The equation x2 = 25 has two solutions. This is because both 5 • 5 = 25, and also -5 •
-5 = 25. So, 5 is a solution, and also -5 is a solution. But! The equation x3 = 125 only
has one solution, which is 5. This is because 5 • 5 • 5 = 125, and there are no other numbers you can cube to make 125. (Think about why -5 is not a solution!)
Find all the solutions to each equation.

x^3 = 8

Answer:

Step-by-step explanation:

it is ASA

by definition if two pairs of corresponding angles and the side between them are known to be congruent, the triangles are congruent. This shortcut is known as angle-side-angle (ASA)

Population density refers to the number of people who live in a square mile or kilometer.

It measures the concentration or distribution of a population within a given area and is calculated by dividing the total population by the land area.Population density is a key indicator of how crowded or sparse an area is in terms of human habitation. It provides insights into the level of urbanization, resource allocation, and social dynamics within a region.

High population density typically indicates a greater concentration of people within a specific area, while low population density suggests a more spread-out or rural population distribution. This information is crucial for urban planning, resource management, and understanding the social and environmental impacts of human settlements.

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The margin of error is a measure of the degree of uncertainty associated with the point estimate of a population parameter. Confidence intervals are constructed to estimate the true value of a population parameter with a certain level of confidence.

The margin of error and the width of the confidence interval are related, in that a larger margin of error implies a wider confidence interval.

When constructing a one-sample z-confidence interval to estimate the population proportion, the margin of error increases as the sample size increases. This is because larger sample sizes provide more information about the population and, as a result, the estimate becomes more precise. Conversely, as the sample size decreases, the margin of error increases, making the estimate less precise.

The margin of error also increases as the population proportion approaches 0.50. This is because when p=0.50, the population is evenly split between the two possible outcomes. As a result, more variability is expected in the sample proportions, leading to a larger margin of error.

Finally, the margin of error decreases as the confidence level (1-a) increases. This is because a higher confidence level requires a wider interval to account for the additional uncertainty associated with a higher level of confidence. In conclusion, the margin of error in one-sample z confidence intervals is affected by sample size, population proportion, and confidence level.

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The 95% confidence interval for the proportion of horses with enteroliths that are fed at least two flakes of alfalfa per day is approximately 0.597 to 0.834.

To calculate the confidence interval, we can use the formula for proportions. The point estimate for the proportion is calculated by dividing the number of horses fed two or more flakes of alfalfa (42) by the total sample size (62), resulting in a point estimate of 0.677.

To determine the margin of error, we use the formula:

Margin of Error = Critical Value * Standard Error

The critical value is obtained from the standard normal distribution, corresponding to a 95% confidence level. For a two-tailed test, the critical value is approximately 1.96.

The standard error is calculated using the formula:

Standard Error = √[(p * (1 - p)) / n]

where p is the point estimate and n is the sample size.

Plugging in the values, we find that the standard error is approximately 0.064.

Next, we calculate the margin of error:

Margin of Error = 1.96 * 0.064 ≈ 0.125

Finally, we construct the confidence interval by subtracting and adding the margin of error to the point estimate:

Lower bound = 0.677 - 0.125 ≈ 0.552

Upper bound = 0.677 + 0.125 ≈ 0.80

Therefore, the 95% confidence interval for the proportion of horses with enteroliths that are fed at least two flakes of alfalfa per day is approximately 0.597 to 0.834.

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Step-by-step explanation:

this is how we response to these questions.

Option (a) is correct. There'll be No Solution to the given system of linear equations.

According to the solutions of linear equations, we know the following things,
1. If two intersecting lines are at one common point, the system has only one solution.
2. If two coincidental lines mean both equations give the same line, that means the system has infinitely many solutions.
3. If the lines are parallel to each other, the system will have no solution.

We can see lines are parallel but we can also find whether the given lines are parallel or not by simply finding their slope m.

