If a cube has side lengths of 8 centimeters, what is the volume of the cube? cubic centimeters

Answer:

[tex]\large\boxed{r^2=(x+5)^2+(y-4)^2}[/tex]

Step-by-step explanation:

The equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have diameter endpoints.

Half the length of the diameter is the length of the radius.

The center of the diameter is the center of the circle.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute the coordinates of the given points (-8, 2) and (-2, 6):

[tex]d=\sqrt{(6-2)^2+(-2-(-8))^2}=\sqrt{4^2+6^2}=\sqrt{16+36}=\sqrt{52}[/tex]

The radius:

[tex]r=\dfrac{d}{2}\to r=\dfrac{\sqrt{52}}{2}[/tex]

The formula of a midpoint:

[tex]\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]

Substitute:

[tex]x=\dfrac{-8+(-2)}{2}=\dfrac{-10}{2}=-5\\\\y=\dfrac{2+6}{2}=\dfrac{8}{2}=4[/tex]

[tex](-5,\ 4)\to h=-5,\ k=4[/tex]

Finally:

[tex](x-(-5))^2+(y-4)^2=\left(\dfrac{\sqrt{52}}{2}\right)^2\\\\(x+5)^2+(y-4)^2=\dfrac{52}{4}\\\\(x+5)^2+(y-4)^2=13[/tex]

Answer:

B. 5.2%

Step-by-step explanation:

Total number of tables = 20

Number of tables next to window = 5

Number of tables next to salad bar = 5

Probability that the first customer chooses the window table = 5 out of 20 = [tex]\frac{5}{20}[/tex]

When this table is chosen, the total remaining tables are 19 out of which 4 tables are next to windows.

So, now the probability that a customer will choose a window table = 4 out of 19 = [tex]\frac{4}{19}[/tex]

Since the selection of two customers is independent of each other, the probability that two customers will chose the window table will be the product of probabilities of their individual selections.

Therefore, the probability that the next two customers will choose to sit at the window = [tex]\frac{5}{20} \times \frac{4}{19} = 0.052[/tex]

Thus, the probability that the next two customers will choose to sit at the window is 0.052 or 5.2%

Answer:

5x³

Step-by-step explanation:

As discussed in one of my videos, whenever you divide, you subtract the exponents.

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

Answer:

x=2

Step-by-step explanation:

2(5x+3)=4x+18                       Remove the brackets

10x + 6 = 4x + 18                   Subtract 4x from both sides.

10x - 4x + 6 = 4x-4x + 18      Combine

6x + 6 = 18                            Subtract 6 from both sides

6x + 6 - 6 = 18 - 6                 Combine

6x = 12                                  Divide by 6

6x/6 = 12/6                           Do the division

x = 2

Answer:

The third one, x+(x+1)+(x+2)=-21 because x, x+1 and x+2 are three consecutive numbers.

Answer:

The percentage of the people surveyed that have a cat is 68%

Step-by-step explanation:

we know that

To find the percentage of the people surveyed that have a cat, multiply the given fraction by 100

so

[tex]\frac{17}{25}*100=17*4=68\%[/tex]

Answer:

probability is 50 percent

Step-by-step explanation:

total area= 30000

area of secknd ring=15000

therefore 15000/30000 times 100

equals 50 percent

Answer:

Option D.

Step-by-step explanation:

From he given information, we get

Total area of a dartboard = 30,000 mm²

The area of the second ring = 15,000 mm²

We need to find the probability of landing in that second ring.

[tex]Probability=\dfrac{\text{The area of the second ring }}{\text{Total area of a dartboard}}[/tex]

[tex]Probability=\dfrac{15000}{30000}[/tex]

[tex]Probability=0.5[/tex]

Multiply the probability by 100 to find the percentage.

[tex]Probability=0.5\times 100[/tex]

[tex]Probability=50[/tex]

Hence the correct option is D.

The given function [tex]f(x)=(2x+3)^2(3x+5)^2[/tex] is a polynomial function of degree 4, with a leading coefficient of 36 determined by multiplying the squares of the leading terms of the binomials.

