Is 60×60=3600
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Given that pq=qr=rs=sp, what additional information is required to conclude that pqrs is a square?

In order to conclude that pqrs is a square, the additional information required is that the sides of the quadrilateral are perpendicular to each other (i.e. they form 90-degree angles).

We know that pq=qr=rs=sp, which means that all four sides of the quadrilateral are equal in length.

However, this information alone is not sufficient to conclude that pqrs is a square, as there are many other quadrilaterals that have all four sides equal in length.

For instance, a rectangle has all four sides equal in length, but its sides are not necessarily perpendicular to each other. Thus, we require the additional information that the sides of pqrs are perpendicular to each other in order to identify that pqrs is a square.

In conclusion, the additional information needed to conclude that pqrs is a square is that the sides of the quadrilateral are perpendicular to each other (i.e. they form 90-degree angles).

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Answer:

Step-by-step explanation:

(8 x 6) x 25 =

48 x 25 =

1200 ft2

A logarithmic function is a type of inverse function.

A logarithmic function is a type of inverse function that is commonly used in mathematics and science. It is typically written in the form of y = log base b (x), where b is the base of the logarithm, and x is the input value. The most common bases for logarithms are 10 (common logarithm) and e (natural logarithm).

The logarithmic function is the inverse of the exponential function with base b. This means that if y = log base b (x) then x = b^y

One way to describe a logarithmic function is to say that it represents the exponent to which the base number must be raised in order to produce the input value x. For example, log base 10 of 100 is 2, because 10^2 = 100.

Another way to describe a logarithmic function is to say that it is a way of expressing very large or small numbers in a more manageable form. For example, instead of expressing a number like 10^9 as 1 billion, it can be expressed as 9 using a logarithm to base 10.

It is also important to note that logarithmic function have some key characteristics such as:

The domain of a logarithmic function is x>0, since the logarithm of a non-positive number is undefined.

The range of a logarithmic function is all real numbers.

The graph of a logarithmic function has a vertical asymptote at x=0, since the logarithm of a non-positive number is undefined.

A logarithmic function is increasing over its domain and concave down.

The x-intercept of the graph is (1,0), since the logarithm of 1 is always 0.

Overall, logarithmic functions are mathematical tools that allow us to simplify the representation and manipulation of very large and small numbers, and are used in many areas of science and engineering.

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To find the maximum area of the lawn that can be watered by the sprinkler, we can use the formula for the area of a circle:

A = πr^2

Given that the radius of the sprinkler's spray is 22ft, we can substitute this value into the formula:

A = 3.14 * (22)^2

A ≈ 3.14 * 484

A ≈ 1519.76

Rounded to the nearest tenth, the maximum area of the lawn that can be watered by the sprinkler is approximately 1519.8 ft^2.\(\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}\)

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The equation of function g(x) is g(x) = 2(x -7)² - 1, and the values of h and k are 7 and -1, respectively

The function is given as:

f(x) = 2x² - 1

When the function is translated 7 units left, the transformation rule is:

(x,y) -> (x + 7, y)

So, we have:

g(x) = 2(x -7)² - 1

A quadratic function is represented as:

g(x) = a(x -h)² + k

By comparison, the values of h and k are 7 and -1, respectively

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The team scored 2 field goals, 2 safeties, and 4 touchdowns.

A statement proving the equality of two mathematical expressions is known as an equation. The goal is frequently to ascertain the values of the variables that make the equation true, and it may have one or more variables.

The football team scored 8 times and a total of 38 points.

Let T be the number of touchdowns, F be the number of field goals, and S be the number of safeties.

We know, T = F + S and F + S = 4

Substituting, T = F + S into the equation for total points,

we get, 7T + 3F + 2S = 38

Solving for F and S, we get F = 2 and S = 2.

Therefore, the team scored 2 field goals, 2 safeties, and 4 touchdowns.

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Solve for F and S then get F = 2 and S = 2.

The team scored 4 touchdowns, 2 field goals, and 2 safeties.

The football group scored 8 times, totaling 38 points.

Let,

T is the no.of touchdowns,

F is the no.of field goals, and

S is the no.of safeties.

Touchdown: The ball is in possession of a runner who has moved from the field of play into the end zone and is on, above, or behind the plane of the opposing goal line (extended).

