The process of eliminating a radical from the denominator of a radical expression is called

The given statement is FALSE.

If one or more data items are much greater than the other items, the median, rather than the mean, is more representative of the data.

When one or more data items are much greater than the other items, these extreme values can greatly influence the mean.

When you have a skewed distribution, the median is a better measure of central tendency than the mean

The median and mean can only have one value for a given data set. The mode can have more than one value

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There are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.

In order to determine which treatment effects differ significantly from others, we need to make pairwise comparisons between all possible pairs of treatment groups. Let's consider an example with four treatment groups labeled A, B, C, and D.

To determine which treatment effects differ significantly from others, we need to compare the mean scores of each treatment group with the mean scores of every other treatment group. This means we need to make the following pairwise comparisons:

A vs B

A vs C

A vs D

B vs C

B vs D

C vs D

Therefore, there are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.

It's worth noting that when making multiple pairwise comparisons, there is an increased risk of making a Type I error (i.e., rejecting the null hypothesis when it is actually true) due to the multiple testing problem. To control for this, researchers may choose to adjust the significance level or use methods such as the Bonferroni correction to adjust the p-values of the individual tests.

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Rose sold 53.6 pretzels.

P x ? + W = 135

2.50 x 53.6 + 1.00 = 135

No, Lydia's assertion that δSTU is a right triangle is not correct.

A right triangle is a triangle in which one of the angles measures 90 degrees (a right angle). To determine if δSTU is a right triangle, we need to examine the angles formed by the given coordinates.

Using the coordinates:

s (-3, 0)

t (0, -3)

u (3, -3)

We can calculate the slopes of the lines formed by connecting these points to see if any of them are perpendicular (indicating a right angle).

The slope of the line connecting points s and t is:

m(st) = (y₂ - y₁) / (x₂ - x₁) = (-3 - 0) / (0 - (-3)) = -3/3 = -1

The slope of the line connecting points s and u is:

m(su) = (y₂ - y₁) / (x₂ - x₁) = (-3 - 0) / (3 - (-3)) = -3/6 = -1/2

The slope of the line connecting points t and u is:

m(tu) = (y₂ - y₁) / (x₂ - x₁) = (-3 - (-3)) / (3 - 0) = 0/3 = 0

None of the slopes calculated are perpendicular to each other, meaning none of the angles formed by the given coordinates are 90 degrees. Therefore, δSTU is not a right triangle.

In summary, Lydia's assertion that δSTU is a right triangle is incorrect because the angles formed by the given coordinates do not include a 90-degree angle.

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The given velocity components are:

u = 2xt - 3xyz + 4xyw = 3x - 5yzt + yz

To satisfy the continuity equation, the third velocity component must be of the form

v = -ux - wy

Thus,v = -2xt + 3xyz - 4xy (from u)v = -3x + 5yz t - yz (from w)

The third velocity component

v = -2xt + 3xyz - 4xy - 3x + 5yz t - yz

= -2xt + 3xyz - 4xy - 3x + 5yz (t - 1)

The velocity of the fluid particle is given by,

v = (u, v, w) = (2t, -2t + 3z, 3 - 5zt + y)at (1, 0, 1) and t = 1 (last digit),v = (2, -2, -2)

The acceleration of the fluid particle is given by,

a = (at, av, aw)

= (∂u/∂t, ∂v/∂t, ∂w/∂t)at (1, 0, 1) and t = 1 (last digit),a = (2, 3, -5)

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The height of the jet is approximately 6603.6 meters.

Let AB be the line joining the two observation points A and B and let C be the position of the jet.

Let AC = h be the height of the jet above the horizontal line AB.

From A and B, respectively, angles of elevation of the jet are 43° and 62°. Let D be the foot of the perpendicular from C to AB.

Since angle of elevation of the jet from point A is 43°,

angle ADC = 90° - 43°

angle ADC = 47°.

Similarly,

angle ABD = 90° - 62°

angle ABD = 28°.

Now in triangle ADC, we have

tan 47° = h / AD

=> AD = h / tan 47°.

In triangle ABD, we have

tan 28° = h / BD

=> BD = h / tan 28°.

