The number of random samples (without replacement) of size 3 that can be drawn from a population of size 5 is ___

Final answer:

The possible side lengths of a triangle, according to the Triangle Inequality Theorem, must adhere to the principle that the sum of any two sides must be greater than the third side. Option B, with side lengths of 4 cm, 8 cm, and 10 cm, fulfills this requirement and forms a valid triangle.

Explanation:

The question asks which set of side lengths can form a triangle. In order to determine the possible side lengths of a triangle, we must use the Triangle Inequality Theorem. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Now, let's evaluate the options provided:

A. 3 cm, 5 cm, 9 cm: Here, 3 + 5 is not greater than 9, so these sides do not satisfy the theorem.

B. 4 cm, 8 cm, 10 cm: In this case, 4 + 8 is greater than 10, 8 + 10 is greater than 4, and 4 + 10 is greater than 8, satisfying the inequality.

C. 6 cm, 9 cm, 17 cm: For these measurements, 6 + 9 is less than 17, failing to meet the criteria.

D. 8 cm, 10 cm, 18 cm: Here too, 8 + 10 is less than 18, thus not compliant.

Hence, the correct answer is B. 4 cm, 8 cm, 10 cm, as these are the only side lengths that satisfy the Triangle Inequality Theorem and can form a triangle.

Final answer:

The volume of a cube with side length 2.5 units can be calculated using the formula V = s³, resulting in a volume of 15.625 cubic units.

Explanation:

To find the volume of a cube with a side length of 2.5 units, we can use the formula for the volume of a cube, which is V = s³, where V represents volume and s represents the side length of the cube.

Using this formula:

s = 2.5 units

V = 2.5³ = 2.5 × 2.5 × 2.5 = 15.625 units³

So, the volume of the cube is 15.625 cubic units.

Answer:

y ≤ x – 4  will be the linear inequality is represented by the graph.

Step-by-step explanation:

Given : graph.

To find :  Linear inequality equations .

Solution : We have given graph,

We can see from graph here y intercept is -4 and solid line shaded below ,

Since , For shaded below graph we can say equation have less than equal sign. and y intercept -4.

Therefore, y ≤ x – 4  will be the linear inequality is represented by the graph.

Answer:

B

Step-by-step explanation:

because the line goes through -4 evenly

K is the middle letter of the triangle JKL so it would be the same as the middle letter of the triangle EFG

so K = F

 F = 62 degrees, so K = 62 degrees

Both triangles are congruent so the corresponding angle will be the same K is the mid-latter of JKL thus K will be the same as the mid-later of EFG therefore, K=F=62°.

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.

As per the given question,

△EFG≅△JKL

Now it is known that all corresponding angles in two congruent triangles are the same.

Now K is the mid-latter of JKL thus K will be the same as the mid-later of EFG.

Mid latter of EFG = F

Given that m∠F = 62°

Therefore, m∠K = m∠F = 62°

Hence "Both triangles are congruent so the corresponding angle will be the same K is the mid-latter of JKL thus K will be the same as the mid-later of EFG therefore, K=F=62°".

To learn more about congruence,

https://brainly.com/question/12413243

#SPJ5

Answer:

constant of variation(k) is, 250.

[tex]y = \frac{250}{x}[/tex]

Step-by-step explanation:

The inverse variation says that:

[tex]y \propto \frac{1}{x}[/tex]

then, the equation is in the form of :

[tex]y = \frac{k}{x}[/tex]        ....[1] where, k is the constant of variation

As per the statement:

Suppose that y varies inversely with x.

then,

by definition of inverse variation we have;

[tex]y = \frac{k}{x}[/tex]

When x = 2.5 and y = 100 then

Substitute these in [1] we have;

[tex]100 = \frac{k}{2.5}[/tex]

Multiply 2.5 both sides we have;

[tex]250 = k[/tex]

or

k = 250

⇒[tex]y = \frac{250}{x}[/tex]

Therefore, the constant of variation is, 250 and the equation we get [tex]y = \frac{250}{x}[/tex]

Answer: 24.52%

Step-by-step explanation: Convert times into decimals by dividing the seconds by 60. (7:45 = 7.75 | 5:51 = 5.85) Subtract 7.75 and 5.85 which equals 1.9

1.9/7.75 = 0.2451612903

Rounded to 0.2452 = 24.52%

Final answer:

The most likely function of the cells in this pulse-chase experiment is to synthesize, process, and degrade or secrete proteins. This is deduced from the movement of radioactivity from the ER to the Golgi apparatus, then to lysosomes and the extracellular space over time.

Explanation:

Based on the data provided, which stem from a pulse-chase experiment, we can infer the most likely function of the cells. Initially, radioactivity is high in the endoplasmic reticulum (ER), indicating that newly synthesized proteins, likely labeled with radioactive amino acids, are present there.

As time progresses, radioactivity moves to the Golgi apparatus, implying that proteins are being processed and modified.

Eventually, the highest levels of radioactivity are found in the lysosomes and then the extracellular space, suggesting that these proteins are being degraded and secreted respectively.

This sequence of events indicates that the cells are involved in synthesizing, processing, and secreting proteins, with some being targeted for degradation in lysosomes.

This is a fundamental part of the protein secretory pathway in cells. The data reveal the dynamic movement of molecules within the cell, reflecting the pathway from synthesis to secretion or degradation.

