use the data below make a frequency table take a picture of you frequency table and attach it to your answer marathon time

So the product of (2-x) and (1-x) is equal to x^2 - 3x + 2

Given: A surveyor standing 50 feet from the base of a large tree measures the angle of elevation to the top of the tree as 75.8 degrees.

Required: To determine how accurately the angle must be measured if the percent error in estimating the tree's height is less than 5%.

Explanation: To estimate the angle, we will use the trigonometric ratio

where h is the tree's height, and x is the angle of elevation to the top of the tree.

Hence we get

Now differentiating equation 1, we get

We can write the above equation as:

Also, it is given that the error in estimating the tree's height is less than 5%.

So

Also, we need to convert the angle x in radians:

Putting these values in equation (2) gives:

Solving the above equation gives:

Let

Then,

Final Answer:

The domain is all the values of the independent variable (in this case, x) for which the function is defined.

In this case, as it is indicated with the arrows in both ends, the function continues for greater and smaller values of x.

As there is no indication that for some value or interval of x the function is not defined (a discontinuity, for example), then it is assumed that the function domain is all the real values.

Example function:

We have the function y=1/(x-2)

We can look if there is some value of x that makes the function not defined.

The only value of x where f(x) is not defined is x=2. When x approximates to 2, the value of the function gets bigger or smaller whether we are approaching from the right or from the left.

Then, the function is not defined for x=2. So, the domain of f(x) is all the real numbers different from x=2.

The domain is, by default, all the real numbers, but we have to exclude all the values of x (or intervals, in some cases like the square roots) for which f(x) is not defined.

hello

to solve this question we need to know or understand the standard form of a linear equation

the standard form of a linear equation is given as

from the options given in the question, only option D does not corresponds with the standard form of a linear equation

we are given a table of inputs and ouputs of a function. We notice that each output is obtained by multiplying the input by -4:

Therefore, the right answer is A.

The given data plot will look thus:

a) Building a model using just the 1999 and 2019 years:

b) The cost of insurance in 2030

c) When do we expect the cost to reach $12,000

The most appropriate choice for fraction will be given by

6 pieces of wood are cut by the carpenter

What is a fraction?

Suppose there is a collection of objects and some part of the objects are taken from the collection. The part which has been taken is called fraction. In other words, part of a whole is called fraction.

The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.

Total length of wood = [tex]16\frac{1}{2}[/tex] m

                                   = [tex]\frac{33}{2}[/tex] m

Length of one piece of a wood = [tex]2\frac{3}{4}[/tex] m = [tex]\frac{11}{4}[/tex]

Number of pieces of wood cut by carpenter =  [tex]\frac{33}{2}[/tex] ÷ [tex]\frac{11}{4}[/tex]

                                                                        = [tex]\frac{33}{2}[/tex] [tex]\times \frac{4}{11}[/tex]

                                                                       = 6

6 pieces of wood are cut by the carpenter

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The value of the lesser integer is 5.

According to the question,

We have the following information:

When an integer is subtracted from 4 times the next consecutive odd integer, the difference is 23.

Let's take the lesser integer to be x.

So, the next consecutive odd integer is (x+2).

Now, we have:

4(x+2)-x = 23

4x+8-x = 23

3x+8 =23

3x = 23-8

3x = 15

x = 15/3

(3 was in multiplication on the left hand side. So, it is in the division on the right hand side.)

x = 5

Hence, the lesser integer in the given situation is 5.

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The equation of a line in Slope-Intercept form is:

Where "m" is the slope and "b" is the y-intercept.

Solve for "y" from the equation given in the exercise in order to write it in Slope-Intercept form:

You can notice that the equation has this form:

Where "b" is the y-intercept.

Then, it's a horizontal line, which means that its slope is:

Since it is a horizontal line, the lines perpendicular to that line is a vertical line, whose slope is undefined and whose equation is:

Where "k" is the x-intercept.

Knowing that the x-coordinate of any point on a vertical line is always the same, and knowing that this line passes through this point:

You can determine that the equation of the line is:

EXPLANATION

The answer is no, because 8:7 and 4:2 are different relationships.

Answer:

Explanation:

Here, we start by finding the lowest common denominator

From what we have, the lowest common denominator is the lowest common multiple of both denominators which is equal to 8

We divide the first denominator by this and multiply the result by its numerator. We take the same step for the second denominator

Mathematically, we have it that:

Since the triangles are similar there exists correspondance in the angles, so in order to solve this you just have to clear the function:

Since D is the midpoint of VU, VD=50

then

let x be the money daniel has. So we get that

Daniel has at least $87

Given:

To Determine: The percentage increase round to the nearest 1oth of a percent

The formula for percentage increase is given below:

Substitute the given into the formula

Hence, the percentage increase to the nearest 10th of a percent is 2.5%

Let

y ------> the year

x ----> revenue

so

Plot the given ordered pairs

see the attached figure

(please wait a minute to plot the points)

In the graph the x-coordinate 0 represent year 1990

Find out the equation of the line

take two points

(1990, 5.7) and (2006, 11.5)