Adding these two, we have:

AB = AD + BD

AB = h / tan 47° + h / tan 28°

Applying the formula of the distance between two points in terms of their coordinates, we have:

AB = sqrt((28.5)² + h²)

Putting the two expressions of AB equal to each other and solving for h, we get:

h / tan 47° + h / tan 28° = sqrt((28.5)² + h²)h * (1 / tan 47° + 1 / tan 28°)

= sqrt((28.5)² + h²)h² * (1 / tan 47°² + 1 / tan 28°² + 2 / (tan 47° * tan 28°)))

= (28.5)² * tan² 47°(1 / tan 47°² + 1 / tan 28°² + 2 / (tan 47° * tan 28°)))h²

= (28.5)² * tan² 47° / (1 / tan 47°² + 1 / tan 28°² + 2 / (tan 47° * tan 28°)))h

= 6603.6 meters (approx.)

Therefore, the height of the jet is approximately 6603.6 meters.

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Answer:

x = 4

Step-by-step explanation:

30x = 29x + 4

subtract 29x from both sides

x = 4

Answer:

38 marbles

Step-by-step explanation:

56 x 1/4 = 14

56 x 3/7 = 24

14 + 24 = 38

Answer:

8/9

Step-by-step explanation:

3/6 + 7/ 18

Make the denominator common by finding the LCM = 18

Multiply 3 by 3

Therefore sum = 3*3 + 7/ 18

sum = 9+7/18

sum = 16/18

=> 8/9

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Answer:

Distance ≈ 14.8

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 4, 6) and (x₂, y₂ ) = (3, - 7)

Hope this helps!!!!

Answer:

its the first one...

Step-by-step explanation:

keep change flip

keep the first fraction

change the symbol from divide to multiply

flip next fraction so it would be 4 over 3

then multiply straight across

DONT forget the negative tho

Hope this helped!

Answer:

Lulu spent $151.

Step-by-step explanation:

67 + 35 + 49 = 151

Answer:

Lulu spent 151$

Step-by-step explanation:

To answer this question you would have to add 67$ then 35$ and lastly 49$ which leaves you with 151$, so Lulu spent 151$. :)

67+35+49 = 151$

To find the volume of the figure.

volume of the figure=volume of the cone+volume of the rectangle prism.

volume of the figure=72+81=153 inch cube.

Answer:

A) 4 Hours (of running)

B) 5 Hours (of biking)

Step-by-step explanation:

So Suzette ran and biked for a total of 80 miles,

and she did all of that in 9 hours.

Let x equal the total hours of Suzette ran and let y equal the total hours of Suzette biked.

Therefore:

\(x+y=9\)

This represents the total hours. We know that the hours she had ran and biked totals 9. Thus, x plus y must equal 9.

And also:

\(5x+12y=80\)

The 5x represents the miles she had ran in x hours, while the 12x represents the miles she had biked in y hours. All together, they must equal 80 miles total.

Therefore, our system is:

\(x+y=9\\5x+12y=9\)

We can solve this using substitution. First, subtract x from the top equation:

\(x+y=9\\y=9-x\)

Now, substitute the y into the second equation:

\(5x+12y=80\\5x+12(9-x)=80\)

Distribute:

\(5x+108-12x=80\)

Combine like terms:

\(-7x+108=80\)

Subtract 108 from both sides:

\((-7x+108)-108=(80)-108\\-7x=-28\)

Divide both sides by -4:

\(x=4\)

Therefore, Suzette ran for a total of 4 hours.

Since she biked and ran for a total of 9 hours, she must have biked for 9-4 or 5 hours.

Checking:

4 hours of running plus 5 hours of biking does indeed equal 9 hours total:

\(4(5)+5(12)=20+60=80\)

So by running 5mph for 4 hours and by biking 12mph for 5 hours, she did indeed reach a total of 80 miles.

Answer:

$7.50

Step-by-step explanation:

$50 x .15 = $7.50

$7.50 estimated to nearest cent is $7.50

Answer:

2 I guess tell me if it's right

eight divided by two is four

BE is four

Answer:

7x - 2y - 20 = 0

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, - 3 ) and (x₂, y₂ ) = (4, 4 )

m = \(\frac{4-(-3)}{4-2}\) = \(\frac{4+3}{2}\) = \(\frac{7}{2}\) , then

y = \(\frac{7}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, 4 )

4 = \(\frac{7}{2}\) (4) + c = 14 + c ( subtract 14 from both sides )

- 10 = c

y = \(\frac{7}{2}\) x - 10 ← in slope- intercept form

multiply through by 2

2y = 7x - 20 ( subtract 2y from both sides )

0 = 7x - 2y - 20 , that is

7x - 2y - 20 = 0 ← required equation

True, the image shows a transformation where the figure has been moved to a different position while maintaining its size and shape.

what is a triangle?

