a small cube with side length 6y is placed inside a larger cube with side length . what is the difference in the volume of the cubes?

The length of the shadow of the second pole is 75 meters, was solved by using the concept of similar triangles.

The concept of similar triangles is based on the idea that if two triangles have the same shape but different sizes, they are called similar triangles. This means that their corresponding angles are equal and their corresponding sides are in proportion.

A triangle is a 2-dimensional geometric shape with three sides, three angles, and three vertices. It is one of the basic shapes in geometry and is used to describe many real-world objects and phenomena.

In the given question,

Length of shadow of first pole / Height of first pole = Length of shadow of second pole / Height of second pole

Substituting the given values, we get:

20√3 / 20 = x / 25√3

Simplifying, we get:

x = (20√3 / 20) * 25√3

x = 25*3

x = 75

Therefore, the length of the shadow of the second pole is 75 meters.

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Answer:

We can use the slope-intercept form of a linear equation to model the balance y after t months, where the slope represents the rate of change of the balance and the y-intercept represents the initial balance.

The initial balance (y-intercept) is the amount Tina borrowed to buy the refrigerator, which we don't know. But we can find the slope using the two data points provided:

Four months: balance = $630

Six months: balance = $520

The change in the balance over the two-month period is:

$520 - $630 = -$110

The slope of the line is the rate of change of the balance per month, which is:

slope = Δy/Δt = (-$110)/(6-4) = -$55/month

Using the point-slope form of a linear equation, we can plug in one of the data points to find the y-intercept:

y - 630 = -$55(t - 4)

y - 630 = -$55t + 220

y = -$55t + 850

Therefore, the equation that models the balance y after t months is:

y = -$55t + 850.

Answer:

surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh; where 'b' is the bottom edge of the base triangle, 'h' is the height of the base triangle, L is the length of the prism and S1, S2 and S3 ...

Surface Area of Triangular Prism - Formula, Examples

Step-by-step explanation:

Triangle ABC is similar to triangle DEF. The tangent of angle A is equal to 5/12 and the sine of angle F is 1/13.

The sine of the angle is the proportion of a right-angled triangle's hypotenuse to its perpendicular.

Triangle ABC and triangle DEF are similar in that their respective sides are proportional and their corresponding angles are equal. As a result, we have:

BC/EF = AC/DF = AB/DE

To determine the ratio AB/BC, we can utilise the tangent of angle A:

Tan(A) = 5/12 = AB/BC

By multiplying both sides by 12, we may make this simpler:

AB/BC = 12 tan(A).

We can now determine the ratio AB/EF using the ratio BC/EF:

AB/DE = BC/EF

This can be rearranged to yield AB/EF:

BC/EF * DE/AB = AB/EF

Due to the similarity of the triangles, we know that BC/EF = 12/13 and can therefore insert this into the equation:

(12/13) * (AB/DE) = AB/EF

Using the formula AB/DE = 5/12 (from above), we can reduce this:

AB/EF = (12/13) * (5/12) = 5/13

Finally, we may calculate the sine of angle F using the sine ratio:

sinning(F) = EF/DF

Using the ratio AB/EF that we recently discovered, we may rephrase this as follows:

sin(F) = (1/AB) * (AB/EF) = (1/AB) * (5/13)

Simplifying and substituting AB = 5k results in:

sin(F) is equal to (1/5k) x (5/13) x 1/(k*13).

We can select k = 1 because we want the response in its simplest form:

sin(F) = 1/13

As a result, 1/13 is the sine of angle F.

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The following equations will have the same value of x as the one provided:

(B) 18x - 9 = 72; (D) 3(6x - 3) = 72; (E) x = 4.5

A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation.

Like 3x + 5 = 15, for instance.

Equations come in a wide variety of forms, including linear, quadratic, cubic, and others.

