From the top of a cliff, the angle of depression of a boat on the sea is 22°. If the height of the cliff above sea level is 40 m, calculate, correct to two significant figures, the horizontal distance of the boat from the bottom of the cliff.​

A normally distributed data set has a mean of 0 and a standard deviation of 2. The closest to the percent of values between -4.0 and 2.0 would be 84%.

According to the empirical rule, also known as the 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95%, and 99.7% of the values lies within one, two, or three standard deviations of the mean of the distribution.

[tex]P(\mu - \sigma < X < \mu + \sigma) \approx 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) \approx 99.7\%[/tex]

A normally distributed data set has a mean of 0 and a standard deviation of 2.

[tex]Z=(x-\mu)/\sigma[/tex]

[tex]P(x=-0.4)\\\\z=(-0.4-0)/2\\\\= -0.2\\\\P(x=2)\\z=(2-0)/2\\\\=1[/tex]

[tex]P(-0.4 < x < 2)=p(-0.2 < z < 1)=p(-0.2 < z < 0)+p(0 < z < 1)[/tex]……….(by symmetry)

=.49865+.3413

.83995…….(by (http://83995…….by) table value)

=.8400 × 100

=84%

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Answer:

B. Multiply the top equation by-3 and the bottom equation by 2.

Step-by-step explanation:

-3(4x-2y=7)

2(3x-3y=15)

-12x + 6y= -21

6x  - 6y = 30                  

6y and -6y both cancel each other out which gives us 0 when -3 is multiplied by the top and the bottom is multiplied by 2, which gives us the answer B.

Answer:

mean: 106900

median: 8500

mode: 7,000, 8,000, and 11,000

Step-by-step explanation:

To calculate mean, add them all together and divide the number of how many numbers it has. For median make out the sequence from small to large. For this one is 5,000, 7, 000, 7,000, 8,000, 8,000, 9,000, 10,000, 11,000, 11,000, 1,000,000. The middle is between 8,000 and 9,000 so find it's middle number. The mode is the number that appears the most. In this case 7,000, 8000, 11,000 all appeared twice so they are the mode.

Answer:

100

Step-by-step explanation:

She wants to average 85, so adding ALL three of her scores, divided by 3 needs to equal 85.

(75 + 80 + x)/3 = 85

Times by 3.

75 + 80 + x = 255

155 + x = 255

subtract 155.

x = 100

She needs 100 on the third test.

Answer:

120 degrees.

Step-by-step explanation:

360 * 1/3 = 120

Answer:

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

Answer:

Shade 6 bars.

Step-by-step explanation:

You are asked to shade 2/3 of the strip. It is given that the strip has 9 equal parts. Multiply the number and fraction together:

[tex]9 * \frac{2}{3} = \frac{9}{1} * \frac{2}{3} = \frac{9 * 2}{1 * 3} = \frac{18}{3} = 6[/tex]

You will shade 6 of the 9 bars given.

~

Answer:

2,3,7 are the prime factorization of number of 252

Hi Student!

Prime factorization is the process of stripping down a number to it's basic elements.  We take a number and bring it down the most we can.  For example we take 4 and make it 2 x 2.  In this case we are given a number of 252 so we can began by dividing by 2.

[tex]252 / 2[/tex]

[tex]126[/tex]

Looking at the numbers that we have now, 126 x 2, we can see that 126 can still be divisible by another 2 so lets do that again.

[tex]126 / 2[/tex]

[tex]63[/tex]

Now, looking at the numbers that we have, 63 x 2 x 2, we see that we can no longer divide it by a 2 because 63 is not divisible by 2.  However, we can divide 3 away from the number so lets do that.

[tex]63 / 3[/tex]

[tex]21[/tex]

Once again, looking at the numbers that we have, 21 x 3 x 2 x 2, we see that we can once again divide a 3 away from our first number so lets do that again.

[tex]21 / 3[/tex]

[tex]7[/tex]

Finally, we have come down to the last line where our final elements are 7 x 3 x 3 x 2 x 2.  This is our prime factorization of the number 252 and this is where we can conclude our solution seeking.

Answer:

Step-by-step explanation:

Comment

(Fans who received a baseball) = 2500

Total number of seats in Yankee Stadium = 50086

P(those who got a baseball) = 2500 / 50086

Answer P(Those who got a baseball) = 0.04991 rounded.

The reason that best supports statement 5 is: B. multiplication property of equality.

When you multiply both sides of an equation by the same quantity, you have applied the multiplication property of equality.

In statement 5, both sides of the equation was multiplied by 2. Therefore, the best reason is: B. Multiplication Property of Equality.

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Answer:

55

Step-by-step explanation:

Answer:

  x = 20

Step-by-step explanation:

The problem tells you the relationship between time, distance, and speed. Use the given relations to find the total journey time.

