What is the relationship between a scalene triangle and
the location of its centroid? Explain.
O A. The centroid will always be inside the scalene
triangle, since the centroid is always inside
any type of triangle.
O
O
O
B. The centroid will always be outside the
scalene triangle, since the centroid is always
outside any type of triangle.
C.
The centroid will always be on the scalene
triangle, since the centroid is always on a
triangle with no congruent side lengths.
D.
The centroid will be inside, on, or outside the
scalene triangle, depending on whether it is
acute, right, or obtuse, respectively. The
number of congruent sides does not affect
the location of the centroid.

Answer:

As repetition is not allowed,

For first digit selection, we have 8 choices.

for second digit selection 7 choices.

Similarly, 6 choices for 3rd digit, 5 choices for 4th digit and 4 choices for 5th digit.

Hence, total choices 8*7*6*5*4 = 6720

Step-by-step explanation:

Answer: Multiply the centimeters number by 10.

Step-by-step explanation: There are 10 millimeters in every centimeter.

Answer:

Step-by-step explanation:

In right triangle sum of two angles is 90°

Angle y is exterior angle and equals non-adjacent interior angles

The radius of convergence, r, is infinite (r = ∞). The series converges for all real values of x.

To find the radius of convergence, r, of the series, we can use the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms of a series is L as n approaches infinity, then the series converges if L is less than 1, and diverges if L is greater than 1.

Let's apply the ratio test to the given series. The absolute value of the ratio of consecutive terms is:

|(x - 7)/n * 8n+1 / (x - 7)/(n+1) * 8n| = |(x - 7)/ (x - 7) * 8n / n(n+1)| = |8n / (n^2 + n)| = |8n / n(n + 1)| = |8 / (n + 1)|.

Taking the limit as n approaches infinity, we have:

lim(n→∞) |8 / (n + 1)| = 0.

Since the limit is less than 1, the series converges for all values of x.

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Answer:

y = 2√5.

Step-by-step explanation:

Consider the smallest triangle.

Applying Pythagoras theorem:

y^2 = x^2 + 2^2

The smallest and larger triangle (the one with one side = 8) are similar so we have the proportions :

x/2 = 8/x

---> x^2 = 16

---> x = 4.

Therefore , substituting for x  in the first equation:

y^2 = 4^2 + 2^2

---> y^2 = 20

--->  y = √20

---> y =  2√5.

Answer:

y = 2\(\sqrt{5}\)

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it ) × ( whole hypotenuse )

y² = 2 × (2 + 8) = 2 × 10 = 20 ( take square root of both sides )

y = \(\sqrt{20}\) = \(\sqrt{4(5)}\) = \(\sqrt{4}\) × \(\sqrt{5}\) = 2\(\sqrt{5}\)

INFORMATION:

We know that:

- A cube has an edge of 5 feet

- The edge is increasing at the rate of 2 feet per minute

And we must express the volume of the cube as a function of m, the number of minutes elapsed

STEP BY STEP EXPLANATION:

First, we need to use that the volume of a cube of edge e is given by:

Second, we can find an expression for the variation of the edge in terms of the time. The edge starts at 5 feet, and increases at the rate of 2 feet per minute

Finally, replacing the function for the edge variation in the formula for the volume of a cube

ANSWER:

The expression for the volume of the cube as a function of m is:

Given:

The fees for a day student are $600 a term.

The fees for a boarding student are $1200 a term.

The school needs at least $720000 a term.

To show:

That the given information can be written as \(x + 2y\geq 1200\).​

Solution:

Let x be the number of day students and y be the number of boarding students.

The fees for a day student are \(\$600\) a term.

So, the fees for \(x\) day students are \(\$600x\) a term.

The fees for a boarding student are \(\$1200\) a term.

The fees for \(y\) boarding student are \(\$1200y\) a term.

Total fees for \(x\) day students and \(y\) boarding student is:

\(\text{Total fees}=600x+1200y\)

The school needs at least $720000 a term. It means, total fees must be greater than or equal to $720000.

\(600x+1200y\geq 720000\)

\(600(x+2y)\geq 720000\)

Divide both sides by 600.

\(\dfrac{600(x+2y)}{600}\geq \dfrac{720000}{600}\)

\(x+2y\geq 1200\)

Hence proved.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

\((\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-3}-\stackrel{y1}{(-7)}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-4)}}} \implies \cfrac{-3 +7}{4 +4} \implies \cfrac{ 4 }{ 8 } \implies \cfrac{ 1 }{ 2 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{ \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{(-4)}) \implies y +7 = \cfrac{ 1 }{ 2 } ( x +4) \\\\\\ y+7=\cfrac{ 1 }{ 2 }x+2\implies {\Large \begin{array}{llll} y=\cfrac{ 1 }{ 2 }x-5 \end{array}}\)

Answer:   n > -9

Step-by-step explanation:

this is too simple! just divide both sides by -5!