So, the given equation is:

3/5(30x-15)=72

Now, we have:
3/5 * 30x - 3/5 * 15 = 72

18x - 9 = 72

Using common 3 as an example, we have the following on the left side of the equation:

3(6x-3) = 72

6x-3 = 72/3

6x-3 = 24

6x = 24+3

6x = 27

x = 27/6

x = 9/2

x = 4.5

Therefore, the following equations will have the same value of x as the one provided:

(B) 18x - 9 = 72; (D) 3(6x - 3) = 72; (E) x = 4.5

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Answer:

infinitely many solutions

Step-by-step explanation:

When you put the equations in desmos, the lines are the same therefore it has infinitely many solutions.

Answer:

✔️ c) infinitely many

Step-by-step explanation:

This is impossible because the third column does not depend on the first two columns.

The third column's values are linear combination of the first two columns. the third column of the matrix as a linear combination of the first two columns, This can be seen by the fact that the third column has values which don't fit the pattern of the first two columns. For example, the first value in the third column (21) is not equal to an any linear combination of the first two columns. Thus, it is impossible to write the third column as a linear combination of the first two columns.

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The probability that the arborist will break a saw chain on a day in which he spends 1/2 of his time climbing, 3/8 limbing, and 1/8 felling and bucking is 0.007

We are given the probabilities of an arborist breaking a saw chain in a day's work are 0.004 for a small climbing saw, 0.008 for a medium limbing saw, and 0.04 for a large felling and bucking saw.

The time that he spends on each saw are 1/2 of his time climbing, 3/8 limbing, and 1/8 felling and bucking.

Let us find the probability that he will break a chain when he uses the small climbing saw.

P(small climbing saw) = 1/2P(Break a chain using small climbing saw) = 0.004

Using the medium limbing saw: P(medium limbing saw) = 3/8P(Break a chain using medium limbing saw) = 0.008

Using the large felling and bucking saw: P(large felling and bucking saw) = 1/8P(Break a chain using large felling and bucking saw) = 0.04

Now, to find the probability that he will break a chain on a day, we use the weighted average. Probability is a weighted average because the probability of breaking the saw chain is different for each saw that he uses.

Hence, the probability that he breaks a saw chain when he uses each saw is weighted according to how much time he spends on that saw.

P = P(small climbing saw)* P(Break a chain using small climbing saw) + P(medium limbing saw) * P(Break a chain using medium limbing saw) + P(large felling and bucking saw) * P(Break a chain using large felling and bucking saw)P = (1/2 * 0.004) + (3/8 * 0.008) + (1/8 * 0.04)P = 0.007

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The percentage of rents between $1,300 and $1,720 is 34.13%.

To calculate this, we need to use the z-score formula to convert the rent range into a z-score range. The z-score formula is (x-μ)/σ, where x is the rent range, μ is the mean rent and σ is the standard deviation.

To calculate the lower z-score, the formula becomes (1300-1510)/210 = -1.19.

To calculate the higher z-score, the formula becomes (1720-1510)/210 = 1.14. The z-score of -1.19 to 1.14 corresponds to 34.13% according to the z-table. Therefore, 34.13% of rents are between $1,300 and $1,720.

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The distance from point A to point B is approximately 1363.7 feet.

Using slope concept:

tan(θ1) = h/d

tan(θ2) = h/(d+x), where x is the distance from point A to the boat when Dominic measured the angle of depression at point B.

We can rearrange these equations to solve for h and x:

h = d*tan(θ1)

h = (d+x)*tan(θ2)

d*tan(θ1) = (d+x)*tan(θ2)

d*(tan(θ1)-tan(θ2)) = x*tan(θ2)

d = x*tan(θ2)/(tan(θ1)-tan(θ2))

Substituting the given values, we get:

d = x*tan(32°)/(tan(6°)-tan(32°))

Using a calculator, we can evaluate this expression to get:

d ≈ 1363.7 feet

Therefore, the distance from point A to point B is approximately 1363.7 feet.

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Answer:

(-2,-3)  

Step-by-step explanation:

3x+y=-9                      

-3x    -3x

y=-3x-9

5x-3(-3x-9)=-1

14x+ 27= -1

-27      -27

14x= -28

/14    /14

x=-2

plug in x    

3(-2)+y=-9  

    -6+y=-9

     +6    +6

          y=-3

Answer:

0

Step-by-step explanation:

-2(-3)+27÷(-3)+3

6-9+3

0

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

It will take Stella 24 days to finish all the oatmeal in the container if she eats 1/4 cup every day for breakfast.

