Question 5 of 40Roxanne likes to fish. She estimates that 30% of the fish shecatches are trout, 20% are bass, and 10% are perch. Shedesigns a simulation.

Ticket price as a function of time. If you write the number [tex]2040[/tex] where you see [tex]x[/tex] in this function and take the value where you see [tex]y[/tex], you will reach the correct answer.

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:

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.

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:}

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.

SOLUTION

The range of the function is given as:

The asymptote of the function is at points

The function is shown in the graph below

Therefore, the equation of the session is

The following completes the proof: D. The Alternate Interior Angles Theorem shows that the angles BAC and DCA are congruent.

The Alternate Interior Angles Theorem: What is it?

According to the alternate interior angles theorem, when a transversal cuts over two (2) parallel lines, the alternate interior angles that are created are congruent.

We can infer and logically derive from the Alternate Interior Angles Theorem that the sentence that correctly concludes the proof is that angle BAC and angle DCA are congruent.

Segment AB is parallel to segment DC, while segment BC is parallel to segment AD, according to the information provided. Create the diagonals A and C using a straight edge. By virtue of the Reflexive Property of Equality, it is congruent to itself.

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

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

Answer:

x = 5/6 or x = 0.83

Step-by-step explanation:

6x + =5

6x + 0 = 5

6x = 5

6x/6 = 5/6

x = 5/6 or x = 0.83

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.

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%

By working with percentages, we will see that there are 10 gallons of ethanol in the mixture.

We know that we have a mixture with a volume of 100 gallons, and 10% of that mixture is ethanol, so we just need to find the 10% of 100 gallons.

To work with percentages, we will use the equation:

Volume of ethanol = total volume*ratio of ethanol.

V = 100gal*(10%/100%)

V = 100gal*0.10 = 10 gal

There are 10 gallons in the mixture.

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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 length of an arc = 13.26 ft

The length of an arc is given by the formula:

Substitute θ = 8°, r = 95 ft, and π = 3.14 into the formula

The length of an arc = 13.26 ft

We are given the following graph:

The inverse of the graph is shown below:

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

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

EXPLANATION

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

A 15% discount means that the retail price is 85% of the original price.

To calculate said retail price, we'll use a rule of three:

Thereby,

Therefore, we can conclude that the available price is $102

We have to use the simple interest formula.

Replacing the given information, we have.

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

Daniel has at least $87

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 are given the following equation:

We are asked to solve for "q". To do that, we will first add "5" on both sides, like this:

Now we will divide by 3 on both sides, like this:

Therefore, the value of q is 6.

ok, remember that the answer will be available in your profile.

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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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

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:

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

r(t)=t^2

r(t)=4​

t = ?

Step 02:

r(t)=4​

t ² = 4

t = √4

t = 2

The answer is:

t = 2

Answer:   t=2

Step-by-step explanation:

Because we know that for some value of t, r(t)= 4, and for ALL values of t, r(t)= t^2, then we know for some value of t, that t^2 = 4.

Based off of this information, we can take the square root of both sides, resulting in this equation.

t = [tex]\sqrt{4}[/tex]

This can be simplified.

t=2

Solution:

Given the expression:

This expression is evaluated as

Hence,

is evaluated to be 25

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%