A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles. It is one of the most basic and fundamental shapes in geometry.

The image shows a transformation where the figure has been moved to a different position while maintaining its size and shape. This type of transformation is called a translation, which involves sliding an object in a particular direction without changing its size or shape.

To perform a translation, we need to know how far the object has been moved horizontally and vertically. In the image, we can see that the blue triangle has been moved 2 units to the right and 3 units up. We can represent this translation using vector notation, where the vector (2, 3) represents the horizontal and vertical distances that the triangle has been moved.

Therefore, true the image shows a transformation where the figure has been moved to a different position while maintaining its size and shape.

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391 children swam at the public pool that day and 667 - 391 = 276 adults swam.

What is algebraic equation ?

An algebraic equation or polynomial equation is an equation of the form P=0 where P is a polynomial with coefficients in some field, often the field of the rational numbers.

Let's call the number of children that swam "x". The number of adults that swam would then be 667 - x.

The total revenue from the children was 1.75x and the total revenue from the adults was 2.25(667 - x).

set up an equation to represent the total revenue from both groups of swimmers

1.75x + 2.25(667 - x) = 1312.25

Expanding the second term on the left-hand side:

1.75x + 1507.75 - 2.25x = 1312.25

Combining like terms:

-0.5x + 1507.75 = 1312.25

Solving for x:

-0.5x = -195.5

x = 391

So, 391 children swam at the public pool that day and 667 - 391 = 276 adults swam.

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199 children and 468 adults swam at the public pool that day.

Let x be the number of children and y be the number of adults. Then we have the following two equations:

x + y = 667 (the total number of people)

1.75x + 2.25y = 1312.25 (the total amount of money collected)

We can substitute the first equation into the second to eliminate x:

1.75x + 2.25y = 1312.25

1.75(667 - y) + 2.25y = 1312.25

1175 - 1.75y + 2.25y = 1312.25

1175 = 1312.25 - 1.75y + 2.25y

1175 = 1312.25 - 1.75y + 2.25y

1175 = 1312.25 - 4y/2 + 9y/4

1175 = 1312.25 - (4/2)y + (9/4)y

1175 = 1312.25 - (6/4)y + (9/4)y

1175 = 1312.25 - (15/4)y

1175 + (15/4)y = 1312.25 + (15/4)y

15/4y = 137.25

y = 468

So there were 468 adults and 667 - 468 = 199 children.

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The telescope sum technique works because it is a special case of partial fraction decomposition.

The technique works for the recursive equation, an example being: `

an = an-1 + bn-1`,

which is the same as saying `an - an-1 = bn-1`.

Applying the telescoping sum technique to this equation yields:```
\(an - a_0 = b_0 + b_1 + b_2 + ... + bn-1\)

The answer to the second part of the question is yes, the telescope sum technique will work for the given equation `an = an-1 + an-2 + 1`.

This is because the equation can be written as `an - an-1 = an-2 + 1`.

When the telescoping sum technique is applied to this equation, it results in:```

\(an - a_0 = a_1 - a_0 + a_2 - a_1 + ... + an-1 - an-2 + 1 = an - a_0 - (a_1 - a_0) + (a_2 - a_1) - ... + (-1)^(n-1) \times (an-1 - an-2) + 1\)

Therefore, the telescope sum technique can be used to simplify this recursive equation as well.

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Answer:

w > 2

Step-by-step explanation:

w + 8 > 10

w > 10 - 8

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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Answer:

\(8\).

Step-by-step explanation:

Notice that in equation for the total dollar amount collected (\(12+ 1.75\, n\)), every additional bottle sold at the new price brings in \(1.75\) dollars:

\(\begin{aligned}& 12 + 1.75\, n && \text{$n$ bottles at new price} \\ -\; & 12 + 1.75\, (n+1) && \text{$(n+1)$ bottles at new price} \\ =\; & 1.75\end{aligned}\).

Therefore, the per-bottle price after the \(\$0.25\) price increase would be \(\$1.75\). The per-bottle price before the price increase would be \(\$1.75 - \$0.25 = \$1.50\).

Also notice that when \(n = 0\), the total amount collected was \(t = 12 + 1.75\, n = 12\). In other words, the total amount collected was \(\$12\) before any bottle was sold at the new price.

