City A is 300 km due east of city B. City C is 200 km on a bearing of 123° from city B. How far is it from C to A?​

Answer:

a)  No, it does not matter whether you roll the die or flip the coin first, as these two events are independent of each other, which means they do not affect each other.

b) Yes.

The likelihood that any outcome will occur will not change, as the events are independent.

c) see attached

d)   12 outcomes  (H = head, T = tail, numbers represent the value of the die)

H 1           T 1

H 2          T 2

H 3          T 3

H 4          T 4

H 5          T 5

H 6          T 6

e)  

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

[tex]\implies \sf P(even)=\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}=\dfrac{3}{6}=\dfrac{1}{2}[/tex]

[tex]\implies \sf P(head)=\dfrac{1}{2}[/tex]

[tex]\implies \sf P(even)\:and\:P(head)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}[/tex]

Answer:

3/2    or   1.5

Step-by-step explanation:

(-3/8) ÷ (-1/4)

Copy dot flip

=(-3/8)* (-4/1)

=12/8

=3/2    or 1.5

Answer:

38.88

Step-by-step explanation:

Convert the problem to an equation using the percentage formula: P% * X = Y.

P is 10%, X is 150, so the equation is 10% * 150 = Y.

Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.

The sum of the infinite geometric sequence 16, 8, 4, 2 is 32

The sum can be represented as follows:

s∞ = a / 1  - r

where

r = common ratio

a = first term

Therefore,

r = 8 / 16 = 1 / 2

a = 16

hence,

s = 16 / 1 - 1 / 2

s = 16 / 1 / 2

s = 16 × 2 / 1

s = 32

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Answer: $86.65

Step-by-step explanation:

First, find how much Justine paid in tax. To do this, first convert 13% to a decimal by dividing by 100. This gets a tax rate of 0.13. Now, multiply the price of the boots by the tax rate. 76.68*0.13 = 9.9684. Round to the nearest cent to get $9.97.

Now, add the amount paid in tax to the price of the boots. 76.68+9.97 = $86.65.

Answer:

mean: $13.50

median: $11

mode: $10

range: $26

hope this helps:)

Answer:

The mean is 13.5, median is 11, mode is 10, and for the range, it's 26

Step-by-step explanation:

For the mean, you add all the numbers up 4+30+10+12+10+20+12+10 = 108. Then you divide by how many terms there are which is 8 and then you get 13.5.

The median is the middle value in a list ordered from smallest to largest. So that is why you get 11.

The mode is the most frequently occurring value on the list and we can tell that 10 is the most occuring in this list.

Finally we have the range. To find the range you subtract the highest amount to the lowest amount. 30 - 4 = 26.

Using the t-distribution, it is found that:

At the null hypothesis, it is tested if the mean GPA of the students is of 3.3, that is:

[tex]H_0: \mu = 3.3[/tex]

At the alternative hypothesis, it is tested if the mean GPA is different than 3.3, hence:

[tex]H_1: \mu \neq 3.3[/tex].

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

The values of the parameters are given as follows:

[tex]\overline{x} = 3.25, \mu = 3.3, s = 0.02, n = 20[/tex]

Hence, the test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{3.25 - 3.3}{\frac{0.02}{\sqrt{20}}}[/tex]

t = -11.18.

We are testing if the mean is different of a value, hence we have a two-tailed test, with 20 - 1 = 19 df and a standard significance level of 0.05, hence, using a t-distribution calculator, the critical value is [tex]t^{\ast} = \pm 2.093[/tex].

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Answer:

2

Step-by-step explanation:

8gallons=16 cup

8x16=128

62+2=64

128÷2=64

Answer:the mean is 90

Step-by-step

you find the sum of the values then divide them by the amount of numbers in the set

Answer:

2 cups

Step-by-step explanation:

Formula: divide the volume value by 16

so its 32 divided by 16

The speed of the raft if the speed of the motorboat in still water is 3 km/h

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

Let the speed of the raft (current) - r

Speed of motorboat - 12 km/h

The distance between villages - is 44 km

Let the time spent by Aniskin  - t

The time the thief was in travel = 2 hr 40 min + t = 2 40/60 + t = 3/8 + t

The distance the thief traveled = 44 - 27 = 17 km

We have the following equations:

r(8/3 + t) = 17

(12 - r)t = 27

Simplify the equations:

r(8/3 + t) = 17 ⇒ rt + 8/3r = 17

(12 - r)t = 27 ⇒ 12t - rt = 27

Add up the equations and solve for r:

rt + 8/3r + 12t - rt = 44

8/3r + 12t = 44

r = 16.5 - 4.5t

Substitute r into the second equation:

