A ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. Twenty minutes later the angle of depression was 6°.

Answer:

[tex]\frac{b+1}{a} , \frac{6}{a}+\frac{b}{4}, a+\frac{1}{4}b, ab-17, \frac{b}{2} +4, 5a-6[/tex]

Step-by-step explanation:
1) When b=8,

[tex]\frac{b}{2}+4=\frac{8}{2}= 4+4= 8[/tex]

2) When a=3,

    5a-6= 5(3)-6

            = 15-6

            = 9

3) When a=3 and b=8,

[tex]\frac{b+1}{a} = \frac{8+1}{3} = \frac{9}{3} = 3[/tex]

4) When a=3 and b=8,

    ab-17= (3)(8)-17

             = 24-17

             = 7

5) When a=3 and b=8,

[tex]a+\frac{1}{4} b= 3+\frac{1}{4} (8)= 3+2=5[/tex]

6) When a=3 and b=8,

[tex]\frac{6}{a}+\frac{b}{4}= \frac{6}{3}+\frac{8}{4}= 2+2= 4[/tex]

The main difference between these exponential properties is that for (a^n)^m=a^(nm) we have the same base, hence we just just multiply the powers, applying the power of power rule. For a^nb^n=(ab)^n, we have different bases, hence the exponent is just a common factor.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

It can be applied if the bases are the same, that is:

(a^n)^m = a^(n x m) = a^(nm).

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to get the equation of any straight line, we simply need two points off of it, let's use those two provided in the picture below.

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{33.7})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{48.7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{48.7}-\stackrel{y1}{33.7}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{5}}} \implies \cfrac{15}{1}\implies 15[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{33.7}=\stackrel{m}{15}(x-\stackrel{x_1}{5}) \\\\\\ y-33.7=15x-75\implies {\Large \begin{array}{llll} y=15x-41.3=R(x) \end{array}}[/tex]

Answer:

-1/2 is the answer of this question

The degrees of freedom for a chi-square goodness-of-fit test are calculated as the number of categories minus 1.

Suppose we wish to determine if an ordinary-looking six-sided die is fair, or balanced, meaning that each face has a probability of 1/6

of arrival on top when the die is tossed. We could toss the die dozens, maybe hundreds, of times and compare the actual number of times each face arrival on top to the scheduled number, which would be 1/6

of the total number of tosses. We would not expect each number to be exactly 1/6 of the total, but it should be close.

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Answer:

all real number

Step-by-step explanation:

domain are the value of x axis. as you can see the the graph goes for ever. there is no limitation. basically the domain of exponential graph are all really number.

The total value of Mr. Liling's shares at the end of 2016 was $1388.50.

The value of a share, also known as the stock price, represents the price per unit of ownership in a company. It is determined by supply and demand for the stock in the stock market and can fluctuate based on a variety of factors such as the company's financial performance, industry trends, and overall market conditions.

At the beginning of 2016, Mr. Liling bought 10 shares of stock in QIZ Software for $198.58 per share, so the total cost was 10 * $198.58 = $1985.80.

In 2016, the stock price of QIZ Software changed by -$59.73, so the value of Mr. Liling's shares at the end of 2016 was $1985.80 - 10 * $59.73 = $1985.80 - $597.30 = $1388.50.

So, the total value of Mr. Liling's shares at the end of 2016 was $1388.50.

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The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

We can find the intersection point between these two lines;

y = 3x - 6

y = -2x + 8

Set these two equations equal to each other.

3x - 6 = -2x + 8

5x - 6 = 8

Add 6 to both sides of the equation.

5x = 14

Divide both sides of the equation by 5.

x = 14/5  

Find the y-value where these points intersect by plugging this x-value back into either equation.

y = 3(14/5) - 6

y = 42/5 - 6

Multiply 6 by (5/5) to get common denominators.

y = 42/5 - 30/5  

Subtract and simplify.

y = 12/5

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

(I) 0 = 3x - 6  

Add 6 both sides of the equation.

6 = 3x

x = 2  

Set the second equation equal to 0.

(II) 0 = -2x + 8

Add 2x to both sides of the equation.

2x = 8

x = 4

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

Formula for the Area of a Triangle:

A = 1/2bh

Substitute 2 for b and 14/5 for h.

A = (1/2) · (2) · (12/5)

Multiply and simplify.