Answer:

12 chocolate bar cost rs 180

1 chocolate bar cost rs 180÷12

= rs 15

The cost of 30 chocolate bar cost = 15×30

=rs 450

If 12 chocolate bars cost Rs. 180, what would be the cost of 30 chocolate bars?

12 chocolate bars cost = Rs. 180

Cost of 30 chocolate bars = x

12:180 = 30:x

Means = Extremes

180 × 30 = 12 × x

( 3 × 4 = 12, 3 × 10 = 30)

( 4 × 45 = 180)

Therefore, 30 Chocolate Bars Costs Rs.450.

The rectangle which should go in position I is rectangle A.

We are given that;

The rectangles A,B,C and D with numbers

Now,

To take the same the number of side

If we take A on 1 place

F will be on second place

And  B will be on 4th place

Therefore, by algebra the answer will be rectangle A.

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The least number of trips that Ava must make in order to deliver 250 cartons of books is 10 trips.

The least number of trips that Ava must make in order to deliver 250 cartons of books can be found by dividing the total number of cartons by the number of cartons that her car can hold per trip.

This can be written as:
Least number of trips = Total number of cartons / Number of cartons per trip

Substituting the given values into the equation, we get:
Least number of trips = 250 cartons / 26 cartons
Least number of trips = 9.62

Since Ava cannot make a fraction of a trip, we need to round up to the nearest whole number. Therefore, the least number of trips that Ava must make in order to deliver 250 cartons of books is 10.

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Answer:

144

Step-by-step explanation:

Multiply 48 by 3

Age will be 40 years old.

R, in beats per minute, can be approximated by the formulas, where a represents the person's age.

where R= 143 - 0.65a for women.... (1)

and R= 165 - 0.75a for men,..... (2)

So by implementing these two equation we get a = 40

If the sum of ages is X and Y, and the ratio of their ages is p:q, then the age of Y can be calculated using the formula shown below: Y's age = Y's ratio/Sum of ratios x sum of ages The age dependency ratio is the ratio of dependents (people under the age of 15 or over the age of 64) to the working-age population (people between the ages of 15 and 64). The proportion of dependents per 100 working-age population is shown in the data.

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Answer:

c

Step-by-step explanation:

Answer:

7.61 Kg

Step-by-step explanation:

Total mass of all the cheese.

Answer:

8 ounces

Step-by-step explanation:

50×2=100

100-92=8

there ya go

Answer:

19 houses

Step-by-step explanation:

The expected correlation between the supply of a commodity (x) and the price of a commodity (y) depends on the nature of the commodity and market dynamics. However, in general, we would expect a **negative correlation** between the supply of a commodity and its price. Correct option is C.

The law of supply states that as the supply of a commodity increases, assuming demand remains constant, the price tends to decrease. This is because an increase in supply leads to a higher quantity of the commodity available in the market, potentially causing an excess supply or surplus. In such situations, suppliers may lower prices to attract buyers and reduce their inventory.

Conversely, when the supply of a commodity decreases, assuming demand remains constant, the price tends to increase. A decrease in supply results in a lower quantity available in the market, potentially leading to a scarcity or shortage. In such scenarios, suppliers may increase prices to maximize their profits due to the limited availability of the commodity.

It's important to note that real-world markets can be influenced by various factors, including changes in demand, production costs, technological advancements, government policies, and market competition, which can complicate the relationship between supply and price. Nonetheless, the general expectation is that a decrease in supply tends to lead to an increase in price, and an increase in supply tends to lead to a decrease in price, indicating a negative correlation.

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Answer:

$126

Step-by-step explanation:

A deposit adds money into your checking account, so add $150 to $37.

150+37=187

If you write a check, you take money out, so subtract $61 from $187

187-61=126

Your final answer is $126. Hope this helps!

Solution

A hexagonal pyramid is a three-dimensional object with a hexagon-shaped (6 sides) base and six triangular faces originating from each side to a common vertex.

The distance between the center of the hexagonal base and the common vertex is the altitude or height (h) of the pyramid.

The length of the base's side is the base edge or base length (a) of the pyramid.

A 95% confidence interval for the mean weight level based on a sample is (25.504, 25.67)

We know that, the confidence interval is:

\(\bar{x}\pm z\frac{\sigma}{n}\)

where,

\(\bar{x}\) is the sample mean.

z is the critical value.

n is the sample size.

σ (OR s) is the standard deviation for the population.

In this question, we need to calculate the 95% confidence interval for an experiment that found the sample mean temperature for a certain city in August was 101.82, with a population standard deviation of 1.2

The critical value is z = 1.96

We have been given x¯ = 25.6, σ = 0.6 and n = 150

\(\Rightarrow \bar{x}+ z\frac{\sigma}{\sqrt{n} } \\\\= 25.6+ 1.96\frac{0.6}{\sqrt{150} } \\\\=25.67\)

And

\(\Rightarrow \bar{x}- z\frac{\sigma}{\sqrt{n} } \\\\= 25.6- 1.96\frac{0.6}{\sqrt{150} } \\\\=25.504\)

Required interval is (25.504, 25.67)

Thus, the mean weight level( 25.6 grams) is accurate.