Field Goal: a three-point goal in football obtained by kicking the ball over the crossbar during normal play.

Safeties: NFL defences can score a safety, worth two points, by tackling the offensive player with the ball behind his own goal line or forcing him to run or throw the ball out of bounds behind his own goal line.

We know that,

T = F + S and

F + S = 4

For total points, put T = F + S into the equation.

We get,

7T + 3F + 2S = 38

Solve for F and S,

we get,

F = 2 and S = 2.

As a result, the team tallied 2 field goals, 2 safeties, and 4 touchdowns.

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The equation of the surface of revolution generated by revolving x = (1/z)^z about the z-axis is x = e^(-y).

To find the equation of the surface of revolution, we start with the parametric equation x = (1/z)^z, y = t, z = t. We eliminate the parameter t by substituting z for t in the equation x = (1/z)^z. Simplifying further, we obtain x = e^(-y).

This equation represents the surface of revolution generated by revolving the curve x = (1/z)^z about the z-axis. The exponentiation by e^(-y) signifies that the x-coordinate changes exponentially as the y-coordinate varies.

Therefore, as we revolve the curve around the z-axis, it forms a surface with an exponential decay in the x-direction. Hence, the equation x = e^(-y) describes the surface of revolution.

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Answer:

Simple interest after 2 year = $36

Step-by-step explanation:

Given:

Amount invested = $300

Number of year amount invested = 2 year

Rate of interest per year = 6% = 6/100 = 0.06

Find:

Simple interest after 2 year

Computation:

Simple interest formula;

Simple interest = [Amount invested][Rate of interest][Number of year]

Simple interest after 2 year = [300][0.06][2]

Simple interest after 2 year = [18][2]

Simple interest after 2 year = $36

Answer: 371.28

I hope that this helps! :)

Answer: 371.28

Step-by-step explanation: hope it helps mark brainlist if helpful

Answer:

6,400-4,700

Step-by-step explanation:

Answer:

57.

Step-by-step explanation:

Answer:

57.8 888888 = 8...0000

Answer:

2\(x\) + 10

Steps:

1- Formulate

2- Simplify or expand

3- Multiply

4- Combine like terms

Answer:

2x² - 2x - 8y + 4

Step-by-step explanation:

Assuming you mean

2x² + 3x - 4y + 7 - (5x + 4y + 3) ← distribute parenthesis by - 1

= 2x² + 3x - 4y + 7 - 5x - 4y - 3 ← collect like terms

= 2x² - 2x - 8y + 4

Answer:

overlapping congruent triangles:

ΔACE ≅ ΔBCD

Proof:

given: AC ≅ BC, angle A ≅ angle B

angle ACB ≅ angle BCA by the reflexive property

ΔACE ≅ ΔBCD by the ASA triangle congruence property

The critical point of the given expression is (\(2^(5/3)\), 2).

The critical point is classified as a  saddle point.

To find the critical points of the function

\(f(x,y) = x^3 + y^3 - 6xy,\)

find all points (x,y) where the partial derivatives of f are zero or do not exist.

The partial derivatives of f are:

\(df/dx = 3x^2 - 6y\\df/dy = 3y^2 - 6x\)

Setting these partial derivatives to zero, we get:

\(3x^2 - 6y = 0\\3y^2 - 6x = 0\)

Solve these equations simultaneously,

\(x^2 = 2y\\y^2 = 2x\)

Substitute the first equation into the second

\((2y)^(3/2) = 2x\)

Simplifying, we obtain:

\(x = 2^(2/3) y^(1/3)\)

Substituting this expression for x into the first equation, we get:

\(3(2^(4/3) y^(2/3)) - 6y = 0\)

\(y^(2/3) = 2^(2/3)\)

Therefore, y = 2 and x = \(2^(5/3)\).

Thus, the critical point is \((2^(5/3)\), 2).

To classify this critical point, we need to compute the second partial derivatives of f:

\(d^2f/dx^2 = 6x\\d^2f/dy^2 = 6y\\d^2f/dxdy = -6\)

At the critical point \((2^(5/3), 2)\), we have \(d^2f/dx^2 > 0\) and \(d^2f/dy^2 > 0\), hence, this point is a local minimum.

Furthermore, since \(d^2f/dy^2 > 0\), therefore, the critical point is classified as saddle point.

