio of short length to hypotenuse

= cos60

= 1/2

Answer:

x = 16

Step-by-step explanation:

The product of the lengths theorem is a property that can be sued to describe the relationships of the sides between the tangents and secants in a circle. One of these products states the following;

The distance between the point of tangency and its intersection point with the exterior secant squared is equal to the product of the exterior secant times the interior secant.

This essentially means the following equation can be formed;

[tex](AB)^2=(DC)(CB)[/tex]

Substitute,

[tex]12^2=x*9[/tex]

Simplify,

[tex]144=9x[/tex]

Inverse operations,

[tex]\frac{144}{9}=x\\\\16=x[/tex]

Answer:

[tex]\boxed{\sf x=7}[/tex]

Step-by-step explanation:

By Targent-secant theorem...

[tex]\sf 9(x + 9) = {12}^{2} [/tex]

Use the distributive property to multiply 9 by x+9.

[tex]\sf 9x+81= {12}^{2} [/tex]

Now, let calculate 12 to the power of 2 and get 144.

[tex]\sf 9x+81=144[/tex]

Subtract 81 from both sides.

[tex]\sf 9x=63[/tex]

Divide both sides by 9.

[tex] \sf \cfrac{ 9x}{9} = \cfrac{63}{9} [/tex]

[tex]\sf x=7[/tex]

Answer:

8d68d68fu9d6rf0d

c9yd7xpjd

puf68d6rif7

Answer:

2/15

Step-by-step explanation:

(-3/5) (-2/9)

Rewriting

-3/9 * -2/5

-1/3 * -2/5

A negative times a negative is a positive.

2/15

Answer:

See explanation

Step-by-step explanation:

Required

The average

The data whose average is to be calculated are not given.

However, the formula to calculate the average is:

[tex]\bar x = \frac{\sum x}{n}[/tex]

Assume the data is:

[tex]1287\ 1215\ 1221\ 1229[/tex]

This means that the number of schools is 4

So:

[tex]\bar x = \frac{1287+ 1215+ 1221+ 1229}{4}[/tex]

[tex]\bar x = \frac{4952}{4}[/tex]

[tex]\bar x = 1238[/tex]

The average of the assumed data is 1238

Answer:

Olha a foto.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

B. Less than 1

Step-by-step explanation:

You could plug in values of n greater than 1 and see what happens....

Example n=2 gives |(.5+.2i)^2|

Simplifying inside gives |(.5)^2+2(.5)(.2i)+(.2i)^2|

=|.25+.2i+.04i^2|=|.25+.2i-.04|=|.21+.2i|.

Applying the absolute value part gives sqrt(.21^2+.2^2)=sqrt(.0441+.04)=sqrt(.0841)=.29

This value is less than 1.

We should also be able to do the absolute value first then the power.

|.5+.2i|=sqrt(.25+.04)=sqrt(.29)

So |.5+.2i|^2=.29 which is what we got long way around.

Anyways (sqrt(.29))^n where n is greater than 1 will result in a number greater than 0 but less than 1.

Answer:

5 points per post and 2 points per replies

9514 1404 393

Answer:

  ≈ 1000√10∠-129.04464° = -1992 -2456i

Step-by-step explanation:

  3 -i = √(3³+(-1)²)∠arctan(-1/3) ≈ √10∠-18.4349°

Then (3-i)^7 = 10^(7/2)∠(7×-18.4349°) = 1000√10∠-129.04464°

  = 1000√10(cos(-129.04464°) +i·sin(-129.04464°))

  = -1992 -2456i

Answer:

[tex]Pr= 0.00725[/tex]

Step-by-step explanation:

Given

[tex]p = 0.05[/tex] ---- probability that each component fails

[tex]n = 3[/tex]

Required

[tex]P(System\ Overheats)[/tex]

We understand that the system will overheat if at least 2 component fails; Assume the components are: x, y and z

The events that the system will overheat are: xyz', xy'z, x'yz and xyz

Where ' means that the component did not fail, and the probability is 1 - p (i.e. complement rule)

So, we have:

[tex]xyz' \to 0.05 * 0.05 * (1 - 0.05) = 0.002375[/tex]

[tex]xy'z \to 0.05 * (1 - 0.05)* 0.05 = 0.002375[/tex]

[tex]x'yz \to (1 - 0.05)* 0.05 * 0.05 = 0.002375[/tex]

[tex]xyz \to 0.05 * 0.05 * 0.05 =0.000125[/tex]

So, the required probability is:

[tex]Pr= 0.002375 +0.002375 +0.002375 + 0.000125[/tex]

[tex]Pr= 0.00725[/tex]

Hello,

there are 5 differents sums:

16,18,20,22,24.