The container has 6 cups of oatmeal and Stella eats 1/4 cup every day for breakfast.

To find the number of days it will take Stella to finish all the oatmeal, we can use the formula:

Total amount of oatmeal in the container = 6 cups

Amount of oatmeal consumed by Stella per day = 1/4 cup

Therefore, it will take Stella 24 days to finish all the oatmeal in the container if she eats 1/4 cup every day for breakfast.

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An American rapper, is known for his poetic, and complex lyrical style.

Kendrick Lamar is a highly talented storyteller, however, some people may not like his music when he raps quickly as it can be unpleasant.What are the aspects of Kendrick Lamar's music?

An American rapper, is known for his highly poetic, socially conscious, and complex lyrical style.

However, his musical talent has been highly praised by critics and   audiences alike.

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The set of ordered pairs (2,1), (3,3), (4,6), (2,3) is NOT a function because the input value of 2 corresponds to both the output values of 1 and 3.

For a set of ordered pairs to be a function, each input (x-value) must correspond to only one output (y-value). Therefore, if there exists an input (x-value) that corresponds to more than one output (y-value), then the set of ordered pairs is NOT a function.

Let's check each set of ordered pairs:

Therefore, the set of ordered pairs that is NOT a function is (2,1), (3,3), (4,6), (2,3).

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Answer:

negative linear association

Step-by-step explanation:

The best description of the association between life expectancy and infant mortality rate in the given graph is option B. Countries with higher infant mortality rates tended to have shorter life expectancies.

The negative linear association between life expectancy and infant mortality rate in the attached graph,

Life Expectancy,

Life expectancy refers to the average number of years a person is expected to live from birth.

In the graph, life expectancy is represented on the vertical axis (y-axis).

Infant Mortality Rate,

Infant mortality rate refers to the number of deaths of infants under one year of age per 1,000 live births.

In the graph, the infant mortality rate is represented on the horizontal axis (x-axis).

Negative Linear Association,

A negative linear association means that as one variable increases, the other variable tends to decrease at a consistent rate.

here, as the infant mortality rate increases (moving right on the x-axis), the life expectancy tends to decrease (moving down on the y-axis).

Interpretation,

Looking at the graph, we can see that countries with higher infant mortality rates are positioned towards the right side of the graph,

and they tend to have shorter life expectancies, which are positioned towards the bottom of the graph.

Conversely, countries with lower infant mortality rates are positioned towards the left side of the graph, and they tend to have longer life expectancies,

which are positioned towards the top of the graph.

Implication,

The negative linear association in the graph indicates that countries with higher rates of infant mortality are likely to have lower life expectancies.

This is because higher infant mortality rates often indicate poorer healthcare systems, lower living standards,

and other factors that can impact life expectancy negatively.

Therefore, based on the graph's trend, we can conclude that the statement B is the best description of the association between life expectancy and infant mortality rate.

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The above question is incomplete , the complete question is :

The Graph Below Shows The Relationship Between Life Expectancy And Infant Mortality Rate In A Random Sample Of Countries.

Which statement is the best description of the association between these variables? Choose all that apply.

A. Countries with higher infant mortality rates tended to have longer life expectancies.

B. Countries with higher infant mortality rates tended to have shorter life expectancies.

C. There is no clear relationship between infant mortality rates and life expectancy.

Attached graph.

Answer:

[tex]y=3cos(3\pi x)+4[/tex]

Step-by-step explanation:

[tex]f(x)=cos(x)\\[/tex]

[tex]A(f(Bx+C)+D)[/tex]

The outside constants, A & D stretch and shift vertically. The inside constants, B & C stretch and shift horizontally. B & C work oppositely, basically multiplying by B stretches by a factor of 1/B and similarly adding C shifts f(x) horizontally to the left.