For Line 1, we have the following data
\($\left(\mathrm{x}_1, \mathrm{y}_1\right)=(0,2)$\)

\($\left(\mathrm{x}_2, \mathrm{y}_2\right)=(3,1)$\)

For slope m of the line 1,
slope m₁ = \(\frac{y_2-y_1}{x_2-x_1}=\frac{1-2}{3-0}=-\frac{1}{3}\)

For Line 2, we have the following data

\($\left(\mathrm{x}_1, \mathrm{y}_1\right)=(0,-1)$\)

\(- $\left(x_2, y_2\right)=(3,-2)$\)

For slope m of line 2,
slope m₂\($=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-(-1)}{3-0-x_1}=-\frac{1}{3}$\)

As the slope of both lines is equal, so lines are parallel to each other, and hence, if lines are parallel so there'll be no solution to the system.
Hence, option (a) is correct.

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Your question was incomplete, the most probably question you asked was:

How many solutions does the system of linear equations represented in the graph have? Coordinate plane with one line that passes through the points (0, 2) and (3, 1) and another line that passes through the points (0, -1) and (3, -2).
(a) No solution
(b) One solution at (−1, 0)
(c) One solution at (0, −1)
(d) Infinitely many solutions

A graph of the relationship between Sam’s age and Matt’s age has been plotted in the graph shown in the image attached below.

An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

In order to solve this word problem, we would assign variables to Sam and Matt's age, and then translate the word problem into algebraic equation as follows:

Translating the word problem into an algebraic equation, we have;

x = 5 + y

Re-arranging the algebraic equation, we have;

y = x - 5

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To approximate the change in volume, we can use the formula for the total differential of the volume:

dV = (∂V/∂r)dr + (∂V/∂h)dh

where (∂V/∂r) and (∂V/∂h) are the partial derivatives of V with respect to r and h, respectively.

Using the formula for the volume of a cone, we have:

∂V/∂r = 2πrh/3

∂V/∂h = πr^2/3

Plugging in the given values, we get:

∂V/∂r = 2π(6.7)(4.17)/3 ≈ 56.13

∂V/∂h = π(6.7)^2/3 ≈ 74.44

Now we can approximate the change in volume:

dV ≈ (∂V/∂r)Δr + (∂V/∂h)Δh

≈ (56.13)(6.7 - 5.9) + (74.44)(4.17 - 4.20)

≈ 60.03

Therefore, the approximate change in volume is dv = 60.03 (rounded to two decimal places).

Note: The units for dv would be cubic units, depending on the units used for r and h.

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Answer:

Are there two you're asking for?

#2: x ≥ 9

#3: x > -2

Step-by-step explanation:

#2 Work:

x - 13 ≥ -4

Step 1: Add 13 to both sides

x - 13 + 13 ≥ -4 + 13

Add -4 and 13 to get 9.

x ≥ 9

#3 Work:

x/2 > -1

Multiply both sides by 2. Since 2 is positive, the inequality direction remains the same

x/2 * 2 > -1 * 2

x > -2

Answer:

21

Step-by-step explanation:

The values for the third side of a triangle must be greater than the difference of the two other sides and less than the sum of the two other sides

12 -8 < x < 12+8

4 < x < 20

The third side cannot be 21

Answer:

21

Step-by-step explanation:

The sum of two sides of a triangle must be greater than the third side

Since two sides and one included angle is equal in △PQS and △PRS, we can conclude that they are congruent under the SAS congruence criterion.