A = 12/5

The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

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Find the area of the region bounded by the line y=3x-6 and line y=-2x+8.

A: the x-axis.

Answer:

Step-by-step explanation:

8.75 cm  length can Nuka weave in 5 minutes.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

they can weave 7 cm of the strip in 4 minutes

so, Nuka weave in 5 minutes = 7/4 *5

                                                = 8.75 cm

Hence, 8.75 cm  length can Nuka weave in 5 minutes.

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The proof that (n+5)^2(n+3)^2 is a multiple of 4 is below

We can prove that (n+5)^2(n+3)^2 is a multiple of 4 by showing that both (n+5)^2 and (n+3)^2 are multiples of 4.

From the question, we can see that the exponents of both factors is 2

When these exponents are added, we have

Sum = 2 + 2

Evaluate the sum

Sum = 4

4 is a multiple of 4

Hence,  (n+5)^2(n+3)^2 is a multiple of 4

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Answer:

40 miles per hours

Step-by-step explanation:

We know

A truck driver drove 350 miles in 8 3/4 hours.

8 3/4 = 35/4 = 8.75

So, the truck driver drove 350 miles in 8.75 hours

What is the speed of the truck in miles per hour?

We take

350 divided by 8.75 = 40 miles per hours

So, the speed of the truck is 40 miles per hour.

Answer:2/5x+2/5y

Step-by-step explanation: Since you are multiplying both terms by 2/5, just distribute and you get that value for both the coeffiencents.

The result of the long division of the polynomial (6x³ - 2x² + 10x -25) ÷ (2x - 2) is   3x²  + 2x + 7 ( - 11 / 2x - 2 ).

A long division polynomial is an algorithm for dividing polynomial by another polynomial of the same or a lower degree.

The quotient of the polynomial is obtained by using long division method as shown below.

                          3x²  + 2x + 7

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

            2x - 2  √ ( 6x³ - 2x² + 10x -25 )

                           - (6x³  - 6x² )

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

                                      4x² + 10x -25

                                  - ( 4x² - 4x )

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

                                             14x - 25

                                          - ( 14x - 14 )

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

                                                      - 11

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It take 4 hours to paint a house working alone.

Betty and karen have been hired to paint the houses in a new development. Working together the women can paint a house in two thirds the time that it takes karen working alone. Betty takes 8 hours to paint a house alone. How long does it take karen to paint a house working alone?

According to the problem, when Betty and Karen work together, they can paint a house in two-thirds the time it takes Karen to paint a house alone, so t * 2/3.

Let k = time it takes Karen to paint the house alone

then

(2/3)(k)(1/k + 1/8) = 1

(2k/3)(1/k + 1/8) = 1

(2k)(1/k + 1/8) = 3

(2 + k/4) = 3

K=4

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2.5% of regular grade gasoline sold for more than $3.71 per gallon.

The empirical rule states that for a normal distribution:

68% of the data will fall within one standard deviation of the mean.

95% of the data will fall within two standard deviations of the mean.

Almost all (99.7%) of the data will fall within three standard deviations of the mean

a) 3.31 and 3.71 are 2 standard deviations below and above the mean respectively.

So,

95.0% of regular grade gasoline sold between $3.31 and $3.71 per gallon.

b) 3.31 and 3.61 are 2 standard deviations below and one standard deviation above the mean respectively.

percentage of regular grade gasoline sold between $3.31 and $3.61 per gallon

=(0.95/2)+(0.68/2)

=0.475+0.34=0.815 or 81.5%

c)2.5% of regular grade gasoline sold for more than $3.71 per gallon.

The complete question is:

The Energy Information Administration Reported That The Mean Retail Price Per Gallon Of Regular Grade Gasoline Was $3.51 . Suppose That The Standard Deviation Was $0.10 And That The Retail Price Per Gallon Has A Bell-Shaped Distribution. (Hint: You Must Use The Empirical Rule For This Problem. ) A. What Percentage Of Regular Grade Gasoline Sold Between

The Energy Information Administration reported that the mean retail price per gallon of regular grade gasoline was $3.51 . Suppose that the standard deviation was $0.10 and that the retail price per gallon has a bell-shaped distribution. (Hint: You must use the empirical rule for this problem. )

a. What percentage of regular grade gasoline sold between $3.31 and $3.71 per gallon (to 1 decimal)?

b. What percentage of regular grade gasoline sold between $3.31 and $3.61 per gallon (to 1 decimal)?

c. What percentage of regular grade gasoline sold for more than $3.71 per gallon (to 1 decimal)?

