EO GEOMETRYVolume of a sphereThe diameter, D, of a sphere is 19.8 m. Calculate the sphere's volume, V.Use the value 3.14 for it, and round your answer to the nearest tenth. (Do not round any intermediate computations.

To solve the exercise, we subtract the given numbers:

The number of bottles of tonic that must be sold to make at least $130 in profit is [10, 75]

The profit function is given as

P(x) = -x^2 + 85x - 620

The earnings are given as

Earnings = at least $130

This means that

P(x) ≥ 130

So, we have

-x^2 + 85x - 620 ≥ 130

Subtract 130 from both sides of the inequality

So, we have

-x^2 + 85x - 750 ≥ 0

Divide through by -1

So, we have

x^2 - 85x + 750 ≤ 0

Expand the expression

x^2 - 75x - 10x + 750 ≤ 0

Factorize

x(x - 75) - 10(x - 75) ≤ 0

Factor out x - 75

(x - 75)(x - 10) ≤ 0

Split

x - 10 ≤ 0 and x - 75 ≤ 0

Solve for x

x ≤ 10 and x ≤ 75

Combine the inequality

10 ≤ x ≤ 75

Express as interval

10 ≤ x ≤ 75 = [10, 75]

Hence, the number of bottles is [10, 75]

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The required solution of the function f(x) = -3x + 5 at x = -2 is 11.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given function,
f(x) = -3x + 5
Substitute x with -2 to find f(-2).
f(-2) = -3(-2) + 5
f(-2) = +6 + 5

f(-2) = 11

Thus, the required solution of the function at x = -2 is 11.

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Total votes of the residents of the city = 4,440

Ratio of yes to no = 5:3

Yes votes = 4,440 * 3/5 = 2,664

No votes = 4,440 - 2,664 = 1,776

For the given relation

With domain {-2, -1, 0}.

The domain represents all possible values of x, also called input, of the relationship and the range represents all the values of y, also called output, obtained when you replece the formula with the given values of x.

To determine the range of the valiable you have to do as follows:

For x=-2

For x=-1

For x=0

For the relation with domain {-2,-1,0} the range is {2, -1, 0}

The correct option is number 2)

The sum of the angles in a triangle is 180 degrees. It means that

110 + 5x + 2x = 180

110 + 7x = 180

7x = 180 - 110

7x = 70

x = 70/7

x = 10

The value of x in the triangle is 10

Therefore, the correct option is

D. None of the above

Answer: it’s c

Step-by-step explanation: dude that’s ez

The total compound interest is $7,081.8 , which interest will this investment earn.

What is compound interest?

Initial balance= 21,800$

Interest rate =9.6%

Term=3yrs0mos

Compounding frequency=semi-annually (2/Yr)

CI= P(1+(r/n)^nt-P

The final balance is $28,881.8.

The total compound interest is $7,081.8.

The total compound interest is $7,081.8 , which interest will this investment earn.

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A 180-degree rotation about the origin transforms point (x, y) into (-x,-y). then:

M(-8, 3) → M'(8, -3)

Given

The figure.

To find the area of the shaded region.

Explanation:

It is given that,

The radius of the whole circle is 11cm.

And, the radius of the small circle is 3cm.

Then,

The area of the shaded region is,

Hence, the area of the shaded region is 351.85cm^2.

The absolute value of 8|Cosθ| is 8√(x² - 8²)/|x|.

The value of the angle θ is Sin−1 (8/x). We need to find the absolute value of 8|Cosθ|.

θ = Sin−1 (8/x)

Sinθ = 8/x

We know the trigonometric identity that Sin²θ + Cos²θ = 1.

Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles.

(8/x)² + Cos²θ = 1.

Cos²θ = 1 - (8/x)²

Cos²θ = (x² - 8²)/x²

Cosθ = √[(x² - 8²)/x²]

Cosθ = √(x² - 8²)/x

Multiply both the sides with 8.

8Cosθ = 8√(x² - 8²)/x

Apply modulus on both the sides.

A modulus function is one that returns the absolute value of a number or variable.

8|Cosθ| = 8√(x² - 8²)/|x|

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We need to find the linear and the angular speeds of an object traveling around a circle.

The radius r of the circle is 3 feet. Thus, the perimeter p of the circle is:

Also, we know that the object completes one full revolution every 5 seconds.

Thus, to find the linear speed V, we need to divide the number of feet it travels by the number of seconds it takes:

ow, tnotice that the complete revolution has 2π radians.

Then, to find the angular speed ω, we need to divide the number of radians it travels by the number of seconds it takes:

Therefore:

Given data:

The given number is | -32| .

The value of given modulus function is,

The opposite of 6 on number line is -6.

Thus, the value of first number is 32, and second is -6.

he needs to walk the dog 6 times more}

Step 1:

The model of the table is shown below:

Step 2:

The equation of the model is

y = 140.6t + 371.6

Step 3:

To predict the number of people infected in 15 days, substitute t = 15

Final answer

2481

The end of shaft is 137.731m lower at the beginning.

An angle is formed when two straight lines or rays meet at a single terminal.

The place where two points converge is known as an angle's vertex.

Angles' Components:

Vertex: The intersection of two lines or sides at an angle is called a vertex.

Arms: The angle's two sides linked at a single end.

Initial Side: A line that is straight from which an angle is made.

from the given figure:

tan(19) =  BC/AB

BC = 400 × tan(19)

BC = 137.731m

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A year has 52 weeks.

Since Officer Milton has 3 weeks of vacation, then he works for 49 weeks a year.

Since he visits 3 groups per week, the total number of groups that he visists in a year is:

Therefore, the correct choice is option C) 147.

Answer

Option C is correct.