Which means :

▪︎Angle S = Angle S

▪︎PS = PS

▪︎QS = RS

Given :

Measure of segment QS = 6n+3

Measure of segment RS = 4n+11

Thus :

\( = \tt6n + 3 = 4n + 11\)

\( = \tt6n + 3 - 4n = 11\)

\( =\tt 2n + 3 = 11\)

\( = \tt2n = 11 - 3\)

\( = \tt2n = 8\)

\( =\tt n = \frac{8}{2} \)

\(\hookrightarrow\color{plum}\tt n = 4\)

Thus, the value of n = 4

Measure of segment QS :

\( =\tt 6n + 3\)

\( = \tt6 \times 4 + 3\)

\( = \tt24 + 3\)

\(\color{plum}\tt \: \bold{QS = 6n + 3 = \tt\bold{27}}\)

Thus, measure of QS = 27

Measure of RS :

\( =\tt 4n + 11\)

\( =\tt 4 × 4 + 11 \)

\( =\tt 16+11 \)

\(\color{plum}\tt \: \bold{RS = 4n + 11 = \tt\bold{27}}\)

Measure of QR :

\( =\tt 27+27\)

\(\color{plum}\tt \: \bold{QR = 27+27 \tt\bold{=54}}\)

Thus :

▪︎QS = 27

▪︎RS = 27

▪︎QR = 54

Therefore, the correct options are :

▪︎(C) SR = 27

▪︎(D) QR = 54

Answer: I think that the answer is all of the above.

I am not 100% sure if that is completely correct so just pick some answers and see if they are correct.

Step-by-step explanation:

Answer: 130\(\pi\)

Step-by-step explanation:

SA=2\(\pi\)rh+2\(\pi\)r²

Substitute Values:

SA=2\(\pi\)5×8+2\(\pi\)5²

Solve by removing \(\pi\):

2×5×8+2×5² = 130

Plug \(\pi\) back in to get:

130\(\pi\)

Answer:1.00

Step-by-step explanation:I misses u

Answer:

I think its a dollar..

Step-by-step explanation:

Answer:

B. Sometimes

Step-by-step explanation:

When there is an odd set of numbers the mean will ALWAYS be one of the data values.

When there is a even set of numbers the mean will sometimes be one of the data values.

This means only SOMETIMES it can go with date values!

(please give brain i don't normally ask but every time i answer somebody correct i don't get it and i cant lvl up cuz of it  ;-;)

~ LadyBrain

The area of the quadrilateral EFCD is 102 sq. units.

A quadrilateral with at least one pair of parallel sides is called a trapezoid.

Given that, In trapezoid ABCD, the parallel sides AB and CD have lengths 8 and 20 units. The height of the trapezoid is 12 units. Points E and F are midpoints of sides AD and BC, respectively.

We know that, A trapezoid midsegment is parallel to the set of parallel lines in a trapezoid and is equal to the average of the lengths of the bases.

Length of EF = AB + DC / 2 = 28/2 = 14 units.

Since, EF is the midsegment therefore, height of the quadrilateral EFCD = 12/2 = 6 units.

Area of the quadrilateral EFCD = (14 + 20 / 2) x 6 = 102 sq. units.

Hence, the area of the quadrilateral EFCD is 102 sq. units.

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ooof 2 weeks ago, sorry mate, i want the points doe...

Answer:

B

Step-by-step explanation:

a fraction is equal to 0 when the numerator is 0

x - 4 = 0

x = 4

The correct answer is x=4.

Step-by-step explanation:

When the numerator is 0, a fraction is equal to 0.

x - 4 = 0

x = 4

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Answer:

x=-6

Step-by-step explanation:

Answer:

\(h^{-1}\) (x) = 2x - 6

Step-by-step explanation:

let y = h(x) and rearrange making x the subject

y = \(\frac{1}{2}\) x + 3 ( multiply through by 2 to clear the fraction )

2y = x + 6 ( subtract 6 from both sides )

2y - 6 = x

Change y back into terms of x with x = \(h^{-1}\) (x)

\(h^{-1}\) (x) = 2x - 6

Answer:

4 MPH

Step-by-step explanation:

If you ran 1 1/2  miles in 20 minutes than in an hour you have ran 4 1/2 miles

The unit price in dollars per centimeter is 80 cents.