[tex]f(x)=cos(x) \text{ The function which we are transforming}\\\text{It currently has a amplitude of 1, time period of $2\pi$ and mid line at $y=0$}[/tex]

[tex]A=3 \text{ As we want to stretch it by 3 units vertically.}\\\text {To find B:}\\T' = T*(1/B)\\\text{Where $T'$ is new time period and T is existing time period}\\2/3=2\pi*(1/B)\\B=3\pi\\\text{C is not needed}\\D=4 \text{ To shift function by 4 units up}[/tex]

I hope this helps

Answer:

To create a line plot for this data, we can first convert all the fractions to a common denominator, such as eighths:

Monday: 6/8 of an hour

Wednesday: 4/8 of an hour

Friday: 2/8 of an hour

Sunday: 4/8 of an hour

Then, we can draw a number line with tick marks representing each day of the week and plot a dot for each amount of time spent working out:

0         1         2         3         4

|---------|---------|---------|---------|   <- Number line

         .     .

       .             .

   .                     .

.                             .

To find out how much time June should work out each day to spend an even amount of time working out, we can first find the total amount of time she spent working out:

6/8 + 4/8 + 2/8 + 4/8 = 16/8 = 2 hours

Since there are four days she worked out, to find out how much time she should work out each day, we can divide the total time by four:

2 hours ÷ 4 = 0.5 hours

Therefore, June should work out for 0.5 hours, or 30 minutes, each day to spend an even amount of time working out.

Since mXOY = mWOV, we can form the following equations so, m--XZ = m--ZV.

An equation is a mathematical statement that states the equality of two expressions. It usually consists of two terms, with an equals sign between them, representing the relationship between the terms. Equations are often used to describe relationships between variables, such as in physics and chemistry, and can be used to calculate unknown values.

Proof:

Since mXOY = mWOV, we can form the following equations:

m--YZ = m--ZW (Given)

Subtract both sides of the equation by m to get:

YZ = ZW

Then, multiply both sides of the equation by X to get:

XZ = XW

Now, substitute Y for V and W for V in the equation to get:

XZ = ZV

Finally, subtract both sides of the equation by m to get:

m--XZ = m--ZV

Therefore, m--XZ = m--ZV.

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The value of any number raised to the power of 0 is always 1, irrespective of the value of x, as long as x is not 0. So, x^0 = 1.

Answer:

1 ft per 4 seconds

120 seconds

72 seconds

Step-by-step explanation:

In response to the stated question, we may state that The coordinates of equation triangle ABC in green are: A" (-3,-3); B" (-2,1); C" (1,-4)

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

The x-axis is horizontal and the y-axis is vertical.

     4   B(−2, 4)

     |   *

     |  / \

     | /   \

     |/_____\

    A(−3, 0) C(1, −1)

     4   B(−2, 4)         C'(4, 1)

     |   *                *

     |  / \              / \

     | /   \            /   \

     |/_____\-3, 0    -1, 1 A'(0, -3)

    A(-3, 0) C(1, −1)   B'(4, -2)

A' (-3,0) ➜ (0,-3)

B' (-2,4) ➜ (4,-2)

C' (1,-1) ➜ (-1,1)

     1   C(1, −1)         C"(1, -4)

     |   *                *

     |  / \              / \

     | /   \            /   \

     |/_____\-3, -3    -2, 1 A'(-3, -3)

    A(-3, 0) B(-2, 4)   B'(-2, 1)

A' (-3,0) ➜ A" (-3,-3)

B' (-2,4) ➜ B" (-2,1)

C (1,-1) ➜ C" (1,-4)

The coordinates of triangle ABC in green are:

A" (-3,-3)

B" (-2,1)

C" (1,-4)

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The probability that Mark selects a car key or door key from the key ring is 0.3 or 30%.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory provides a framework for understanding random events and the laws of chance, and it is an important tool for modeling and simulating complex systems.

Calculating the probability that he selects a car key or door key :

In this context, we are asked to find the probability of Mark selecting a car key or door key from the key ring. To calculate this probability, we need to first determine the total number of keys on the key ring and then count the number of car keys and door keys.

