Last weekend, 5% of the tickets sold at Seaworldwere discount tickets. If Seaworld sold 60 tickets inall, howmany discount tickets did it sell? Use thepercent proportion.

As the first step, let us say that the velocity of the boat in relation to a fixed point in the map of this travel is equal to its velocity in relation to the water PLUS the water velocity in relation to the fixed point WHEN it is in the same direction (travel downstream), and MINUS when traveling in the opposite direction (upstream).

From this, we will remember the definition of velocity by:

The ΔS is the distance ran by the boat, which is 60 miles. Δt is 4h for the upstream case, and 3h for the downstream case.

From this, we say that the value of V is for the boat in relation to the water (which is what we need here) and v for the water. Now, we have the following system of equations.

Now, to proceed with the solution, we will sum up the equations, which will result in the following:

We have the following expression:

Now let's recall two properties of the exponents that will help to solve this exercise:

Then we have:

Now, we have all the exponents with positive sign

The base of the exponents is different (a,b and c), therefore there is no additional step we can take

Student became unresponsive. Closing the session

Solution

The final answer

Option B

Then the correct answer is A. 5/8 barrel/hour

Answer:

Side length of the box: 6 cm

Volume of the box/cube: 216 cm³

Volume of the box without cone: 190.88 cm³

Explanation:

The sides of a cube are all equal, so in this case, the side length of the box is 6 cm.

Then, the volume can be calculated as

Volume = side x side x side

Volume = 6 cm x 6 cm x 6 cm

Volume = 216 cm³

To know the volume of the box with the cone shape cut of it, we need to calculate the volume of the cone with the following equation

Where π = 3.14, r is the radius and h is the height. The diameter of the cone is 4 cm, so the radius is

r = 4 cm/2 = 2 cm

Then, replacing r = 2 cm and h = 6 cm, we get

Now, the volume of the box without the cone shape is

V = 216 cm³ - 25.12 cm³

V = 190.88 cm³

So, the answers are

Side length of the box: 6 cm

Volume of the box/cube: 216 cm³

Volume of the box without cone: 190.88 cm³

Answer:

11

Step-by-step explanation:

You have an equation [tex]f(x)[/tex] and you set [tex]x=5[/tex], and the result is 2.

You have another equation [tex]g(x)[/tex] and you set [tex]x=5[/tex], and the result is 9.

Therefore, if you add both equations, represented by [tex](f+g)(x)[/tex], and you set [tex]x=5[/tex], the result is simply 2 + 9 = 11.

Given:

A committee has seven men and four women.

four people are selected to go to a conference

We will use the combinations as follows

the number of ways to choose the four people are:

The rule of combinations is:

so, the number of ways will be:

The number of ways to make a group of two men and two women will be:

So, the chance that the group is two men and two women =

so, the answer will be 7/33

1. Identify the given from the statements.

• Let the side of the square base= s

• Height of the rectangular box be= h

• Given that :

s^2h = 20ft^3

solving for sh: s^2h = 20

s^2=20/h

s*s/s = 20/h /s

s = 20/hs

• Therefore sh = 20/s

Expandingthe given statements , we learn that :

• Material cost for base per square foot = 20 cents

• Material cost for sides per square foot = 18 cents

• Material cost for the top per square foot = 14 cents

2. Calculate Total cost

Total cost = {(s^2*20) + 4(sh)*18 +s^2*14}cents

= 20s^2 + 72*20/s + 14s^2

=34s^2 + 1440/s

• Expressing Total cost in terms of x , let s = x .

• Then Total cost (x) = 34x^2 +1440/x

2. Calculating the domain of TC(x) =34x^2 +1440/x

x <0 or x> 0

Domain (-∞;0) U(0;∞)

the given diagram:

We have to find the value of DE

Since all the lines intersect at right angle

Answer : DE = 8ft

1) We need to consider the fact that perpendicular lines described by linear functions have opposite and reciprocal slopes when compared to the original linear function.

2) So we can state that the perpendicular line to y=-5x-3 has a slope of :

3) Now, the next step is to plug into the Slope-intercept form the following point (15,4) and then find the y-intercept:

4) Thus, the equation of a perpendicular line to the line described by the linear function y=-5x-3 is:

Explanation

Step 1

Zeros

A(-6,0) B(4,0)

because

Step 2

table

I hope this helps you

Initially we have 3 quarts of a 50% antifreeze solution

We want to obtain a 60% antifreeze solution by adding x quarts of pure antifreeze

Therefore we can set the following equation,

where x are the quarts of pure antifreeze added

let's solve for x

rounding to the nearest tenth, 0.8 quarts of pure antifreeze must be added

The expression we have is:

In this expression, we have two terms: 2x and 5.

The elements in these terms are variables, coefficients, and constants.

A variable is a letter that can take different values, a coefficient is a number that accompanies the variable, and a constant is a number that does not have any variable next to it (its value will not change).

In this case:

2 is the coefficient,

x is the variable,

and 5 is the constant.

Answer: a) 5

The total discount in Arlene's purchase was 4.20, this includes the discount applied over both, the case and the charging cord. We already know the original price of the phone case, the discount applied and the value of the discount, use it to find the original price of the chargind cord:

The original price of the charging cord is $10

80%

1) Since the prices on Target dropped from $15 to $12 to find the equivalent percentage of $12 in comparison to $15 we need to write down the following ratio:

Note that we cross multiplied that ratio and then on the second step we have divided both sides by 15.