:: Total wire length = 19.5 cm

:: Total amount paid = $15.60

Per unit price = [ (total amount paid) / (total wire length) ]

Per unit price = (15.60 / 19.5) $/cm

Per unit price = 0.8 ($/cm)

And as we know, $1 = 100 cents,

So,

$0.8 = 0.8 x 100 cents = 80 cents.

Therefore, the unit price in dollars per centimeter is 80 cents.

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while if\(R^2 = 1,\) it means that the regression equation explains all of the variation in fare.

To determine what percentage of the total variation in fare is explained by the regression equation or distance, we can calculate the coefficient of determination, denoted by R^2.

\(R^2\) is defined as the proportion of the variance in the dependent variable (fare) that is explained by the independent variable (distance). It is given by:

\(R^2 = Explained variation / Total variation\)

where Explained variation = Sum of squares regression and Total variation = Sum of squares total.

In other words, \(R^2\) measures the goodness of fit of the regression model. It ranges from 0 to 1, with higher values indicating a better fit of the model.

To calculate\(R^2,\) we need to first calculate the sum of squares regression and the sum of squares total. Let's assume we have already obtained the regression equation and calculated the values of the dependent variable (fare) based on the independent variable (distance).

The sum of squares regression is given by:

\(SSR = ∑(ŷ - ȳ)^2\)

where ŷ is the predicted value of fare based on the regression equation, and ȳ is the mean of the actual values of fare.

The sum of squares total is given by:

\(SST = ∑(y - ȳ)^2\)

where y is the actual value of fare, and ȳ is the mean of the actual values of fare.

Once we have calculated SSR and SST, we can calculate \(R^2\) as:

\(R^2 = SSR / SST\)

This will give us the proportion of the total variation in fare that is explained by the regression equation or distance, expressed as a percentage.

Note that if\(R^2 = 0\), it means that the regression equation does not explain any of the variation in fare, while if\(R^2 = 1,\) it means that the regression equation explains all of the variation in fare.

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Answer:

4(0.5-3)=n-0.25(12-8n)

2-12=n-3+2n

-10=-3+3n

-10+3=3n

-7=3n

n=-2.3

Answer: n= -7/3

Step-by-step explanation:

4(0.5 - 3) = n - 0.25(12 -8n)  solve for n .

2 - 12 = n - 3 + 2n  

 -10 = 3n - 3

+ 3           +3

n = -7/3

The mall and bus stand are straight angles.

What is the Location of the angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

What is a Straight angle?

A straight angle in geometry is an angle with a vertex point that is at 180 degrees. In essence, it creates a straight line with sides that face away from the vertex.

Here, In the figure, it is given that:

Gas station/restaurant (vertical angles)

Your house/school (corresponding angles)

Courthouse/bank (alternate exterior angles)

Grocery store/hair salon (alternate interior angles)

Library/park (same side exterior angles)

Movie theater/car wash (same side interior angles)

Movie theater/arcade (linear pair)

Fire Station (obtuse angle)

And, According to the figure,

The mall and the bus stand are straight from each other.

Hence, The angle formed by the bus stand and the mall is a straight angle.

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The triangles in this problem are similar.

Similar triangles share these two features:

For this problem, we have that the side lengths are proportional, as:

3/6 = 4/8 = 5/10 = 0.5.

(same ratio, applying the trigonometric ratios we would find them to have the same angle measures).

However, the triangles in this problem are not congruent, as they have different side lengths.

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Fraction 12 over 2 can be used to calculate the rate per second at which the machine launches the balls

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The x axis label is Time in seconds, and the x axis values are from 0 to 10 in increments of 2 for each grid line.

The y axis label is Number of Balls, and the y axis values from 0 to 60 in increments of 12 for each grid line

A line is shown connecting points on ordered pair (2, 12) and (4, 24) and (6, 36) and (8, 48)

m=24-12/4-2

m=12/2

Hence,  fraction 12 over 2 can be used to calculate the rate per second at which the machine launches the balls

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