The function[tex]f(x)=(2x+3)^2(3x+5)^2[/tex] is indeed polynomial. To determine the degree and the leading coefficient of a polynomial, we need to expand the given expression. However, without full expansion, we can deduce the degree by adding the exponents of the individual factors since the bases are polynomials of degree 1 (2x+3 and 3x+5).

Each factor is squared, so [tex](2x+3)^2[/tex] has degree 2 and ([tex]3x+5)^2[/tex]also has degree 2. By adding these, we find that the polynomial's degree is 2+2=4. To find the leading coefficient, we consider the leading terms of each binomial which are 2x and 3x. Squaring these and then multiplying them together [tex](2x)^2 * (3x)^2 = 4x^2 * 9x^2,[/tex]we get 36 as the leading coefficient when x is raised to the 4th power. Therefore, the correct answer is: This is a polynomial function of degree 4 with a leading coefficient of 36.

Answer:

Option C. Shape

Step-by-step explanation:

How the data set rises and drops can best be summarized by the shape of the data set.

For example look at the graph attached: Just by looking at the graph you know at which points the graph increases or decreases and how fast it does. To know exact values, working with the equation/data set is better.

Answer:

C. Shape

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]5^{7x-3}=625\\\\5^{7x-3}=5^4\iff7x-3=4\qquad\text{add 3 to both sides}\\\\7x=7\qquad\text{divide both sides by 7}\\\\x=1[/tex]

Answer:

X = 1

Step-by-step explanation:

Answer:

  1.7% compounded continuously

Step-by-step explanation:

The model used for continuous compounding is ...

  f(t) = Pe^(rt)

where P is the principal amount, and r is the interest rate being compounded. Assuming a typo in your given equation, you have ...

  f(t) = 1000·e^(0.017t)

Matching the various parts of the equation, we see that P = 1000 and r = 0.017 = 1.7%.

The balance grows at a continuous rate of 1.7%.

To find the growth rate of the account balance in the given function, we differentiate it to obtain [tex]f'(t) = 1000 × 0.017e^(0.017t)[/tex], which shows that the balance grows at a continuous compound rate of 1.7% per year.

The student's question refers to a savings account where the money is compounded continuously. We are given the function [tex]f(t) = 1000e^{0.017t,[/tex]that models the account balance over time t. To find the rate at which the balance grows, we can differentiate this function concerning time.

The derivative of the function[tex]f(t) = 1000e^{0.017t[/tex] concerning t gives us [tex]f'(t) = 1000 × 0.017e^{0.017t[/tex]. This represents the rate of change of the account balance at any time t, which is also the growth rate. Therefore, the rate at which the balance grows is 0.017 or 1.7% per year.

Answer:

cos x cos (-x) -sin x sin (-x) = 1 ⇒ proved down

Step-by-step explanation:

* Lets revise the angles in the four quadrants

- If angle x is in the first quadrant, then the equivalent angles to it are

# 180 - x ⇒ second quadrant (sin (180 - x) = sin x , cos (180 - x) = -cos x

  tan (180 - x) = -tan x)

# 180 + x ⇒ third quadrant (sin (180 - x) = -sin x , cos (180 - x) = -cos x

  tan (180 - x) = tan x)

# 360 - x ⇒ fourth quadrant (sin (180 - x) = -sin x , cos (180 - x) = cos x

  tan (180 - x) = -tan x)

# -x ⇒fourth quadrant (sin (- x) = -sin x , cos (- x) = cos x

  tan (- x) = -tan x)

* Lets solve the problem

∵ L. H .S is ⇒ cos x cos (-x) - sin (x) sin (-x)

- From the rules above cos x = cos(-x)

∴ cos x cos (-x) = cos x cos x

∴ cos x cos (-x) = cos² x

- From the rule above sin (-x) = - sin x

∴ sin x sin (-x) = sin x [- sin x]

∴ sin x sin (-x) = - sin² x

∴ cos x cos (-x) - sin (x) sin (-x) = cos² x - (- sin² x)

∴ cos x cos (-x) - sin (x) sin (-x) = cos² x + sin² x

∵ cos² x + sin² x = 1

∴ R.H.S = 1

∴ L.H.S = R.H.S

∴ cos x cos (-x) -sin x sin (-x) = 1

In other words, what is y if x is 0.