Total number of keys = 10

Number of car keys = 2

Number of door keys = 1

The probability of selecting a car key or door key can be found by adding the probability of selecting a car key to the probability of selecting a door key. Since there is only one door key and two car keys, the probability of selecting a car key is higher, and we can simplify the calculation by finding the probability of selecting a car key and then adding the probability of selecting a door key that hasn't already been selected.

Probability of selecting a car key = 2/10 = 0.2

Probability of selecting a door key = 1/9 (since one key has already been selected) = 0.1111...

Therefore, the probability of Mark selecting a car key or door key from the key ring is 0.2 + 0.1111... ≈ 0.3 or 30%.

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Answer:

“change” or “the change”

Step-by-step explanation:

Figure E is a rotated and reflected version of Figure D that has been shifted to the right and up as a result of this transformation sequence.

The sequence transformation (which may be dependent on n). This is known as a linear sequence transformation. Nonlinear sequence transformations are nonlinear sequence transformations.

We can use the following transformations to map Figure D onto Figure E:

Figure D should be translated 4 units to the right and 1 unit up.

Figure D should be rotated 90 degrees clockwise around the origin.

Cross the y-axis with the resulting figure.

This transformation sequence results in Figure E, which is a rotated and reflected version of Figure D that has been shifted to the right and up.

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Answer:14

Step-by-step explanation: I added 3 + 5 + 2 + 4 + 1 which gave me 15 and her daughter took 1 fruit so it is 14 fruits left

The expression that best represents the total cost of the charter bus for the field trip is 12n + 50

The total cost of the charter bus for the field trip consists of a $50 reservation fee and an additional $12 per student.

If n represents the number of students going on the field trip, then the expression for the total cost can be written as:

Total cost = 12n + 50

This expression represents the variable cost of the charter bus, which depends on the number of students going on the field trip.

The fixed cost of $50 is added to the variable cost to give the total cost.

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The intersection points of the two conics are therefore[tex](1 + √14, -1 + √14)[/tex]and [tex](1 - √14, -1 - √14).[/tex]Hence, the two conics intersect at two points.

The point or points of intersection and the number of places the following 2 conic intersect is to be determined. The system over the real numbers for [tex]x² + y² = 34 and 3x - 3y = 6[/tex] is to be solved.

To determine how many points the following 2 conic intersect at, the two equations must be solved simultaneously. The points of intersection can then be determined by substituting the value of x or y into the other equation and solving for the remaining variable.The equation 3x - 3y = 6 is the equation of a straight line. Solving the equation for y, [tex]y = x - 2[/tex].

So the line passes through the point (0, -2) and (2, 0) on the x-axis. Now, substitute the value of y into the equation x² + y² = 34 to get[tex]x² + (x - 2)² = 34[/tex], expanding this gives 2x² - 4x - 26 = 0, which simplifies to x² - 2x - 13 = 0.The solution to the quadratic equation [tex]x² - 2x - 13 = 0[/tex] is given as[tex]x = 1 + √14, 1 - √14[/tex]. The corresponding value of y for each x can be calculated by substituting the value of x into the equation y = x - 2.

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Answer:

126305.622 is the town's population after 2 years on percentage  7.4.

Step-by-step explanation:

Answer:

you will asume this rate is constant. so put it into y=mx+b form y=1.74*2+109,500

Step-by-step explanation:

From the given information provided, the value of fog(3) and fog(4) is 0.971 and 27/40 respectively.

a) To find fog(3), we first need to find g(3) and then evaluate f(g(3)).

To find g(3), we substitute x=3 into the formula for g(x):

g(3) = (5(3) - 2)/(3 + 2) = 13/5

Now, we can evaluate f(g(3)) by substituting g(3) into the formula for f(x):

f(g(3)) = f(13/5) = 3(13/5)² / (4(13/5)² + 4) = 0.971

Therefore, fog(3) = 0.971.

b) To find fog(4), we follow the same process. First, we find g(4):

g(4) = (5(4) - 2)/(4 + 2) = 18/6 = 3

Now, we can evaluate f(g(4)) by substituting g(4) into the formula for f(x):

f(g(4)) = f(3) = 3(3)² / (4(3)² + 4) = 27/40

Therefore, fog(4) = 27/40.

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