__

  total time = Journey A time + Journey B time

  total time = (distance A)/(speed A) + (distance B)/(speed B)

  total time = 15/x +6/(x+4) = 1 . . . . . using the given values

Multiplying by x(x+4) we have ...

  15(x +4) +6(x) = (x)(x +4)

  21x +60 = x² +4x

  x² -17x -60 = 0 . . . . . rearrange to standard form

  (x -20)(x +3) = 0 . . . . factor the equation

  x = 20  or  x = -3 . . . values of x that satisfy the equation

We know the speed must be positive, so x = -3 is an extraneous solution.

The value of x is 20 (km/h).

The statement that is true about the slope of the ramps is: A. Slope of ramp A = slope of ramp B.

Slope = gradient = rise / run = vertical distance / horizontal distance.

Slope of the side view of ramp A = rise / run = 20 / 30 = 2/3.

Slope of  the side view of ramp B = rise / run = 14 / 21 = 2/3.

The slope of A = slope of B = 2/3

The statement that is true of the slopes of both ramps is therefore: A. Slope of ramp A = slope of ramp B.

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Answer:

12

Step-by-step explanation:

Split into 2 shapes, the to find the area of the triangle you multiply base×height divided by 2.

4×3=12

12/2=6

after that find the area of the rectangle

2×3=6

add the area's together

6+6=12

Answer:

The answer is below.

Step-by-step explanation:

Elk: Total elk is 225

Mountain Goat: Total Goat is 164

Deer: Total Deer is 105

Moose: Total Moose is 86

I hope this will help you a lot..

Answer:

(30x⁴+36x²y⁴)+(36x⁴y²+30xy⁴).

Step-by-step explanation:

x⁶+3x⁴y⁴+xy⁶

1) df/dx=6x⁵+12x³y⁴+y⁶; d²f/dx²=30x⁴+36x²y⁴;

d²f/(dxdy)=48x³y³+6y⁵ (note, d²f/(dxdy)=d²f/(dydx) !!);

df/dy=12x⁴y³+6xy⁵; d²f/dy²=36x⁴y²+30xy⁴;

2) finally

(30x⁴+36x²y⁴)+(36x⁴y²+30xy⁴).

Answer:

x = 3

Step-by-step explanation:

The pattern is that every other number increases by 1, while the next decreases by 2

1. 17,18,19,20

2. 9,7,5,x

5-2 =3

3 is the answer.

Solutions:

Odd Terms: 17, 18, 19, 20

Find the common difference.

d = a₂ - a₁

d = 18 - 17

d = 1

Thus, for every odd term, the next terms are derived by adding 1.

Even Terms: 9, 7, 5, x

Find the common difference.

d = a₂ - a₁

d= 7 - 9

d = -2

Find x.

x = 5 + d

x = 5 + (-2)

x = 5 - 2

x = 3

Therefore, x = 3.

In an arithmetic sequence, a term is obtained by adding a constant number to the preceding term. A sequence whose succeeding terms are obtained by adding a constant. Constant is called the common difference. Formula is a_n = a₁ + d(n - 1). The common difference is obtained by subtracting the first term from the second term.  

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Answer:

0.03%

Step-by-step explanation:

[tex]\frac{11}{150}(\frac{10}{149})(\frac{9}{148})[/tex]

≈ 0.03%

Using the given functions, the value of f(3) is 155

From the question, we are to determine the value of f(3) using the given function.

The given function is

f(n) = 5f(n-1) + 5

To determine the value of f(3),

First, we will determine the value of f(2)

From the given function

f(n) = 5f(n-1) + 5

We can find f(2) as shown below

f(2) = 5f(2-1) + 5

f(2) = 5f(1) + 5

From the given information,

f(1) = 5

∴ f(2) = 5(5) + 5

f(2) = 25 + 5

f(2) = 30

Now, we can determine f(3)

Also, from the given function

f(n) = 5f(n-1) + 5

Then,

f(3) = 5f(3-1) + 5

f(3) = 5f(2) + 5

Substituting the value of f(2) into the equation, we get

f(3) = 5(30) + 5

f(3) = 150 + 5

f(3) = 155

Hence, the value of f(3) is 155

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Answer:

In Mathematics, the numbers can be classified into different types, namely real numbers, natural numbers, whole numbers, rational numbers, and so on. Decimal numbers are among them

Types of Decimal Numbers

Decimal Numbers may be of different kinds, namely

Recurring Decimal Numbers (Repeating or Non-Terminating Decimals)

Example-

3.125125 (Finite)

3.121212121212….. (Infinite)

Non-Recurring Decimal Numbers (Non Repeating or Terminating Decimals):

Example:

3.2376 (Finite)

3.137654….(Infinite)

Decimal Fraction- It represents the fraction whose denominator in powers of ten.