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Answer:

a) is the correct answer

Answer:

18.8

Step-by-step explanation:

Circumference

A linear programming problem with two decision variables can be solved by a graphical solution method. In this method, the constraints and the objective function of the linear programming problem are graphed on a two-dimensional coordinate plane, and the optimal solution is found at the intersection of the feasible region (the area defined by the constraints) and the level curve of the objective function.

The graphical solution method is a simple and intuitive way to solve linear programming problems with few decision variables, but it becomes impractical as the number of decision variables and constraints increase. In such cases, more complex algorithms, such as the simplex method or interior point methods, are used to find the optimal solution.

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The volume of the right circular cylinder is approximately 14,864.77 cubic meters.

What is the right circular cylinder?

A right circular cylinder is a three-dimensional solid shape that consists of a circular base and a curved side that is perpendicular to the base. The term "right" refers to the fact that the axis of the cylinder is perpendicular to the base, and the term "circular" refers to the shape of the base, which is a circle.

The formula for the volume of a right circular cylinder is V = πr^2h, where r is the radius of the base and h is the height of the cylinder. The formula for the surface area of a right circular cylinder is A = 2πrh + 2πr^2, where r is the radius of the base and h is the height of the cylinder.

Right circular cylinders are commonly used in engineering, architecture, and everyday objects such as cans, pipes, and containers.

The formula for the volume of a right circular cylinder is \(V = \pi r^2h\), where r is the radius of the base and h is the height of the cylinder.

In this case, the radius is 17.2 meters and the height is 15.3 meters.

Plugging in these values, we get:

\(V = \pi (17.2)^2(15.3)\)

V ≈ 14,864.77 cubic meters

Therefore, the volume of the right circular cylinder is approximately 14,864.77 cubic meters.

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Answer:

Rowing speed: 10.6 miles per hour
speed of the current: 3.8 miles per hour.

Step-by-step explanation:

Let the team's rowing speed in still water be "x" and the speed of the current be "c".

x + c = 14.4

x - c = 6.8

(x + c) + (x - c) = 14.4 + 6.8

2x = 21.2

x = \(\frac{21.2}{2}\)

x = 10.6

10.6 + c = 14.4

c = 14.4 - 10.6

c = 3.8

The team's rowing speed in still water is 10.6 miles per hour, and the speed of the current is 3.8 miles per hour.

The difference is not significant enough to indicate a drastic deviation from the historical rate.

(a) The population under consideration in the dataset is the entire production of computer chips during the week at the factory.

(b) The parameter being estimated is the rate of chips with severe defects in the population.

(c) The point estimate for the parameter is the proportion of defective chips in the sample, which is found by dividing the number of defective chips (27) by the total number of sampled chips (212), resulting in a point estimate of approximately 0.1274 or 12.74%.

(d) The statistic used to measure the uncertainty of the point estimate is the standard error.

(e) To compute the standard error, we use the formula: sqrt((p*(1-p))/n), where p is the point estimate (0.1274) and n is the sample size (212). The computed value for the standard error in this context is approximately 0.021.

(f) Comparing the observed rate of defects (12.74%) with the historical rate of defects (10%), the engineer might be slightly surprised, but the difference is not significant enough to indicate a drastic deviation from the historical rate.

Variations in defect rates can occur naturally in production processes, and the observed rate falls within a reasonable range of expectations.

(g) If the true population value is known to be 10%, the value of the standard error in part (e) can be recomputed using the true proportion (p = 0.1). Applying the same formula, the revised standard error would be approximately 0.0158.

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Answer:

Step-by-step explanation:

25, i think

Answer:

100% on plato

Step-by-step explanation:

The raffles in ascending order of their expected values to the player is

player will be choose from A to J and the player wins $150.

player will be choose from A to O and the player wins $240.

player will be choose from A to E and the player wins $85.

Ascending order is a method of arranging numbers from smallest value to largest value. The order goes from left to right. Ascending order is also sometimes named as increasing order. For example, a set of natural numbers are in ascending order, such as 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8… and so on.

We have,

Tickets for all of the described charity raffles cost $2 per ticket.

Here first the player will be choose from A to J and the player wins $150.

Second, the player will be choose from A to O and the player wins $240.

Third, the player will be choose from A to E and the player wins $85.