Thus, the vendor had collected \(\$12\!\) by selling at the initial price of \(\$1.50\) per bottle. The number of bottles sold at that price would be:

\(\begin{aligned}\frac{12}{1.50} = 8\end{aligned}\).

Overall, sampling offers a practical and efficient approach to obtain information about a population while still providing accurate and reliable results. It strikes a balance between accuracy, cost-effectiveness, and feasibility, making it a preferred method for many research studies and surveys.

Cost-Effectiveness: Sampling is usually more cost-effective than conducting a census. A census involves collecting data from every individual in the population, which can be time-consuming and expensive. Sampling allows researchers to gather representative information using a smaller sample size, reducing costs while still providing accurate estimates.

Time Efficiency: Conducting a census can be time-consuming, particularly for large populations. Sampling allows researchers to collect data more efficiently by focusing on a subset of the population. This saves time and enables quicker analysis and decision-making.

Feasibility: In some cases, it may not be practical or feasible to conduct a census. For example, in populations with millions or billions of individuals, it would be extremely challenging and resource-intensive to collect data from every member. Sampling provides a more manageable approach, allowing researchers to obtain meaningful insights without overwhelming logistical constraints.

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Given that ACE is an isosceles triangle, the measure of ∠CDB is: 55°

The two base angles of any isosceles triangle are always congruent to each other.

Therefore:

m∠CBD = m∠CDB

m∠CBD = 180° - 125° (supplementary angles)

m∠CBD = 55°

Therefore:

m∠CBD = m∠CDB = 55°

In summary, given that ACE is an isosceles triangle, the measure of ∠CDB is: 55°

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For Pearson correlation the most common purpose to examine is given by option a. The relationship between 2 variables.

The Pearson correlation is a statistical measure that indicates the extent to which two continuous variables are linearly related.

It measures the strength and direction of the relationship between two variables.

Ranging from -1 perfect negative correlation to 1 perfect positive correlation.

And with 0 indicating no correlation.

It is commonly used in research to examine the association between two variables.

Such as the relationship between height and weight, or between income and education level.

Therefore, the most common purpose of a Pearson correlation is to examine the relationship between 2 variables.

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The above question is incomplete, the complete question is:

The most common purpose for a Pearson correlation is to examine,

a. The relationship between 2 variables

b. Relationships among groups

c. Differences between variables

d. Differences between two or more groups

For the first equation, the particular solution for the first equation is y(t) = 3et.

For the second equation,  the particular solution for the second equation is y(t) = 1 - 4t + 4t2.

For the third equation,  the particular solution for the third equation is y(t) = -1/2 sin(t) - 1/2 cos(t).

For the fourth equation,  the particular solution for the fourth equation is y(t) = y(0).

For the first equation, y(t) = Aet, let's try a solution of the form y(t) = Aet and solve for the coefficients. Taking the derivative of y(t) and substituting it in the original equation, we get: dy/dt = Aet * et = Aet2 = 3e. Solving for A, we get A = 3e/et2 = 3. Therefore, the particular solution for the first equation is y(t) = 3et.

For the second equation, dy + y = 1 + 2 + 2, let's try a solution of the form y = B + Ct. Taking the derivative of y and substituting it in the original equation, we get: dy/dt = C = 2 + 2. Solving for C, we get C = 4. Substituting this in the original equation, we get y = B + 4t. Solving for B, we get B = 1 - 4t. Therefore, the particular solution for the second equation is y(t) = 1 - 4t + 4t2.
For the third equation, dy + 2y = sin(t), let's try a solution of the form y = A sin(t) + B cos(t). Taking the derivative of y and substituting it in the original equation, we get: dy/dt = A cos(t) - B sin(t) = -2A sin(t) -2B cos(t). Solving for A and B, we get A = -1/2 and B = -1/2. Therefore, the particular solution for the third equation is y(t) = -1/2 sin(t) - 1/2 cos(t).
For the fourth equation, y(t) = A + Bt + Ct2, let's try a solution of the form y(t) = A + Bt + Ct2 and solve for the coefficients. Taking the derivative of y(t) and substituting it in the original equation, we get: dy/dt = B + 2Ct = 0. Solving for B and C, we get B = 0 and C = 0. Substituting these values in the original equation, we get y(t) = A. Solving for A, we get A = y(0). Therefore, the particular solution for the fourth equation is y(t) = y(0).

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Answer:

135

Step-by-step explanation:

5 times 35 equals 135

Answer:

$175

Step-by-step explanation:

because that is how much she deposited