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The number of men required to finish the house in 5 days is 9 men.

The number of men required to finish the house in 5 days can be found using the following formula.

Number of men = 5 x Number of days / (Number of days - 2)

Substituting the given values:

Number of men = ( 5 x 5 )/ (5 - 2)

Number of men = ( 5 x 5 ) / 3

Number of men = 25 / 3

Number of men = 8.33

Since the number of men has to be a whole number, the answer is 9 men.

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Answer: 9.8

Step-by-step explanation:

Use trigonometry.

Cosθ = adjacent/hypotenuse

Since we know both the angle and the hypotenuse, we just need to rearrange to find the adjacent length.

Cos(35°) = x/12

x = cos(35°) * 12

x = 9.8298...

Rounding to the nearest tenth, we get 9.8 as our final answer.

Answer:

identical

Step-by-step explanation:

23 * 100 = 2.3 * 1000

they are the same

Step-by-step explanation:

There are 6 + 1 + 3 = 10 marbles in total.

Out of these, 6 are yellow, so the fraction of yellow marbles is 6/10 = 3/5.

An equivalent expression  of x² - 8x + 5 is  (x - 4)² - 11

To convert this quadratic expression x² - 8x + 5 into the form (x - a)² - b we will use completing the square method.

Comparing expression  x² - 8x + 5 with ax² + bx + c we get,

a = 1, b = -8 and c = 5

First we find the value of the expression (b/2a)² is:

(b/2a)²

= [-8/(2 × 1)]²

= (-8/2)²

= (-4)²

= 16

Now, we add and subtract the value of the term (b/2a)² in the expression  x² - 8x + 5

So the expression  x² - 8x + 5 becomes,

x² - 8x + 5

= x² - 8x + 5 + 16 - 16        

= x² - 8x  + 16 + 5 - 16       ......(commutative property of addition)

= (x - 4)² - 11                      ......(since (x - 4)² = x² - 8x  + 16)

Therefore, the required expression is:  (x - 4)² - 11

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The probability that the sequence of tosses is HTHT is 1/16, which can also be written as 0.0625 rounded to four decimal places.

The probability of getting a specific sequence of coin tosses, such as "htht", in four tosses of a fair coin can be calculated by finding the probability of getting each individual outcome and multiplying them together. The probability of getting heads in a single fair coin toss is 1/2 and the probability of getting tails is also 1/2.

So, the probability of getting the sequence "HTHT" in four tosses of a fair coin is:

= (1/2) * (1/2) * (1/2) * (1/2)

= 1/16

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If the variance of a distribution is 13.53, the value of its standard deviation is, 3.68.

And, If the standard deviation of a distribution is 3.45, the value of variance is, 11.90

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The variance of a distribution is 13.53,

And, The standard deviation of a distribution is 3.45.

We know that;

⇒ Standard deviation = √ Variance

Now, If the variance of a distribution is 13.53,

The value of its standard deviation is,

⇒ Standard deviation = √ Variance

⇒ Standard deviation = √13.53

⇒ Standard deviation = 3.68

And, If the standard deviation of a distribution is 3.45.

The value of variance is,

⇒ Standard deviation = √ Variance

⇒ 3.45 = √ Variance

⇒ Variance = 3.45²

⇒ Variance = 11.90

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Hi there, here's your answer:

From the question,
Given:

Weight limit for the lift = 1000kg

Mean weight of 10 people = 70kg

Therefore, the total weight of 10 people inside the lift is 70 × 10 = 700kg.

Now, remaining weight that can fit in the lift is 1000 - 700 = 300kg.

Assuming the mean weight of the people who get inside the lift is constant, we find the closest number of people who can get inside the lift to be:

300 ÷ 70 = 4.285
Or
Roughly 4 more people.

Hope it helps!