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

Dim i As Integer, j As Integer, k As Integer, l As Integer, u As Integer, v As Integer, nb As Integer

Dim mat(4, 4) As Integer

nb = 0

For i = 1 To 4

   For j = 1 To 4

       If j <> i Then

           For k = 1 To 4

               If k <> j And k <> i Then

                   l = 10 - k - j - i

                   If l > 0 And l < 5 And l <> i And l <> j And l <> k Then

                       mat(1, 1) = i

                       mat(1, 2) = j

                       mat(1, 3) = k

                       mat(1, 4) = l

                       For u = 2 To 4

                           For v = 1 To 4 - u + 1

                               mat(u, v) = mat(u - 1, v) + mat(u - 1, v + 1)

                           Next v

                       Next u

                       'Call visu(mat())

                       nb = nb + 1

                       Print nb,

                       mat(4, 1)

                   End If

               End If

           Next k

       End If

   Next j

Next i

End

Sub visu (m() As Integer)

   Dim i As Integer, j As Integer

   For i = 1 To 4

       For j = 1 To 4 - i + 1

           Print m(i, j);

       Next j

       Print

   Next i

End Sub

Answer: x>1

Step-by-step explanation:

To solve for x, we want to isolate x.

3x+7>10       [subtract both sides by 7]

3x>3             [divide both sides by 3]

x>1

Therefore, we know that x>1.

Answer:

Step-by-step explanation:

3x + 7 > 10

3x > 10 - 7

3x > 3

x > 1

x ∈ ( 1, ∞ )

Answer:

this is the answer I got! i don't know if it helps, but I hope it does

Answer:

7

Step-by-step explanation:

For simple interest,

I = prt

where I = interest,

p = principal (amount deposited)

r = annual rate of interest

t = time in years

We have r = 2% = 0.02

p = $3,000

I = $420

We need to find t

I = prt

420 = 3000 * 0.02 * t

420 = 60t

t = 420/60

t = 7

Answer: 7 years

Answer:

[tex]E(x)=\$9.118[/tex]

Step-by-step explanation:

From the question we are told that:

Available bills

 [tex]\$5=N0 9\\\\\$10=N0 5[/tex]

 [tex]\$20=N0 3[/tex]

Therefore

Total Bills

 [tex]n=5+9+3[/tex]

 [tex]n=17[/tex]

Probability of selecting each bill

 [tex]For\$5[/tex]

 [tex]P(\$5)=\frac{9}{17}[/tex]

 [tex]For\$10[/tex]

 [tex]P(\$10)=\frac{5}{17}[/tex]

 [tex]For\$20[/tex]

 [tex]P(\$20)=\frac{3}{17}[/tex]

Generally the equation for Expected winning is mathematically given by

 [tex]E(x)=\sum(X)*P(X)[/tex]

 [tex]E(x)=5*\frac{9}{17}+10*\frac{5}{17}+20*\frac{3}{17}[/tex]

 [tex]E(x)=\$9.118[/tex]

40

Step-by-step explanation:

Each number is followed by a number that is half its value, so the sequence goes like

320, 160, 80, 40, 20, 10.

......hope it helps......

Answer:

yes,.to obtain sinx as 1 the angle must be 90degrees

so the answer is correct

but there are more solutions like when the cosine angle is 45 the answer is 1

and when x is 450 still sinx = 1..that is to say sin450= 1

Answer:

Bob had 25 cars

Step-by-step explanation:

10+15=25

[tex] \frac{ - 15}{23} + \frac{30}{ - 46} \\ = \frac{ - 15}{23} + \frac{(2) \times (15)}{(2) \times ( - 23)} \\ = \frac{ - 15}{23} + \frac{15}{ - 23} \\ = \frac{ - 15}{23} - \frac{15}{23} \\ = \frac{ -3 0}{23} \\ = - 1.3[/tex]

Answer:

23 / 400 = 0.0575

Step-by-step explanation:

Given the distribution :

_____shops__ free park. food _: location total

male 88 24 40 21 173

female 110 38 56 23 227

total 198 62 96 44 400​

From the table of the distribution Given, we obtain :

n(Female n location) = 23

n(Total) = 400

Hence, the probability that a female who chose location gets the prize will be ;

n(Female n location) / n(Total) = 23 / 400 = 0.0575

Answer:

9

Step-by-step explanation:

Let the number be X

From the problem we have the following equation:

7x - 17 = 3x + 19

-> 4x = 36

-> x = 9

Answer:

9

Step-by-step explanation:

that is the procedure above