Answer:

Ben's house is at point -2

Step-by-step explanation:

Given that Anna lives 2.5 miles to the east of her school, and Ben lives 2 miles to the west of the same school

When Anna draws a map with a number line connecting her house to Ben’s house, with school marked as 0 then to the east would be +2.5

Since Ben lives 2 miles to the west, Ben would be marked as negative -2.

(West denotes negative in number line)

So answer is Ben's house is at point -2

Ben's house is at the point -2 on the map of number line.

A number line is pictorially represented as a horizontal straight line where numbers are placed at equal distance. Usually integers are placed in the number line with negative numbers placed to the left of 0 and positive numbers placed to the right of 0.

Number lines are used in performing basic operations in mathematics such as addition, multiplication, subtraction and division.

Here, it is given that Anna lives 2.5 miles to the east of her school and Ben lives 2 miles to the west of the same school.

So school is a common point here with respect to which both of their distance to house are marked.

On the number line school is at 0.

Anna's and Ben's house lies two opposite sides from the school.

So if one of their houses is at the positive side, the house of other one's will be at the negative side.

Given that, Anna's house is at positive side at the point +2.5.

Then clearly Ben's house will be at the negative side and the point will be -2 since it is 2 miles away from the school.

Hence, Ben's house will be at the negative side of the number line at point -2.

To learn more about Number Line, click on the link given below:

https://brainly.com/question/13425491

#SPJ2

The equation of the horizontal line that passes through the point ( -2 , 5 ) is

y = 5

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , let the point be A ( x₁ , y₁ )

The value of A ( x₁ , y₁ ) = A ( -2 , 5 )

Now , the slope of the line m is given by

Since , the line is a horizontal line , the slope of the line m = 0

Slope m = 0

Now , the equation of line is given by the equation

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 5 = 0 ( x + 2 )

y - 5 = 0

Adding 5 on both sides of the equation, we get

y = 5

Therefore, the value of A is y = 5

Hence ,

The equation of the horizontal line that passes through the point ( -2 , 5 ) is y = 5

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ5

the interior angles of a triangle need to equal 180 degrees

Answer is B

Answer:

180 is the answer

The slope of line containing the points (-2, 5) and (4, -4) is [tex]\frac{-3}{2}[/tex].

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

[tex]m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

Where,

m is the slope of line.

[tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2},y_{2})[/tex] are the two points.

According to the given question.

We have two points (-2,5) and (4,-4).

Therefore, the slope of the line containing the points (-2, 5) and (4, -4) is given by

[tex]m = \frac{-4-5}{4-(-2)}[/tex]

⇒[tex]m = \frac{-9}{6}[/tex]

⇒[tex]m =\frac{-3}{2}[/tex]

Hence, the slope of line containing the points (-2, 5) and (4, -4) is [tex]\frac{-3}{2}[/tex].

Find out more information about slope of the line here:

https://brainly.com/question/14511992

#SPJ2

Answer:

84,000,000

Step-by-step explanation:

To find the number of nickels in the piggy bank, you can set up a system of equations based on the total number of coins and the total value of all the coins. By solving this system, you can determine the number of nickels.

To find the number of nickels in the piggy bank, we need to set up a system of equations. Let's use n to represent the number of nickels and d to represent the number of dimes.

The total value of the nickels can be calculated by multiplying the number of nickels (n) by the value of each nickel, which is $0.05. So, the value of the nickels is 0.05n.

The total value of the dimes can be calculated by multiplying the number of dimes (d) by the value of each dime, which is $0.10. So, the value of the dimes is 0.10d.

We can set up two equations based on the given information:

Equation 1: n + d = 33 (total number of coins)

Equation 2: 0.05n + 0.10d = 2.40 (total value of all coins)

Now we can solve this system of equations to find the number of nickels (n).

Multiplying Equation 1 by 0.05 gives us: 0.05n + 0.05d = 1.65

Subtracting Equation 2 from this gives us: 0.05d - 0.10d = 1.65 - 2.40

Simplifying, we get: -0.05d = -0.75

Dividing both sides by -0.05, we find: d = 15

Substituting this value back into Equation 1, we get: n + 15 = 33

Subtracting 15 from both sides, we find: n = 18

Therefore, there are 18 nickels in the piggy bank.

To find the number of nickels in the piggy bank, set up a system of equations and solve. There are 18 nickels in the piggy bank.

To find the number of nickels in the piggy bank, you need to set up a system of equations based on the information given. Let's assume that the number of nickels is represented by 'n' and the number of dimes is represented by 'd'. From the problem, we know that there are 33 coins in total, so we can write the equation 'n + d = 33'. We also know that the value of the nickels, in cents, is 5n and the value of the dimes, in cents, is 10d. Since the total value of the coins is $2.40, we can write the equation '5n + 10d = 240'. Now we can solve this system of equations to find the number of nickels.

To solve the system of equations, we can use the substitution method. Rearrange the first equation to get 'n = 33 - d', and substitute this expression for 'n' in the second equation: '5(33 - d) + 10d = 240'. Simplify the equation to get '165 - 5d + 10d = 240'. Combine like terms to get '5d = 75'. Divide both sides by 5 to get 'd = 15'. Substitute this value of 'd' back into the first equation to find 'n': 'n + 15 = 33', 'n = 18'.

Therefore, there are in the piggy bank.

Answer:

You should change the direction of the sign.

Step-by-step explanation:

This is a general rule for all inequalities. Whenever multiplying or dividing by a negative, always change the direction of the sign