Example:

81.75 = 8175/100

32.425 = 32425/1000

Converting the Decimal Number into Decimal Fraction:

For the decimal point place “1” in the denominator and remove the decimal point.

“1” is followed by a number of zeros equal to the number of digits following the decimal point.

For Example:

8 1 . 7 5

↓ ↓ ↓

1 0 0

81.75 = 8175/100

8 represents the power of 101 that is the tenths position.

1 represents the power of 100 that is the units position.

7 represents the power of 10-1 that is the one-tenths position.

5 represents the power of 10-2 that is the one-hundredths position.

So that is how each digit is represented by a particular power of 10 in the decimal number.

A ratio shows us the number of times a number contains another number. The number of students the cafeteria should expect to buy chicken is 260.

A ratio shows us the number of times a number contains another number.

The ratio of the number of students to the number of total students can be written as,

Ratio = (Number of students)/(Number of total students)

Ratio = 52/(52+26+30+48+44) = 52/200

Now, the same ratio is applicable to 1000 students, therefore, the ratio will be,

Number of students who prefer burgers= 1000 × (52/200) = 260

Hence, the number of students the cafeteria should expect to buy chicken is 260.

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Reason:

The domain is the set of allowed x inputs.

The graph shows an open hole at x = 7, meaning that 7 itself isn't part of the domain. But any value smaller than this will be part of the domain. So that's why we go for x < 7.

The value x = -1 is allowed since we have a closed endpoint for one of the pieces here.

The arrow pointing to the left indicates that piece goes on forever in that direction.

Answer:

x < 7

Step-by-step explanation:

The domain of the function is less than 7 as indicated by the open dot. (a closed dot indicates ≥ or ≤)

At x = -1, it is part of the domain because there is at least one closed dot indicating it is part of the domain.

The domain of the function is :

Answer:

See below ~

Step-by-step explanation:

Part A

Part B

Answer:

See below

Step-by-step explanation:

The mean is simply adding up each data value and dividing your result by the number of data values:

[tex]\text{Mean}=\frac{6+8+7+5+10+6+9+8+4}{9}=\frac{63}{9}=7[/tex]

The standard deviation is calculated through finding the sum of the squared differences between the mean and each data point, and dividing that result by the number of data values, which we then take the square root of:

[tex]\text{Standard Deviation}=\sqrt{\frac{(6-7)^2+(8-7)^2+(7-7)^3+(5-7)^2+(10-7)^2+(6-7)^2+(9-7)^2+(8-7)^2+(4-7)^2}{9}}=\sqrt{\frac{10}{3}}\approx1.8257[/tex]

What this value means is that each data point is spread about 1.8257 apart from the mean. Standard deviation describes how dispersed the data is in relation to the mean.

Answer:

2√10

Step-by-step explanation:

√40=√4 x 10

2√10

(a) f(0) in the given function in mod 5 is 2.

(b) f(1) in the given function in mod 5 is 2.

(c) f(2) in the given function in mod 5 is 3.

(d) f(3) in the given function in mod 5 is 1.

(e) f(4) in the given function in mod 5 is 2.

The given function is defined as follows;

f(x) = (x³ + 4x + 2) mod 5

f(0) = (0 + 0 +2) = 2 in mod 5 (0 remainder 2) = 2

f(1) = (1 + 4 + 2) = 7 in mod 5  (1 remainder 2) = 2

f(2) = (2³ + 4(2) + 2) = 18 in mod 5 (3 remainder 3) = 3

f(3) = (3³ + 4(3) + 2) = 41 in mod 5 (8 remainder 1) = 1

f(4) = (4³ + 4(4) + 2) = 82 in mod 5 (16 remainder 2) = 2

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Answer: Answer:

The probability that a given student is a graduate, given that he or she is on financial aid, is 30.8%.

Step-by-step explanation:

To determine what is the probability that a given student is a graduate, given that he or she is on financial aid, the following calculation must be performed:

6101 = 100

1879 = X

1879 x 100/6101 = X

187,900 / 6101 = X

30,798 = X

Therefore, the probability that a given student is a graduate, given that he or she is on financial aid, is 30.8%.

Step-by-step explanation:

Answer:

A. 198 gift certificates.

Step-by-step explanation:

The probability of winning on a single spin = 3/8.

Number of expected winners

= 528 * 3/8

= 66 * 3

= 198.

Answer:

10 = x

Step-by-step explanation:

I believe <B = <E.

<B = 50 = <E = 5x

50 = 5x

10 = x

Answer:

40/8

Step-by-step explanation:

last one i think