Look on the graph, a line passes through point, [tex]A(x,y)\longrightarrow A(0,-3)[/tex]

So we can conclude that at that very point the input x was 0 and the output y was -3 therefore,

[tex]\boxed{f(-3)=0}[/tex]

Hope this helps.

r3t40

Answer:

The mistake is that it can be 5.  They forget to include the equals in the less than or equals

Step-by-step explanation:

Start at the inside and work out

quotient of a number and -2

n/-2

difference of -4 and the quotient of a number and -2

-4 - n/-2

product of 3 and the difference of -4 and the quotient of a number and -2

3* (-4 - n/-2)

is at most 5

3* (-4 - n/-2)≤5

The mistake is that it can be 5.  They forget to include the equals in the less than or equals

Answer: C

Step-by-step explanation:

Answer:

Rounded to nearest hundredths is 8.75.

Rounded to nearest tenths is 8.7.

Step-by-step explanation:

Law of sines:

[tex]\frac{\sin(A)}{\text{ side opposite to }A}=\frac{\sin(B)}{ \text{ side opposite to }B}[/tex]

Measure of angle [tex]A[/tex] is 28 and the side opposite to it is [tex]x[/tex].

Measure of angle [tex]B[/tex] is 105 and the side opposite to it is 18.

Plug in to the formula giving:

[tex]\frac{\sin(28)}{x}=\frac{\sin(105)}{18}[/tex]

Cross multiply:

[tex]18 \sin(28)=x \sin(105)[/tex]

Divide both sides by sin(105):

[tex]\frac{18 \sin(28)}{\sin(105)}=x[/tex] is the exact answer.

I'm going to type it in my calculator now:

18*sin(28) / sin(105) is what is going in there.

The output is 8.748589074.

Rounded to nearest hundredths is 8.75.

Rounded to nearest tenths is 8.7.

Answer:

we can use existing theorems to prove new theorems - true

It is true that we can use existing theorems to prove new theorems.

In geometry, new theorems are sometimes dependent on existing theorems.

This means that some new theorems would not exist, if not for the support and the existence of related existing theorems.

Hence, the statement is true

Read more about geometry at:

https://brainly.com/question/25306774

[tex]\huge{\boxed{72}}[/tex]

First, find the total number of apples.  [tex]6*1200=7200[/tex]

Now, multiply this by the probability of picking a rotten apple, which is [tex]\frac{1}{100}[/tex].  This is also the same as dividing by [tex]100[/tex], or moving the decimal point two places to the left.  [tex]7200*\frac{1}{100}=72[/tex]

This means that based on the probability given, [tex]72[/tex] rotten apples will be picked.

Number of rotten apple may be picked are 72.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.

Given

Probability of picking rotten apple in a box is [tex]\frac{1}{100}[/tex].

There are 6 boxes containing 1200 apples each

Number of rotten apple may be picked to be find.

Total number of apples  = [tex]6 \times 1200 = 7200[/tex]

Number of rotten apple may be picked = [tex]7200 \times \frac{1}{100}[/tex]

= 72

Number of rotten apple may be picked are 72.

Find out more information about probability here

https://brainly.com/question/12791270

#SPJ2

The empirical probability of a Great Pyrenees winning the 'Best of Show' at Amboy Kennel Club based on past performances is about 7.143%

The subject at hand is empirical probability, which is calculated by dividing the number of times an event has happened by the total number of outcomes. In this case, the event is a Great Pyrenees winning 'Best of Show' and the total number of outcomes is the total number of dog shows.

According to the data provided, the Great Pyrenees has won 3 times out of a total of 42 dog shows. Therefore, the empirical probability can be calculated as follows:

The empirical probability is then calculated by dividing the number of wins by Great Pyrenees by the total number of dog shows.