Therefore, a 95% confidence interval for the mean weight level based on a sample is (25.504, 25.67)

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There are two possible outcomes where a red counter and a vowel are spun: a)red, A and b) red, E.

To see why, we can make a table listing all the possible outcomes of flipping a red or yellow counter and spinning a spinner labeled A-E:

A B C D E

Red A B C D E

Yellow A B C D E

We can then circle the outcomes that satisfy the condition of spinning a red counter and a vowel: red, A and red, E.

Therefore, the selected outcomes are:

red, A

red, E

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Answer:

less than, it is the answer

As the population (t) grows, the probability of no birthday collision reduces. This is due to the fact that as the population grows, the likelihood of two or more people having the same birthday rises.

The probability of no birthday collision among t people can be computed using the formula:

P(no collision) = 1 x (364/365) x (363/365) x ... x [(365-t+1)/365]

For t = 10, we have:

P(no collision) = 1 x (364/365) x (363/365) x ... x (356/365)
P(no collision) = 0.883
Therefore, the probability of no birthday collision among 10 people is 0.883 or approximately 88.3%.

For t = 25, we have:

P(no collision) = 1 x (364/365) x (363/365) x ... x (341/365)
P(no collision) = 0.568
Therefore, the probability of no birthday collision among 25 people is 0.568 or approximately 56.8%.

For t = 40, we have:

P(no collision) = 1 x (364/365) x (363/365) x ... x (326/365)
P(no collision) = 0.108
Therefore, the probability of no birthday collision among 40 people is 0.108 or approximately 10.8%.

In general, the probability of no birthday collision decreases as the number of people (t) increases. This is because the likelihood of two or more people sharing the same birthday increases as the number of people increases.

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Answer:

honestly sorry what subject that

Answer:

a=11 and b=12

Step-by-step explanation:

1) 106=9b-2 (Angles B and D are congruent)

2)b=12 (Find answer)

3)180-106=74 (Angle C + Angle D= 180)

4)7a-3=74 (Find Angle C)

5) a=11 (Find Answer)

To find an equation of a plane through a given point and perpendicular to a given line, you can follow these steps:

1. Find the direction vector of the given line. This can be done by subtracting the coordinates of any two points on the line. Let's denote this vector as "d".

2. Find the normal vector of the plane. Since the plane is perpendicular to the line, its normal vector will be the same as the direction vector of the line. So, the normal vector of the plane is "d".

3. Use the coordinates of the given point on the plane to find the equation of the plane. Let's denote the coordinates of the point as (x₀, y₀, z₀).

The equation of the plane can be written as:

Ax + By + Cz = D,

where A, B, C are the components of the normal vector "d", and x, y, z are the variables representing any point on the plane.

To find the values of A, B, C, and D, substitute the coordinates of the given point into the equation:

A(x₀) + B(y₀) + C(z₀) = D.

Therefore, the equation of the plane through the given point and perpendicular to the line is:

d₁(x - x₀) + d₂(y - y₀) + d₃(z - z₀) = 0,

where (d₁, d₂, d₃) are the components of the direction vector "d" of the line, and (x₀, y₀, z₀) are the coordinates of the given point.

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Find the equation of the plane passing through the point (−1,3,2) and perpendicular to each of the planes x+2y+3z=5 and 3x+3y+z=0.

The tables is completed as follows

5.1.1

1    8

2   16

4    24

6   48

8    64

12    96

5.1.2

The type of proportion is Direct Proportion

5.2.1

1    8

2   4

4    2

6     1

8    0.5

5.1.3

The type of proportion is Inverse Proportion

Direct Proportion: A direct proportion is a relationship between two variables where an increase in one variable results in a proportional increase in the other variable, and a decrease in one variable results in a proportional decrease in the other variable.

The general formula for a direct proportion is y = kx,

where

k is the constant of proportionality.

Inverse Proportion: An inverse proportion is a relationship between two variables where an increase in one variable results in a proportional decrease in the other variable, and a decrease in one variable results in a proportional increase in the other variable.

The general formula for an inverse proportion is y = k/x,

Joint Proportion: A joint proportion is a relationship between three or more variables where one variable is directly proportional to the product of the other variables.

The general formula for a joint proportion is y = kxy,

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Answer:

the ball reaches a height of 64 feet after 2 sec.

The ball is in the air 4 sec.

Step-by-step explanation:

The ball is following the path of a parabola.  The maximum height is at the vertex of the parabola.

Let (h, k) be the vertex.  h will be the time it takes to reach the maximum height, and k will be that height.

y = \(-16t^{2} + 64t\)

h = -b/2a = 64/(-2)(-16) = 64/32 = 2

k = -16(2)^2 + 64(2)

     -16(4) + 128

     - 64 + 128 = 64

V:  (2, 64)

So the ball reaches a height of 64 feet after 2 sec.

Let \(-16t^{2} + 64t\) = 0       (0 is the height when the balls hits the ground)

-16t(t - 4) = 0

t = 0  or t = 4

The ball is in the air 4 sec.