2) Hence, I paid 80% of the original price that day

To find the slope of the expression:

We need to remember that this is the Slope-intercept Form of the line equation:

Where

m = slope

b is the y-intercept.

Therefore, the slope of the line equation above is m = 3.

SOLUTION

We want to find the number of weeks in 259 days

Now, 7 days make a week. So to get the number of weeks in 259 days, we divide the 259 by 7, we get

So the answer is 37 weeks

Hello!

First, let's remember about the integers numbers.

These numbers can be positive or negative (and include the number 0). The main characteristic is that these numbers don't have a decimal part.

Knowing it, we can say that are integers:

• -1,

• 0,

• 2,

• -2.

In the number line, we'll have:

We have the multiplication of 9.18 * 7.3 and want to know where the decimal point has to be.

In the multiplication we have to sum the decimal position of the numbers and taht is the position of the decimal point of the result.

In this case, the decimal point of 9.18 is 2 places and for 7.3 is one place, so the final result will have 2+1=3 places. The decimal point has to be 3 places.

The number is 67014 and the decimal point is three places from rigth, 67.014

The data provided of the 16 sold shirts can be used to count the frequency of each color.

The results are shown below:

White = 5

Black = 2

Blue = 4

Red = 5

We can check the total is 5 + 2 + 4 + 5 = 16

Now we are ready to draw the bar graph, where each color must have a height that equals its frequency.

We must substitute each pair into our equation:

A. If we substitute point (1,1), we have

then, this point is a solution.

B. If we substitute point (-1,1), we have

this means that this point is not a solution.

C. If we substitute point (-6,7), we have

this means that this point is not a solution.

D. If we substitute point (3,-11), we have

then, this point is a solution.

Therefore, the solutions are option A and D

Kinsley measured a city park

Scale of drawing : 13 milimeter and 5 meter

Actual width is 65 meter

Let the field in Milimeter is x

So,

Answer: 13 milimeters and 5 meters = 169 milimeters and 65 meters

Answer

The red line represents y = x + 1

The blue line represents y = 2x - 7

We can see that the two lines and equation intersect at (8, 9)

Solution

x = 8

y = 9

Explanation

The two equations are

y = x + 1

y = 2x - 7

To solve this graphically, we will plot the two equations on the same graph and the solution will exist at the point where the two lines meet.

To plot the lines for each of these equations, we will use intercepts to obtain two points on each line and then connect the two points to get each of the lines.

y = x + 1

when x = 0

y = x + 1

y = 0 + 1

y = 1

First point on the line is (0, 1)

when y = 0

y = x + 1

0 = x + 1

x = -1

Second point on the line is (-1, 0)

The two points are (0, 1) and (-1, 0)

y = 2x - 7

when x = 0

y = 2x - 7

y = 2(0) - 7

y = 0 - 7

y = -7

First point on the line is (0, -7)

when y = 0

y = 2x - 7

0 = 2x - 7

2x = - 7

Divide both sides by 2

(2x/2) = (-7/2)

x = -3.5

Second point on the line is (-3.5, 0)

The two points are (0, -7) and (-3.5, 0)

The graph of this question will now be presented under answer and the point of intersection will bw evident.

Hope this Helps!!!

Record for the number and types of fish caught in a local lake during a 2-year

period

Fish caught during this period were trout = 796

Fish caught during this period were bass = 43%

Total percentile = 100%

Fish caught during this period were trout = 100 - percentage of fish caught during this period were bass

fish caught during this period were trout = 100 - 43 = 57%

Hence the reports of the number of trout and

bass at this lake are examples of percentile ranks

simplify: 9x^4-27x^6/3x^3​

we have the expression

we have the expression

this is the answer

The ratio 2:4 is equivalent to and 1:3 if both numbers are obtained by the same multiplication:

Since

1 x 2 = 2 and

3 x 2 = 6 (instead of 4)

then they are NOT equivalent

Answer

x = 85°

Explanation

The image of this question shows that the two angles 20° and (x - 15)° both sum up to give a right angle (90°). So,

20° + (x - 15)° = 90°

20° + x - 15° = 90°

x° + 20° - 15° = 90°

x + 5° = 90°

x = 90° - 5°

x = 85°

Hope this Helps!!!

Since the rectangle is composed of 2 right triangles, we can apply the Pythagorean theorem to one of the triangles:

c^2 = a^2 +b^2

Where:

c= hypotenuse (longest side) = 15

a & b = the other two legs of the triangle ( x , 3 )

Replacing:

15^2 = 3^2 + x ^2

Solve for x

225 = 9 + x^2

225-9 = x^2

216 = x^2

√216 = x

x= 14.69

So, to find the value of x, we can use:

A. 3^2 + x^2 = 15^2

So, Sin QOP = QP/OQ = OPPOSITE/ Hyp

Then, cos PQO = QP/OQ = Adjacent/ Hyp

Using the same logic, Cos ROQ = RO/OQ = Adj/Hyp

Then, sin QPO = RO/OQ = Opp/Hyp