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Answer:

50%

Step-by-step explanation:

Answer:

42%

Step-by-step explanation:

The best way to start is to work with common units. In this case, seconds are best.

1 minute = 60 seconds

50 minutes = (60 x 50) = 3000 seconds

3000 + 18 = 3018 seconds

This is our first variable.

1 hour = 3600 seconds(if you change to mins then to seconds is fine too)

2 hours = (3600 x 2) = 7200 seconds

From the question, we can tell;

2 hours = 100%

So we need to find out, 50 minutes 18 seconds = x%

( x is our unknown)

7200 seconds = 100%

3018 seconds = ((3018 x 100) ÷ 7200)

41.916 %

Let's round of to the nearest 1

42% (since 9 is higher than 5, we add 1 to the number before it)

Answer:

2x - 5y = 0

Step-by-step explanation:

Answer:

4 digit

The answer is 2255

Step-by-step explanation:

√5085025 = 2255

Thus, The answer is 2255

-TheUnknownScientist 72

Here we are required to compare the results with the effect of increasing the confidence level on the margin of error. The answer to this comparison is option (B). The margin of error increases with an increase in the level of confidence.

If the sample size is 17, the condition that must be satisfied to compute the confidence interval is the option (B). The sample data must come from a population that is normally distributed with no outliers. What is a Confidence Interval?

A confidence interval is a statistical measure that informs us of the degree of uncertainty that lies in a particular statistic, such as the mean or the proportion, and allows us to make conclusions about a population using sample data. The margin of error is the range of values around the sample statistic within which we are confident that the true population parameter will fall, given a certain level of confidence.

Conclusion: Therefore, The margin of error increases with an increase in the level of confidence, and the sample data must come from a population that is normally distributed with no outliers if the sample size is 17.

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The perimeter of the triangle XYZ according to the midsegment theorem is 37

The midsegment theorem states that the segment that is obtained by joining the midpoints of two sides of a triangle is parallel to the third side and it is half the length of the third side of the triangle.

The specified parameters are;

The midpoint of \(\overline{XY}\) = A

The midpoint of \(\overline{YZ}\) = B

The midpoint of \(\overline{XZ}\) = C

The length of segment AC = 5

The length of segment BC = 6

The length of side XZ = 15

The segments AC, BC, and AB are midsegments of the triangle XYZ

According to the midsegment theorem, we get

AC = 0.5 × \(\overline{YZ}\)

BC = 0.5 × \(\overline{XY}\)

AB = 0.5 × \(\overline{XZ}\)

Therefore;

2 × AC = \(\overline{YZ}\)

2 × BC = \(\overline{XY}\)

2 × AB = \(\overline{XZ}\)

\(\overline{YZ}\) = 2 × 5 = 10 (substitution property)

\(\overline{XY}\) = 2 × 6 = 12 (substitution property)

The perimeter of the triangle = \(\overline{YZ}\) + \(\overline{XY}\) + \(\overline{XZ}\)
Plugging in the values, of \(\overline{YZ}\), \(\overline{XY}\), and \(\overline{XZ}\)  we get;

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Answer:

I'm pretty sure it's 12) ( f * g) (x)

Step-by-step explanation:

Let me know if that's wrong and I'll do my best to fix it!

x = 4

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Answer:

hope this help you!!:))

5y = -3x + 7

y = -3/5x + 7/5

Parallel = same slope

y = -3/5x + b

3 = -3/5 + b, b = 18/5

Standard form: Ax + By = C

y = -3/5x + 18/5

-3/5x - y = -18/5

Multiply by -5

Solution: 3x + 5y = 18

Answer: Scale factor = 2

This is the same as writing \(\frac{2}{1}\)

===============================================

Explanation:

Focus on the left sides of each triangle. They correspond to one another. Note how RS represents the first two letters of RST; while MN represents the first two letters of MNO. We can see the order matters.

To find the scale factor, we divide MN over RS to get

MN/RS = 6/3 = 2

Therefore, the sides of triangle MNO are 2 times longer compared to the sides of triangle RST.

------------------------

Extra info:

If you want to find x, then you would solve the following

MN/RS = ON/TS

6/3 = x/5.5

6*5.5 = 3x

33 = 3x

3x = 33

x = 33/3

x = 11

or we could simply multiply ST = 5.5 by the scale factor 2 getting 5.5*2 = 11, which is the length of segment ON.