Therefore, the empirical probability of a Great Pyrenees winning is 3/42 = 0.07143. So, we could say that there is a 7.143% chance of a Great Pyrenees winning the 'Best of Show' in the future, based purely on historical data.

https://brainly.com/question/1452877

#SPJ12

The empirical probability that the next "Best of Show" winner will be a Great Pyrenees is calculated to be 0.0714 or 7.14%.

Empirical probability is calculated based on observed data. In this case, we want to determine the probability that the next winner of "Best of Show" at the Amboy Kennel Club will be a Great Pyrenees.

Here's the breakdown:

The empirical probability (P) is calculated as:

P(Event) = Number of favorable outcomes / Total number of outcomes.

So, the empirical probability that the next winner will be a Great Pyrenees is:

P(Great Pyrenees) = 3 / 42 = 1 / 14 ≈ 0.0714.

Thus, the empirical probability is approximately 0.0714 or 7.14%.

Answer:

A

Step-by-step explanation:

C is located at (5,3).

If you want to reflect this over the y-axis, you need to have the same distance that (5,3) is to the y-axis on both sides.

If you look at your graph you should see that (5,3) is 5 units a way from the y-axis so when you put it on the other side it should be 5 units a way also.

So the reflection will give you (-5,3)

Answer:

C) (5,-3)

See attached image for explanation.

Answer:

81

Step-by-step explanation:

We know the number is between 50 and 100.  The prime factorization consists of only one prime number, so the number must be a perfect square.  The possible numbers are 64 and 81.

The rectangles that can be made with 64 tiles are:

1×64, 2×32, 4×16, 8×8, 16×4, 32×2, 64×1

The rectangles that can be made with 81 tiles are:

1×81, 3×27, 9×9, 27×3, 81×1

There are 7 rectangles that can be made with 64 tiles.  There are only 5 rectangles that can be made with 81 tiles.  Therefore, the mystery number is 81.

Step-by-step explanation:

The mystery number is 64, sqare number of 8 , the only prime number contributing to it being 2

Being x the mystery number

[tex]50 < x < 100[/tex]

The only two sqare numbers that meet this request are 64 and 81.

Not knowing much about the above mentioned rectangles, 81 being the perfect square number of a perfect square number we would consider 64 the only posible answer

Answer:

x = 1/2

Step-by-step explanation:

Plug in 0 for y

8x + 2(0) = 4

Simplify

8x + 0 = 4

8x = 4

Divide both sides

8x/8 = x

4/8 = 1/2

Simplify

x = 1/2

Answer

x = 1/2

Answer:

X=1/2

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

To find slope here, I'm going to use that slope is rise/run.

I'm going to start at the left dot. How much would I need to go to be on same level as the right point? Up 3.

Now that we are on the same level, how many units right would I need to travel to get to the right point? Right 18.

The slope is 3/18.

You can reduce this to 1/6.

Answer:

A. 1/6

The slope is 1/6.

Step-by-step explanation:

The slope formula is  [tex]\Rightarrow\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{rise}{run}[/tex].

[tex]y_2=6\\y_1=3\\x_2=12\\x_1=(-6)\\[/tex]

[tex]\displaystyle\frac{6-3}{12-(-6)}=\frac{3}{18}=\frac{3\div3}{18\div3}=\frac{1}{6}[/tex]

[tex]\large\textnormal{Therefore, the slope is 1/6.}[/tex]

Answer:

-10 4/64, -.3125, 1/16, 10 51/80, 10 45/48

Step-by-step explanation:

negatives, the larger the number the smaller it is, opposite for positives. 10 45/48 is closer to 11 than 10 51/80

Answer:

x = 4

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve for x

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

(x + 3)² + (4(x + 2))² = 25² ← expand parenthesis on left side

x² + 6x + 9 + 16(x+ 2)² = 625

x² + 6x + 9 + 16(x² + 4x + 4) = 625

x² + 6x + 9 + 16x² + 64x + 64 = 625 ← simplify left side

17x² + 70x + 73 = 625 ( subtract 625 from both sides )