Answer:

[tex]\frac{43}{15}[/tex]x + 30

Step-by-step explanation:

3[tex]\frac{2}{3}[/tex]x - [tex]\frac{4}{5}[/tex] (x - 3[tex]\frac{3}{4}[/tex])

[tex]\frac{11}{3}[/tex]x - [tex]\frac{4}{5}[/tex] (x - [tex]\frac{15}{4}[/tex])

[tex]\frac{11}{3}[/tex]x - [tex]\frac{4}{5}[/tex] x + [tex]\frac{60}{20}[/tex]

[tex]\frac{11}{3}[/tex]x - [tex]\frac{4}{5}[/tex] x + 30

[tex]\frac{55}{15}[/tex]x - [tex]\frac{12}{15}[/tex] x + 30

[tex]\frac{43}{15}[/tex]x + 30

The probability of being no blue marble in the experiment is given as follows:

P(no blue) = 27/100.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The total number of outcomes for this problem is given as follows:

100.

The desired outcomes are those with only white marbles, which are of:

27.

Hence the probability of being no blue marble in the experiment is given as follows:

P(no blue) = 27/100.

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An expression that calculates how much greater Alphaville's annual budget surplus is than Betaville's for a particular amount of tax revenue is, -3x² + 600x - 10000.

And the value is -$16830010000.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Alphaville's Budget Surplus Model is,

-2x² + 500x.

Betaville's Budget Surplus Model is,

x² - 100x + 10000.

The tax revenue that year in each town is $75,000.

An expression that calculates how much greater Alphaville's annual budget surplus is than Betaville's for a particular amount of tax revenue:

-2x² + 500x - x² + 100x - 10000,

= -3x² + 600x - 10000

Now, x = 75000

Then,

= -$16830010000

Hence, an expression is -3x² + 600x - 10000.

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Answer:

P(≥ 4) = 0.44

Step-by-step explanation:

The experimental probability of landing on a number greater than or equal to 4 can be calculated by adding the frequency of outcomes 4, 5, and 6 and dividing by the total number of trials.

The frequency of outcomes 4, 5, and 6 is 6 + 9 + 7 = 22.

The experimental probability of landing on a number greater than or equal to 4 is 22/50 = 0.44.

So, the answer is B. P(≥ 4) = 0.44.

Answer:

P(≥ 4) = 0.44  

Step-by-step explanation:

I took the test and it was right!

The height of the drop can be increased by stacking tables, and we can then observe the effect on the pennies' trajectory.

To increase the height from which the pennies are dropped, we can stack two tables. To do this, first, place one of the tables on a level surface. Then, move the other table so that it is parallel to the first table, and place it on top. Make sure that the two tables are securely stacked and do not wobble. Then, use a ruler to measure the height of the two tables combined. This will give us the new height from which the pennies will be dropped. After that, drop the pennies from the new height and observe their trajectory. We can then compare the trajectory of the pennies when dropped from the increased height with the trajectory when dropped from the original height. This will allow us to determine the effect of the increased height on the pennies' trajectory.

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The annual interest rate of the savings account is 0.04%

Compound interest refers to the interest added to a loan or deposit. Compound interest is the type of interest that is calculated using both the principal and the interest that has accumulated over the preceding period. In contrast to simple interest, compound interest does not factor in the principal when calculating the interest for a subsequent period.

We have the formula

Amount, A = P [1 + (r/t)]ⁿ

where P = principal, r = rate of interest, t = number of times interest is compounded per year, n = time (in years)

Given:

principal = 2500

Amount =  2937.91

t = 1

n = 4

So, 2937.91 = 2500 [1 + (r/1)]⁴

[tex](1.175)^{(1/4)[/tex] = 1 + r

1.041 = 1 + r

r = 0.04

Thus, the annual interest rate is 0.04% .

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Answer:

  4.1%

Step-by-step explanation:

You want the annually compounded interest rate that results in £2500 growing to £2937.91 in 4 years.

The amount in an account earning compound interest is ...

  A = P(1 +r)^t

where P is the principal invested at rate r for t years.

Solving for r, we find ...

  (A/P)^(1/t) = 1 +r

  r = (A/P)^(1/t) -1 = (2937.91/2500)^(1/4) -1 ≈ 0.0412 ≈ 4.1%

The annual interest rate of the savings account is about 4.1%.

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Answer:

2

Step-by-step explanation:

Start at the bottom of the graph.  It starts at (8,0).  From that point go up 2 and one to the right.  You will be back on the line at the point (9,2)

Slope is your rise over your run.  2/1 = 2