8√5 + 2√45 = 14√5

Explanation

We need to simplify

8√5 + 2√45

Note that 45 = 9 × 5

8√5 + 2√45

= 8√5 + 2√(9 × 5)

= 8√5 + 2[√9 × √5]

√9 = 3

8√5 + 2[3 × √5]

= 8√5 + 2(3√5)

= 8√5 + 6√5

= 14√5

Hope this Helps!!!

Coordinates of Point G is (1,-10)

To find Coordinates :

Let the coordinates of G are (x,y)

To find coordinates of G

[tex]\frac{x + (-4)}{2} = -1[/tex]                        [tex]\frac{y + 0}2} = -5[/tex]

= x + (-2) = -1                      y+0 = -5 * 2

x =  -1 + 2                           y = -5 * 2

x = 1                                        y = -10

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we have the function

f(x)=x^4-x^3-7x^2+45x-39

Find out f(-5)

so

Use synthetic division

x^4-x^3-7x^2+45x-39 : (x+5)

x^3-6x^2+23x-70

-x^4-5x^3

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

-6x^3-7x^2+45x-39

6x^3+30x^2

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

23x^2+45x-39

-23x^2-115x

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

-70x-39

70x+350

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

311 ----------------> remainder

therefore

f(-5)=311

Verify

using a graphing tool

For x=-5 ------------> f(x)=311 is ok

Ngoc needs to mix a 10% alcohol solution with a 60% alcohol solution to create 200 milliliters of a 22.5% solution. How many milliliters of each solution must Ngoc use?​

Let

x -----> milliliters of solution at 10%

y -----> milliliters of solution at 60%

we have

x+y=200 ------> equation A

Remember that

10%=0.10

60%=0.60

22.5%=0.225

so

0.10x+0.60y=0.225(200) -----> equation B

solve the system of equation s A and B

Solve by graphing

using a graphing tool

see the attached figure

please wait a minute to draw the system

the solution is the point (150,50)

therefore

We have a dataset: 13, 6, 13, 8, 2, 19, 11, 16, 17, with size n = 9.

We will add 32 to it.

In this case, the mean will be affected, as it depends on each individual value of the dataset. As the number is greater than all the numbers in the dataset, it will be greater than the actual mean. Then, the mean will increase.

The median may or may not change, depending on the values of the set.

Then, we can find the median before and after the addition.

First, we have to sort the data: 2, 6, 8, 11, 13, 13, 16, 17, 19.

The median, for a size n =9, will be located in the fifth place, so the median is 13.

Then, the dataset has 4 values below and 4 values above the median.

When we add 32, it will be the greatest value, so we will have a dataset of size n =10 and sorted as: 2, 6, 8, 11, 13, 13, 16, 17, 19, 32.

The median will be the average between the fifth and sixth place. Both values are 13, so the average, and therefore, the median will be also 13.

Then, in this case, the mean increases but the median does not.

Answer: The mean will increase and the median will remain the same.

[tex]x = 3 + 2y.....(3)equation[/tex]

[tex]y + 3(3 + 2y) = - 5 \\ y + 9 + 6y = - 5 \\ y + 6y = - 5 - 9 \\ 7y = - 14 \\ \frac{7y}{7} = \frac{ - 14}{7} \\ y = - 2[/tex]

[tex]x = 3 + 2y \\ x = 3 + 2( - 2) \\ x = 3 - 4 \\ x = - 1[/tex]

ATTACHED IS THE SOLUTION.

We see that there is a difference of 4 between each number:

and so on. Then, we can propose the following formula:

For instance, when n=0 we have

when n=1, we have

when n=2, we have

and so on. Then, in order to compute the 78th term, we must substitute n=78 in our formula. It yields,

and the answer is -335

The figure is a trapezoid, and the area of a trapezoid can be calculated with the formula below:

Where B is the greater base, b is the smaller base and h is the height.

To find the measure of the smaller base, we need to find the missing piece to the right of the value "3 units" (let's call it x).

To calculate it, we can use the total length of the greater base:

Therefore the smaller base is 3 + 9 = 12 units.

Now, calculating the trapezoid area, we have:

Given the equation:

Since the required table is not given, we will solve for values of x from -3 to 3.

You can then place this in a table of x and y values.

You can use the same process to complete any table.

SOLUTION

Consider the image in the below

From the diagram above,

Then we obtain the coordinate of H and G

Using the coordinate of midpoint formula,

Then

Then use the distance formula to fined the lenght of |EH| and |DG|

The Distance formula is given by

Hence

Then

Hence

Since we obtain the same expression above

Then

therefore

Therefore

Answer: DG is congruent to side EH



The distribution of the number of phone calls with a mean of 41 and a standard deviation of 7. 95.44% is the percentage of the daily phone calls between 27 and 55.

Given that,

The distribution of the number of phone calls handled by each of the 12 receptionists in a mid-sized company is bell-shaped, with a mean of 41 and a standard deviation of 7. When applying the empirical rule.

We have to find what percentage of daily phone calls, on average, fall between the range of 27 and 55.

Mean=41

Standard deviation=7

x=27 and 55

Let, x₁=27 and x₂=55

First calculate z-score for the daily sample of 27 calls.

Formula z-score=(x-mean)/standard deviation.

z-score=(27-41)/7

z-score=-14/7

z-score=-2

So, z-score for the daily sample of 27 calls is -2.

Now, calculate z-score for the daily sample of 55 calls.

z-score=(55-41)/7

z-score=14/7

z-score=2

So, z-score for the daily sample of 55 calls is 2.

We can see that there is a change in z-score of 27 and 55 that is -2 and 2.

By using normal distribution table

The percentage of the daily phone calls between 27 and 55 =

0.9772-0.0228=0.9544

Therefore, 95.44% is the percentage of the daily phone calls between 27 and 55.

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