(12 - 16.5 + 4.5t)t = 27

4.5t² - 4.5t = 27

9t² - 9t - 54 = 0

Solving we get

t = 3 h

Find r:

r = 16.5 - 4.5*3 = 3 km/h

Therefore the speed of the raft if the speed of the motorboat in still water is 3 km/h

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Answer:

Both of the prism are similar , Then

prism A is 10m and it's surface area is 880m²

Now,

prism B is 3m and it's surface area will be = 264m²

4.5, 4.316, 4.32, 4.312

= 4.500, 4.316, 4.320, 4.312

Look at the thousandths and hundreths place in the decimal section.

Least to greatest = 4.312 < 4.316 < 4.32 < 4.5

Answer:

-7.35

Step-by-step explanation:

7/x = cos(60)

x = 7(cos(60))

x = 7/(-0.95)

x = -7.35

Answer:

y = -1/5x + 2.6

Step-by-step explanation:

Put the equation into slope intercept form:

5x - y = 12

-y = -5x + 12

y = 5x - 12

The slope of a perpendicular line will be the opposite reciprocal.

So, the slope of the new line will be -1/5

Then, plug this slope and the given point into the equation y = mx + b to find b

y = mx + b

3 = -1/5(-2) + b

3 = 0.4 + b

2.6 = b

So, the equation will be y = -1/5x + 2.6

Answer:

7(5-2)+6

Step-by-step explanation:

difference - subtraction

putting the 7 next to it means that it will multiply times that first

Answer:

1 11/24

Step-by-step explanation:

u multiply both numeators and both denominators  for example 1 3/4     5/6 i would first turn 1 3/4 into 7/4 and then multiply

The probability that an international flight leaving the United States is delayed given that the flight is a trnaspacific flight is 0.241

The given parameters are:

P(D) = 0.27

P(P) =0.58

P(D and P) = 0.14

The required probability is then calculated using:

P(D | P) = P(D and P)/P(P)

This gives

P(D | P) = 0.14/0.58

Evaluate

P(D | P) = 0241

Hence, the required probability is 0.241

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A circle is a curve sketched out by a point moving in a plane. For the given equation of a circle, the centre will lie at the coordinate (7,-4), while the radius will be equal to 9 units.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

If a circle O has a radius of r units length and it has got its centre positioned at (h, k) point of the coordinate plane, then, its equation is given as:

(x-h)² + (y-k)² = r²

Given the equation of the circle is (x-7)²+(y+4)²=81. The equation can be  rewritten as,

(x-7)² + [y-(-4)]² = 9²

Hence, For the given equation of a circle, the centre will lie at the coordinate (7,-4), while the radius will be equal to 9 units.

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The solutions to the equations are (1.702,4.7) and (-4.7,-1.7).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The two given equations ( x + 3 ) and ( 13 ( x+5)(x-1) intersects at the ponits (1.702,4.7) and (-4.7,-1.7).

The graph of the above equations is attached with an answer.

Therefore the solutions to the equations are (1.702,4.7) and (-4.7,-1.7).

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The displacement is represented from the starting position to the final position.

Your information is incomplete. Therefore, an overview of displacement will be given. It should be noted that displacement simply means a vector whose length is the shortest distance from the initial position to the final position.

In this case, the displacement will be:

= Final position - Initial position

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Then the two solutions of the quadratic equation are 4/5 and 3.

Here we want to solve the quadratic equation:

(-5x + 4)*(x - 3) = 0

The two solutions are the values of x for which each parenthesis becomes equal to zero, so the two solutions are given by:

-5x + 4 = 0

x - 3 = 0

If we solve these two equations we get:

x = -4/-5 = 4/5

x = 3

Then the two solutions are 4/5 and 3.

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Answer:

∠ e = 20°

Step-by-step explanation:

you should have also subtracted 2e from the 360

since UV is a straight line, the angles lying on it sum to 180° , that is

90° + e + 70° = 180°

e + 160° = 180° ( subtract 160° from both sides )

e = 20°

Answer: 23

Step-by-step explanation:

A mathematical symbol, or combination of symbols, representing a value, or relation. Example:  2+2=4 .

Answer:

A

Step-by-step explanation: