A ship's destination is 30 miles north and 12 miles east. At what angle should it head to go straight to its destination?
a) 22°east of north b) 24°east of north
c) 31°east of north d) 66°east of north

Answer:

Theoretical probability is what is expected and experimental probability is the answer.

Step-by-step explanation:

Theoretical probability is what you expected the answer to be. In reality the experimental probability is the actual answer.

Answer:

Step-by-step explanation:

5) Diameter  of the circle = 2 * 11.5 = 23 in

6) Radius of the circle = 11.5 in

7) Circumference = πd = 3.142 * 23 = 72.26 in

8) Area = πr² = 3.142 * 11.5 *11.5 = 415.48 in²

Answer:sadwer

Step-by-step explanation:

To find the length of RT using similarity, set up a proportion using the corresponding sides of similar triangles ABC and RST, and solve for RT using the given lengths of AB, AC, and RS.

To find the length of RT using similarity, we can make use of the concept of similar triangles. Similar triangles have corresponding angles that are equal, and their corresponding sides are proportional.

Here's the reasoning to find the length of RT:

Identify similar triangles: Look for two triangles within the given information that have corresponding angles that are equal. Let's say we have triangle ABC and triangle RST.

Determine the corresponding sides: Find the sides of triangle ABC that correspond to side RT in triangle RST. Let's say side AB corresponds to RT.

Set up a proportion: Since the triangles are similar, we can set up a proportion using the corresponding sides. The proportion will involve the lengths of the corresponding sides.

For example, if AB corresponds to RT, we can write the proportion as:

AB / RT = AC / RS

Here, AB and AC are the corresponding sides of triangle ABC, and RT and RS are the corresponding sides of triangle RST.

Solve the proportion: Substitute the known values into the proportion and solve for the unknown value, which is RT in this case.

If the lengths of AB and AC are known, and RS is known, we can rearrange the proportion to solve for RT:

RT = (AB * RS) / AC

By applying the concept of similarity and setting up a proportion using the corresponding sides of similar triangles, we can find the length of RT.

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Answer:

For one I think the answer is 14 and my brothers name is ethan!

Step-by-step explanation:

The length of minor arc CD is \(\( \frac{5\pi}{3} \)\) units.

1. Let's start by finding the measure of angles x and y. We know that the area of the circle is \(\(81\pi\)\), and since the area of a circle is given by the formula \(\(A = \pi r^2\\)), we can equate it to find the value of \(\(r\). So, \(81\pi = \pi r^2\).\)

  Solving this equation, we get \(\(r^2 = 81\)\), which gives us \(\(r = 9\)\).

2. Since points A, B, C, and D are on the circle, we can consider the angles formed by the lines connecting these points to the center of the circle.

3. Let's assume that the measure of angle x is \(\(a\)\) radians. As per the given information, the measure of angle y is \(\( \frac{5\pi}{9} \)\) radians greater than angle x. So, the measure of angle y is \(\(a + \frac{5\pi}{9}\)\) radians.

4. Since angles x and y are formed by lines from the center of the circle, the sum of their measures should be equal to \(\(2\pi\)\) radians. So we can write the equation \(\(a + (a + \frac{5\pi}{9}) = 2\pi\).\)

5. Simplifying the equation, we get \(\(2a + \frac{5\pi}{9} = 2\pi\).\)

6. Solving for \(\(a\)\), we find \(\(a = \frac{4\pi}{9}\).\)

7. Now that we have the value of angle x, we can find the measure of angle z. Again, since the sum of angles formed by lines from the center of the circle is \(\(2\pi\)\), we can write the equation \(\(a + (a + \frac{5\pi}{9}) + z = 2\pi\)\).

8. Substituting the known values, we have \(\( \frac{4\pi}{9} + (\frac{4\pi}{9} + \frac{5\pi}{9}) + z = 2\pi\)\).

9. Simplifying the equation, we get \(\( \frac{13\pi}{9} + z = 2\pi\)\).

10. Solving for \(\(z\)\), we find \(\(z = \frac{5\pi}{9}\)\).

11. Angle z represents the measure of the central angle that corresponds to minor arc CD.

12. The length of a minor arc in a circle is given by the formula \(\(s = r\theta\)\), where \(\(r\)\) is the radius of the circle and \(\(\theta\)\) is the central angle in radians.

13. Substituting the known values, we have \(\(s = 9 \cdot \frac{5\pi}{9} = \frac{5\pi}{3}\)\).

14. Therefore, the length of minor arc CD is \(\( \frac{5\pi}{3} \)\) units.

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Answer:

Elena's points = 14

Kiran's points = 23

Step-by-step explanation:

Let p = Elena's points

p + 9 = Kiran's points

2p = p + 9 + 5

2p = p + 14

p = 14 = Elena's points

     14 + 9 = 23 = Kiran's points

If Kiran scores 5 more points, he would have 28 points which is twice Elena's 14 points  

Using the slope formula, it is found that the value of j is 12.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line. The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given;

A line with a slope of -1/10 passes through the points (-2,6) and (j,5).

Now,

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

-1/10= 5-6/j+2

-1/10= -1/j+2

10=j+2

j=12

Therefore, by the given slope j will be 12.

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The expression that evaluates to true if and only if the units digit of an integer variable x is less than 8 is :x % 10 < 8 where % is the modulo operator that gives the remainder of x divided by 10. This expression works by extracting the units digit of x using the modulo operator and then checking if it is less than 8. If it is, the expression evaluates to true.

To evaluate the truth value of an expression, we need to first understand the conditions under which it would be true and the conditions under which it would be false. The expression in question is evaluating the units digit of an integer variable x, so we need to consider the possible values that the units digit can take.Let's start by considering the values that would make the expression true. We are told that the units digit of x must be less than 8. This means that the units digit can take on any value from 0 to 7. So if the units digit of x is any of these values (0, 1, 2, 3, 4, 5, 6, or 7), then the expression would be true.Now let's consider the values that would make the expression false. The expression only evaluates to true if the units digit is less than 8, so any value of the units digit that is greater than or equal to 8 would make the expression false. This means that if the units digit of x is 8 or 9, the expression would be false.

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The angle theta between the vectors is found by taking the inverse cosine of the dot product divided by the product of the magnitudes.

First, we calculate the dot product of u and v: (u, v) = (5 * 4) + (-3 * 0) = 20.

Next, we find the magnitudes of u and v:

||u|| = sqrt((5^2) + (-3^2)) = sqrt(34)

||v|| = sqrt((4^2) + 0^2) = 4

Now, we can use the dot product formula to find the angle theta:

cos(theta) = (u, v) / (||u|| * ||v||)

cos(theta) = 20 / (sqrt(34) * 4)

To find the angle theta, we take the inverse cosine of this value:

theta = arccos(20 / (sqrt(34) * 4))

Evaluating this expression, we find the angle theta to be approximately 0.40 radians or 22.91 degrees (rounded to two decimal places).

In conclusion, the angle between vectors u and v is approximately 0.40 radians or 22.91 degrees. The calculations involve finding the dot product of the vectors, calculating their magnitudes, and using the dot product formula to determine the angle.

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Answer:

70 degrees

Step-by-step explanation:

since an isosceles triangle is symmetrical, i cut the triangle in half (vertically) so that it became a right triangle. so the angle sides are now 20 degrees at the top, 90 degrees (right angle, where it was cut), and x degrees. 20 + 90 + x = 180 degrees (total amount of degrees in a right triangle) x = 70 degrees.

hope this helps!

Answer:

test score of new student = 43

Step-by-step explanation:

28 x 72 = 2016 (total points class scored)

29 x 71 = 2059 (total points class scored after student joined)

2059 - 2016 = 43

The test score of the student who joined the class is 43.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The mean test score of 28 students is 72.

A student joins the class and the mean becomes 71.

We have to find the test score of the student who joined the class.

28 x 72 = 2016

29 x 71 = 2059 (total points class scored after student joined)

The difference between 2016 and 2059 is the test score of new student.

2059 - 2016 = 43

Hence, the test score of the student who joined the class is 43.

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1. 53

2. can you  explain more it would really help more

Nature tends to repeat itself, and that means periodic phenomenon is found in many places. One example would be a heart beating. It repeats itself over and over to pump blood throughout the body. The period of the heartbeat varies, so it's not going to be one specific number.

One online source I found states "It beats or contracts about 70 times per minute". So that would make the period 60/70 = 0.86 seconds approximately. Every 0.86 seconds or so, the heart completes a full cycle. This is when the person is at rest and not doing any strenuous physical activity (in which case, the period would be much shorter).

Another biological example would be the act of breathing. This is also dependent on if the person is at rest or if they're doing some physical activity such as jogging.

As for an example that's outside the personal element, you could go for something like the motion of the tides. These periodic events are due to the position of the moon, which is also a periodic phenomenon. More broadly, the motion of the planets overall is periodic. However, there may be slight changes here and there as time goes on due to imperfections.

Periodic phenomena has to do with an event that repeats itself.

The term periodic phenomena has to do with an event that repeats itself. This repetition must follow a well defined pattern and the time in between the occurrence of the phenomena is called the period.

Two common examples of periodic periodic phenomenon are;

1) Day and light

2) The dropping of water from a closing tap.

The former is quite popular and the period of the phenomenon is 24 hours. In the later case, the period may range a little above five seconds or below.

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Answer:

x = 87

Step-by-step explanation:

the ratio SR / RV is equal the ratio ST / TU (both ratios are equal to 1), and the angle in the vertex S is the same for both triangles SUV and STR, so we can affirm that these triangles are similar (case S-A-S).

Then, we have that the ratio SR / SV is the same as RT / UV:

SR / SV = RT / UV = 1 / 2

RT * 2 = UV

2*(x - 37) = x + 13

2x - 74 = x + 13

x = 87

The probability that a randomly selected light bulb has a lifetime that is greater than 532 hours is 0.10027

From the question, we have the following parameters that can be used in our computation:

Normal distribution, where, we have

Mean = 500

Standard deviation = 25

So, the z-score is

z = (x - mean)/SD

This gives

z = (532 - 500)/25

z = 1.28

So, the probability is

P = P(z > 1.28)

Using the table of z scores, we have

P = 0.10027

Hence, the probability is 0.10027

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Answer:

X= 12

Step-by-step explanation:

36/5x =3/5(cross multiplication)

180=15x

divide by 15 both sides

X = 12

Answer:

each friend gets 3 stickers

Step-by-step explanation:

9÷3=3

The annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily is approximately 64.04%.

To determine the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (6.63%)
n = the number of times interest is compounded per year (365 for daily compounding)
t = the number of years (8)
Plugging in the values, we have:
A = 1200(1 + 0.0663/365)^(365*8)
Calculating this, we get A ≈ $1,968.49.
To find the annual percentage yield, we need to find the interest earned:
Interest = A - P = $1,968.49 - $1200 = $768.49
Now, we can find the annual percentage yield using the formula:
Annual percentage yield = (Interest / P) * 100
Plugging in the values, we have:
Annual percentage yield ≈ ($768.49 / $1200) * 100 ≈ 64.04%
Therefore, the annual percentage yield, or the effective interest rate, for $1200 invested at 6.63% over 8 years compounded daily is approximately 64.04%.

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Answer

2.0909090909090909090909090909090909090...

Step-by-step explanation

Answer:

-7

Step-by-step explanation:

3=-3x-18

3x=-18-3

3x=-21

x=-7

Answer: x = -.63, -2.37

Step-by-step explanation:

x=−32±3–√2

x=−0.633975

x=−2.36603

Find the Solution for

2x2+6x+3=0

using the Quadratic Formula where

a = 2, b = 6, and c = 3

x=−b±b2−4ac/√2a

x=−6±62−4(2)(3)/√2(2)

x=−6±36−24/√4

x=−6±12−−√4

The discriminant b2−4ac>0

so, there are two real roots.

Simplify the Radical:

x=−6±23–√4

x=−64±23–√4

Simplify fractions and/or signs:

x=−32±3–√2

which becomes

x=−0.633975

x=−2.36603

If h(x) = 5 4f(x) , where f(1) = 5 and f '(1) = 4, then h'(1) = 20.

To find h'(1), we need to use the chain rule of differentiation, which states that if h(x) = f(g(x)), then h'(x) = f'(g(x)) * g'(x).

In this case, we have h(x) = 5/4 * f(x), where f(1) = 5 and f'(1) = 4. Therefore, g(x) = x, f(x) = 5, and h(x) = 5/4 * 5 = 6.25.

To find h'(1), we need to evaluate f'(g(1)) and g'(1), then multiply them together. Since g(x) = x, we have g'(1) = 1.

Since f'(x) = 4, we have f'(g(1)) = f'(1) = 4. Therefore, h'(1) = f'(g(1)) * g'(1) = 4 * 1 = 4. However, we are looking for h'(1), so we need to multiply this by the coefficient of f(x), which is 5/4. Therefore, h'(1) = 5/4 * 4 * 1 = 20.

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Answer: I do not understand

Step-by-step explanation:

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\(y = {x}^{2} - x - 20\)

\(y = (x - 5)(x + 4)\)

To find the zeroes , Just need to put 0 instead of y .

\(0 = (x - 5)(x + 4)\)

\((x - 5)(x + 4) = 0\)

_________________________________

Hint :

\(a \times b = 0\)

\(a = 0 \: \: \: or \: \: \: b = 0\)

_________________________________

\(x - 5 = 0\)

Add sides 5

\(x - 5 + 5 = 0 + 5\)

\(x = 5\)

Or

\(x + 4 = 0\)

Subtract sides 4

\(x + 4 - 4 = 0 - 4\)

\(x = - 4\)

Thus the zeroes are :

( - 4 , 0 ) and ( 5 , 0 ) .

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Answer:

add all the sides that you have and subtract it from 180

Step-by-step explanation:

378.5 cm is equal to 3785 mm. There are 10 mm in a centimetres , so to convert cm to mm, you need to multiply the number of cm by 10. So, 3785 = 378.5 x 10.

To convert from centimetres to millimetres, we need to multiply the number of centimetres by 10. This is because 1 centimetre is equal to 10 millimetres. Therefore, if we want to convert 378.5 centimetres to millimetres, we need to take 378.5 and multiply it by 10.

When we multiply 378.5 by 10, we get 3785. Therefore, 378.5 centimetres is equal to 3785 millimetres. This is because 10 millimetres makes up 1 centimetre, so to convert from one unit to the other, we need to multiply the number of centimetres by 10.

To summarise, 378.5 centimetres is equal to 3785 millimetres. This is because 1 centimetre is equal to 10 millimetres, so when converting from one unit to the other, we need to multiply the number of centimetres by 10.

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Answer:

C ) 18 hope this helps !!!

Answer:

C. 18

Step-by-step explanation:

If you multiply 30%, or .3 by 60, you get 18.