17x² + 70x - 552 = 0 ← in standard form

with a = 17, b = 70, c = - 552

Using the quadratic formula to solve for x

x = ( - 70 ± [tex]\sqrt{70^2-(4(17)(-552)}[/tex] ) / 34

  = ( - 70 ± [tex]\sqrt{4900+37536}[/tex] ) / 34

  = - 70 ± [tex]\sqrt{42436}[/tex] ) / 34

  = - 70 ± 206 ) / 34

x = [tex]\frac{-70-206}{34}[/tex] = - 8.1176....

or x = [tex]\frac{-70+206}{34}[/tex] = 4

However, x > 0 ⇒ x = 4

Hence

x + 3 = 4 + 3 = 7 and

4(4 + 2) = 24

The triangle is a 7- 24- 25 right triangle

For this case we must indicate a fraction equivalent to 9,315.

 We evaluate the fractions:

[tex]\frac {9315} {999} = 9.32432432432\\\frac {931} {99} = 9,40404040404\\\frac {9105} {333} = 27,3423423423\\\frac {935} {111} = 8,42342342342[/tex]

It is observed that the fraction closest to 9,315 is[tex]\frac {9315} {999}[/tex]

If we round 9.315 we have 9.32

If we round[tex]\frac {9315} {999}[/tex] we have 9.32

Answer:

Option A

Answer:

STV = 153 degrees

Step-by-step explanation:

180 - 18 = 162 (angles on a straight line equal 180 degrees)

3q + 15q = 162

18q = 162

q = 162 / 18

q = 9

STV = 15q + 18

       = 135 + 18

       = 153

Hope this helps!

UTV is a straight line, which equals 180 degrees.

This means both angles UTS and STV when added together must equal 180.

3q + 15q +18 = 180

Simplify:

18q +18 = 180

Subtract 18 from both sides:

18q = 162

Divide both sides by 18:

q = 162 / 18

q = 9

Now you have a value for q to solve the angle.

STV = 15q +18

Replace q with 9:

STV = 15(9) +18

Simplify:

STV = 135 + 18 = 153 degrees.

Answer:

(2y-1/y_2)(3y_2/7)

= 2y*(3y_2/7) - (1/y_2)(3y_2/7)

= 6y*y_2/7 - 3/7 = (6y*y_2 - 3)/7

Note: I'm not sure if the 2y-1 was written correctly. If it were intended as the entire thing being a numerator or as 2y_1, this answer is inaccurate.

Answer:

(6y-3)/7

please give me brainliest

Step-by-step explanation:

(2y-1/y²)(3y²/7) first simplify 3y²/y² =3

(2y-1)(3/7) =

(6y-3)/7

Answer:

a. 2 and 50

b. 10 and 10

Step-by-step explanation:

Let's denote the side lengths by x and y.

The area is 100 which means that x*y=100.

The only whole numbers which satisfy this are the following:

2,50

4,25

5,20

10,10

Just go through them one by one and find your answer.

The rectangle with an area of 100 square units and whole number side lengths with the largest perimeter is 50 by 2 with a perimeter of 104 units. The smallest perimeter rectangle possible for the same area is a square measuring 10 by 10, which has a perimeter of 40 units.

We are tasked with finding the dimensions of a rectangle with an area of 100 square units and whole number side lengths that will result in either the largest perimeter or the smallest perimeter.

Largest Perimeter Rectangle

To find the rectangle with the largest perimeter, we should aim for the rectangle to have the longest possible length and the shortest possible width while still maintaining an area of 100 square units. In the extreme case, this could be a rectangle with a length that approaches infinity and a width that is infinitely small, but we are limited to whole numbers. Therefore, the rectangle with the largest perimeter in this scenario would be 50 by 2, resulting in a perimeter of (50+2)*2 = 104 units.

Smallest Perimeter Rectangle

To find the rectangle with the smallest perimeter, we need to look for the most square-like dimensions, as a square has the smallest possible perimeter for a given area. For an area of 100 square units, the side lengths would be 10 by 10, so the perimeter would be 10*4 = 40 units.

Answer:

y = 4x

Step-by-step explanation:

Let x = length of the side = independent variable

Let y = perimeter of the square = dependent variable

y = 4x

Answer: 85 pounds,

Step-by-step explanation: Americans don't use the other things to measure weight.