Find the slope m

m=(11.5-5.7)/(2006-1990)

m=5.8/16

m=0.3625

Find the equation of the line in slope intercept form

y=mx+b

we have

m=0.3625

point (1990, 5.7)

substitute and solve for b

5.7=(0.3625)(1990)+b

b=-715.675

therefore

EXPLANATION

If Hunter has $300 in savings and the interest rate is 8%, compounded annualy, we can apply the following equation:

Where, P=Principal=300, r=rate (in decimal form) = 8/100 = 0.08, n=number of compounded times = 1 and t = time = 3

Substituting terms:

Adding numbers:

Computing the powers:

Multiplying numbers:

In conclusion, there will be 378.00 in three years

5.2% = 0.052

1/7 = 0.14

-11/5 = -2.2

From the greatest to least:

The second number is: 5.2%

Answer:

5.2%

First, find the equation of the line, given that the points (3,2) and (-3,-6) belong to that line. To do so, use the slope formula and then substitute the value of the slope and the coordinates of a point on the slope-point formula of a line:

The slope of the line, is:

Therefore, the equation of a line (using the point (3,2)) is:

Since the colored region on the coordinate plane is placed above the line

y=(4/3)x-2, then the equation of the inequality is:}

The equivalent expression for the given exponent equation is 16^x/32

Given,

The exponent equation; 2^4x - 5

We have to find the expressions which is equivalent to 2^4x - 5

Exponential equations are inverse of logarithmic equations.

This can also be expressed as;

2^(4x-5) = 2^4x/2^5

2^4x-5 =16^x/2^5

2^4x-4 = 16^x/32

Hence the equivalent expression is 16^x/32

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Answer:it's not 4^x/5

Step-by-step explanation:

We have to use the simple interest formula.

Replacing the given information, we have.

120 percent of 118 is expressed mathematically as;

120% of 118

120/100 * 118

= 12/10 * 118

= 6/5 * 118

= 708/5

= 141.6%

Hence 120 percent of 118 is 141.6%

Given that the pair of triangles are similar, then their corresponding sides are in proportion, this means that:

Substituting with the information of the diagram:

Cross multiplying:

Considering the triangle on the left, and applying the Pythagorean theorem with c = y (the hypotenuse), a = 27, and b = x (the legs), we get:

Answer:

Angle C = 40 degrees

angle D = 75 degrees

Explanation:

From the information given,

Angle A = 75 degrees

Angle B = 40 degrees

AB is parallel to CD. This means that AD and BC are transversals.

Angles A and D have similar positions but they are opposite sides of the transversal. This means that they are alternate angles. Alternate angles are congruent. Thus,

angle D = 75 degrees

Angles B and C have similar positions but they are opposite sides of the transversal. This means that they are alternate angles. Alternate angles are congruent. Thus,

Angle C = 40 degrees

we know that

1 in=2.54 cm

so

840 in

Applying proportion

1/2.54=840/x

x=(840*2.54)/1

x=2,133.6 cm

answer is

we have

2.54 cm/in

Multiply by 840 in

2.54*(840)=2,133.6 cm40/

We can calculate the percent error as the absolute difference between the predicted value ($65) and the actual value ($73) divided by the actual value and multiplied by 100%.

This can be written as:

Answer: the percent error is approximately 11.0%

3x^2 -5x +1 =0

Aplica la formula cuadrática:

Donde:

a = 3

b= -5

c= 1

Reemplazando:

Positivo:

(5+√13) /6 = 1.43

NEgativo:

(5-√13) /6 = 0.23

We are given the following graph:

The inverse of the graph is shown below:

We have two events A and B.

We know that:

P(B) = 0.5

P(A|B) = 0.4

P(A∩B') = 0.4

i) We have to calculate P(A∩B).

We can relate P(A∩B) with the other probabilities knowing that:

So we can write:

We know P(A∩B') but we don't know P(A), so this approach is not useful in this case.

We can try with the conditional probability relating P(A∩B) as:

In this case, we can use this to calculate P(A∩B) as:

ii) We have to calculate P(A) now.

We can use the first equation we derive to calculate it:

iii) We have to calculate P(A∪B).

We can use the expression:

iv. We can now calculate P(A|B') as:

b) We now have to find if A and B are independent events.

To do that we have to verify this conditions:

We can check for the first condition, as we already know the value:

Then, the events are not independent.

Answer:

i) P(A∩B) = 0.2

ii) P(A) = 0.6

iii) P(A∪B) = 0.8

iv) P(A|B') = 0.2

b) The events are not independent.

x² - 20x + 100

Find two numbers, such that its sum gives -20 and its product gives 100

If such numbers exist, this implies that the polynomial is NOT prime

The two numbers are: -10 and -10

Replace the coefficient of x with the two numbers

x² - 10x -10x + 100

x(x-10) - 10(x - 10)

(x-10)(x-10)

(x-10)²

Therefore, the correct option is A.

x² - 20x + 100 = (x-10)²