A hemisphere bowl of radius 7ft has water in it to a depth of 2 ft. At what angle must it be tipped for the water to begin to flow out?

Given:

Given a graph of f(x) and g(x).

Required:

To write the formula for g(x) in terms of f(x).

Explanation:

The graph of g(x) is 5 units left and 1 units up gfrom the graph of f(x).

Therefore the function g(x) is

Final Answer:

The average length of the trout in the area with a 99% confidence interval is between 46.7 cm and 53.3 cm.

The distribution used should be t distribution as the sample standard deviation is to be used.

We need to build the 99% confidence interval for the population mean . The following information is provided:

Sample Mean = 50

Sample Standard Deviation  = 2 cm

Sample Size = 15

The confidence interval for the trout population is computed as shown below:

[tex]\Pr \left({\bar {X}}-{\frac {cS}{\sqrt {n}}}\leq \mu \leq {\bar {X}}+{\frac {cS}{\sqrt {n}}}\right)=0.99\,[/tex]

now we will substitute the values in the equation of the CI.

[tex]{\bar {X}}-{\frac {2.7}{\sqrt {15}}}\leq \mu \leq {\bar {X}}+{\frac {2.7}{\sqrt {15}}}=0.99\,[/tex]

now solving for the confidence interval we get : 47.8 ; 52.3

Lower limit = 50 - 3.307 = 46.69 ≈ 46.7

upper limit = 50 + 3.307 = 53.307 ≈ 53.3

Hence the average length of the trout in the area is between 46.7 cm and 53.3 cm.

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Given the fractions 3/4 and 5/16

In order to determine which is less or greater, we need to first express them in percentage as shown;

3/4 = 3/4*100%

3/4 = 3*25 = 75%

5/16 = 5/16 * 100

5/16 = 500/16 = 31.25%

Since 75% is greater than 31.25% hence;

3/4 is greater than 5/16 and the sign that will be in the box will be the greater than sign i.e 3/4>5/16

Strategy: I compared the fraction to the bench mark of >

The addition of length of each line segment gives the value of AD.

The value of AD is 54.

Step 1:

The slope intercept form formula is

y = mx + c

m = slope

c = intercept on the y-axis

Final answer

Slope Intercept

Step

Ton graph the function, find both x=intercept and y-intercept

Next plot the graph.

STEP - BY - STEP EXPLANATION

What to find?

Percentage decreaase.

Given:

Original price = $600

new price = $504

Step 1

Recall the formula for percentage decrease.

Step 2

Determine the value for the dcerease.

Step 3

Substitute into the formula and simplify.

ANSWER

Percent decrease = 16% decrease

From the graph, we can conclude:

As:

x-intercept:

Asymptote:

Vertical asymptote:

Horizontal asymptote:

ANSWER:

Only in the case that the rays are opposite.

STEP-BY-STEP EXPLANATION:

We have that a ray is part of a line that has an end point and continues infinitely in a single direction.

Therefore, a pair of opposite rays are two rays that have the same end point and extend in opposite directions. So together a pair of opposing rays always form a straight line.

Graphically a ray and a line are like this:

Answer: if the rays are opposite they will always form a straight line but if the are not opposite they will not form a line

Step-by-step explanation:

Given:

The slope of the line is m = -2.

The line passes throught the point (6,-9).

The objective is to find the equation of line.

Explanation:

Consider the point as,

The general equation to find the equation of line in slope intercept form is,

Substitution:

On plugging the given values in the general equation,

Here, slope of the line is -2 and y- intercept is 3.

Hence, the equation of the line in slope intercept form is y = -2x + 3.

one solution: (1, 4)

The equations:

y = -x + 5

y = -5x + 9

To plot the graphs, we can assign values to x. The we get the corresponding values of y for each of the equation.

Rewritting the two equations by making y the subject of formula:

Plotting the graphs:

The point of intersection of the graphs is the solution.

There is one solution: (1, 4)

Answer:

0.82 and 0.83

Given:

is given.

Required:

We need to solve this equation.

Explanation:

Here an equation given as

now add both side negative 3 and we get

now multiply both side with inverse 6

Final answer:

Solution of given equation is

Here, we want to find the translation rule

20 4/5

it means 20 integers and 4/5

4/5 = 0.8

so the number 20 4/5 is equal to 20.8

answer: 20.8

20 7/8 is 20 integers and 7/8

7/8 = 0.875

so 20 7/8 is equal to 20.875

As this is a vertical line, its domain is just one point, x=3. And it's range is all the real numbers

To determine the coordinates of the library, for the x-coordinate, you have to draw a vertical line from the library to the x-axis and read where it intersects the x-axis. And to determine the y-coordinate you have to draw a horizontal line from the position of the library towards the y-axis, and read where the line intersects the y-axis:

The x-coordinate is 4 and the y-coordinate is 3, so the coordinates of the library are (4,3)

ANSWER

f(0) = -1

EXPLANATION

We just have to replace x by 0 into f(x):

As given by the question

There are given that the total of 10 different topping

Now,

According to the question:

There is also talk about 3 different pizzas.

So,

The three different toppings from the 10 different toppings:

Then,

Then,

Hence, 120 different pizzas are possible.

Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for n. A sphere has a radius of 8 centimeters. The volume of the sphere is about cm?.​

we know that

The volume of the sphere is equal to

we have

r=8 cm

pi=3.14

substitute the given values in the formula

answer is

We will use the following variables :

g for glazed

f for cream filled donuts

c for chocolate donuts

So, the equation for combo 1

3 g + 4 f + 5 c = $38

The equation for combo 2:

5 g + 6 f + c = $32

The equation for combo 3:

4 g + 4 f + 4 c = $36

So, the system of equations are:

3 g + 4 f + 5 c = 38 (1)

5 g + 6 f + c = 32 (2)

4 g + 4 f + 4 c = 36 (3)

B) Now, we need to solve the system of equations:

From equation 3:

4 g + 4 f + 4c = 36

divide all terms by 4

So, g + f + c = 9

Solve for c:

c = 9 - g - f

Substitute with the value of c at the equations (1)

At (1):

3 g + 4 f + 5 (9 - g - f) = 38

3g + 4f + 45 - 5g - 5f = 38

-2g - f = 38 - 45

-2g - f = -7

Multiply all terms by -1

2g + f = 7

Solve for f

f = 7 - 2g

Substitute with f at the equation of c

c = 9 - g - (7 - 2g)

c = 9 - g - 7 + 2g

c = g + 2

So, we have reached to :

f = 7 - 2g and c = g + 2

substitute with f and c at the equation (2)

5g + 6f + c = 32

5g + 6 (7 - 2g) + g + 2 = 32

solve for g

5g + 42 - 12 g + g + 2 = 32

5g - 12g + g = 32 - 42 - 2

-6g = -12

Divide both sides by -2

g = -12/-6 = 2

f = 7 - 2g = 7 - 2 * 2 = 7 - 4 = 3

c = g + 2 = 2 + 2 = 4

So, the cost of glazed = $2

The cost of cream filled = $3

The cost of chocolate = $4

We have the following:

We have that the area of a rectangle is the following

replacing:

We have the following:

A.

First we find the slope of the line with the following points:

(0, 3) and (5,0)

now, for b, with the point (0,3)

The equation is:

B.

The area is:

The area is 7.5 square units

for, perimeter:

The perimeter is 13.83 units

C.

when two lines are perpendicular they fulfill the following

therefore,

Therefore, the equation is:

ANSWER

A) 70º

EXPLANATION

In quadrilaterals inscribed in a circle, opposite angles are supplementary - their measures add up 180º. Therefore:

Solution

We are given

Probability of eating out twice in a week = 15% = 0.15

Probability of eating out once in a week = 35% = 0.35

Probability of not eating out in a week = 50% = 0.50

Let X be a random variable of the number of times Piper eats out in a week

So we have the table

Note: The Formula For finding the Expected value E(X) is given by

Substituting we get

Therefore, the expected value is

Since the polygon shown is a regular one, a rotation will carry it onto for every angle that makes a vertex to the place of another vertex.

So, we can fisrt figure the angle we need to rotate to get a vertex onto the next one, that is, we want to find the following angle:

We know tha the polygon is regular, so this angles is the same as the angles between the other consecutive vertexes. Since we have 5 vertexes, this angle is 1/5 of the role 360°. So, this angles is:

That means that a rotation of 72° will always endup in the same figure.

This also means that a rotation of any multiple of 72° will also end up in the same figure.

Thus, we just have to check which alternative is a multiple of 72°.

- 60° isn't a multiple, because it is lower.

- 108° also isn't because the 2*72 = 144, which is higher than 108°.

- 540° isn't, because 7*72 = 504 and 576, which passed through 540°

- 216° is a multiple because 3*72 = 216 exactly.

This means that if we rotate the figure by 210° it will end up in the same figure.

So, the correct alternative is the last one: 216°.

An imaginary unit, i is a solution to the quadratic equation:

Or to simply say,

It can

Answer:

-7/24

Explanation:

Given the expression:

Step 1: Find the lowest common multiple of the denominators.

The L.C.M. of 8 and 3 = 24

Step 2: Use the LCM to combine the fractions.

Step 3: Simplify:

The result of the sum is -7/24.

Given sin(x)=5/13

First, lets find cos(x).

It is known that:

Since π/2 < x < π, we are in 2nd quadrant. Then, cos(x) is negative.

Since we know the values for sin and cos, we can find tan(x):

Now, lets work with the expression tan(2x)

It is known that:

Since we know tan(x), we can substitute in the expression above and find the value of tan(2x):

Answer: -120/119

Let's call the total volume of the tank as V. The rate each pipe fills the tank is given by the total volume of the tank divided by the amount of time it takes to fill the tank. Let's call the rate of the first pipe as r1, the rate of the second pipe as r2 and the rate of the third pipe as r3.

The product between the rate and the time that has passed will give to us the fraction of the tank that has been filled. When we open the three pipes at once, we sum their rates. When the tank is filled, the product between the rate and the time passed must give the total volume of the tank, therefore, we have the following equation:

It will take approximately 9.23 minutes to fill the tank if all pipes are opened together.

When the three pipes are opened, the fraction that has been filled(let's call it as x) is given by:

Then, the slowest pipe(the third pipe) is closed, then, after 3 more minutes we're going to fill an extra y amount of water, given by:

Then, after a time t with the first pipe open, we're going to fill the tank(remember that it has been filled already by the amounts x and y, therefore, we must subtract it from the total volume).

If the slowest pipe is shut off after 3 minutes and the fastest pipe is shut off 3 minutes later, it will take 12.75 minutes for the remaining open pipe to finish filling the tank.