The sum of 5 consecutive even number is 100 the middle number is

The area of the square with radius 17√2 is 1156 square inches.

The area is the amount of space within the perimeter of a 2D shape

The formula for the area of square is

[tex]A = \frac{1}{2} d^{2}[/tex]

Where, d is the length of the diagonal of the square.

According to the given question.

The radius of the square is [tex]17\sqrt{2}[/tex] in.

⇒ Diameter or the length of the square  = 2 × 17 √2 = 34√2

Therefore,

The area of the square

= [tex]\frac{1}{2}( 34(\sqrt{2)} )^{2}[/tex]

= [tex]\frac{2312}{2}[/tex]

=[tex]1156\ in^{2}[/tex]

Hence, the area of the square with radius 17√2 is 1156 square inches.

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Answer:

  53.3

Step-by-step explanation:

Add one standard deviation to the mean:

  45 +1(8.3) = 53.3

Answer:

53.3

Step-by-step explanation:

+1 standard deviation away from the mean is 45+1(8.3)

area of rectangle = l x w

area of rectangle = 2*18 = 36 square meters

 area of square = S^2, or s = square root(area)

sqrt(36) = 6

 length of side of square = 6 meters

The side length of the square garden plot with the same area as a rectangular plot of dimensions 2 meters by 18 meters is 6 meters.

The student is asking about finding the length of a side of a square garden plot that has the same area as a rectangular garden plot measuring 2 meters wide by 18 meters long. To find the area of the rectangular plot, we multiply the length by the width: 2 meters  imes 18 meters = 36 square meters.

Since the area of the square plot must equal the area of the rectangular plot, we can use the formula for the area of a square, A = s2, where s is the side length of the square. Therefore, to find the side length of the square plot, we take the square root of the area of the rectangular plot:
√(36 square meters) = 6 meters

So, the side length of the square garden plot is 6 meters.

The valid method is the owner asked every third customer to rate all the pizza toppings in order of preference. The correct option is A.

information that is utilized as a foundation for improvement, such as data on how people react to a product or how well someone performs a task.

I suggest method 1 because it is unbiased and systematic.  The second method requires a lot of the initiative of customers and is likely to have extreme cases only (liked very much or disliked very much).  

The third is biased towards teenagers, which may not be the only category of customers who ordered pizzas. Again, the fourth requires initiative from the customer, so biased towards customers who had something to say.

Therefore, the valid method is for the owner to ask every third customer to rate all the pizza toppings in order of preference. The correct option is A.

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Here is your answer:

Solving the equation:

Hope this helps!

Step 1

Find the equation of the line that passes through points [tex](1, 2)[/tex] and [tex](2, 5)[/tex]

Find the slope of the line

The formula to calculate the slope is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{5-2}{2-1}[/tex]

[tex]m=\frac{3}{1}[/tex]

[tex]m=3[/tex]

Find the equation of the line

The equation of the line into slope-point form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=3[/tex]

[tex](1, 2)[/tex]

substitutes

[tex]y-2=3(x-1)[/tex]

[tex]y=3x-3+2[/tex]

[tex]y=3x-1[/tex]

Step 2

Find the equation of the inequality

we know that

The solution is the shaded area below the solid line

therefore

the inequality is

[tex]y\leq 3x-1[/tex]

the answer is

[tex]y\leq 3x-1[/tex]

see the attached figure to better understand the problem

To solve this problem, we can use the following ratio formulas to find for the coordinates of the club house:

x = [m / (m + n)] (x2 – x1) + x1

y = [m / (m + n)] (y2 – y1) + y1

Where,

m and n are the ratios (0.5 and 0.5 each since the club house are to be located exactly halfway)

x1 and y1 are the x and y coordinates of the 1st pool (-16, -25)

x2 and y2 are the x and y coordinates of the 2nd pool (18, 23)

Substituting:

x = [0.5 / (0.5 + 0.5)] (18 - -16) + -16

x = 1

y = [0.5 / (0.5 + 0.5)] (23 - -25) + -25

y = -1

Therefore the club house should be located at coordinates (1, -1).

Answer:18 inches

Step-by-step explanation:

The answer would be 18 inches.

The median of a trapezoid is the segment that connects the midpoints of the non-parallel sides.

The length of the median is the average of the length of the bases.

The top base of each tile is 15 inches in length and the bottom base is 21 inches,

Add the top base and bottom base,

So, 15+21=36

Now, divide that by 2

⇒ 18

Hence, the answer would be 18 inches.

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Final answer:

By forming a system of equations and applying the elimination method, we conclude that the ice cream shop sold 51 deluxe cones and 44 regular cones on Saturday.

Explanation:

How to Solve for the Number of Deluxe and Regular Cones Sold

To solve for the number of deluxe cones and regular cones sold at the ice cream shop, we need to set up a system of equations. We are given that a total of 95 cones were sold and the total money collected was $628. Deluxe cones are sold for $8 and regular cones for $5. Let's define our variables:

Now, we can establish our equations:

To solve the system, we can use the substitution or elimination method. Let's use elimination for this example.

Multiply the first equation by 5:

Now subtract this from the second equation:

With 51 deluxe cones sold, we can substitute that into the first equation to find y:

So, 51 deluxe cones and 44 regular cones were sold on Saturday.

An acre, a unit of area commonly used in the Imperial and U.S. customary systems, is approximately 4047 square meters. This is calculable by using the known conversions between acres, square miles, and square meters.

To determine the number of square meters in an acre, it's helpful to understand the relationship between these units. A square mile is equivalent to 640 acres. Therefore, the area of one acre is 1/640 of a square mile. However, these are both Imperial measurements, and we want to convert to a metric measurement - square meters.

To make this conversion, we need to identify the conversion factor between square miles and square meters. There are 2,589,988.11 square meters in a square mile.

Our starting point is that 1 acre = 1/640 square mile. Next, we substitute the number of square meters in a square mile:

1 acre = 1/640 x 2,589,988.11 square meters = 4046.86 square meters.

Therefore, there are approximately 4047 square meters in an acre.

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13 square units

Consider attachment for details.

We make a KLMN rectangle that touches all the vertices of the ABCD parallelogram. Consequently, the ABCD parallelogram is right inside the KLMN rectangle.

Let us take the following strategic steps:

The Process:

As a result, we get the area of the parallelogram ABCD is 13 square units.

Keywords: what is the area of parallelogram ABCD, in square units, graph, cartesian coordinates, triangle, rectangular, congruent, touches all the vertices

A picture helps. There are 2 non-adjacent vertices, so two diagonals can be drawn, resulting in 3 triangles.

Drawing all diagonals from one vertex of a pentagon to the non-adjacent vertices creates three triangles within the pentagon.

When all the diagonals are drawn from one vertex of a pentagon, it divides the pentagon into several triangles.

A pentagon has five sides, and when selecting a single vertex, we can draw diagonals to the non-adjacent vertices. In this case, there are three non-adjacent vertices, which means we can draw three diagonals, thus creating three triangles inside the pentagon.

This is because each diagonal, combined with two sides of the pentagon, forms a triangle.

The expression for the total area made up by the square and the circle as a function of x is f(x) = x^2/16 + (25 - 10x + x^2)/(4*Pi) square inches.

To solve this problem, you need to know the formulas for the areas of a square (Area = side^2) and a circle (Area = pi * radius^2). If a piece of the wire with length x inches is to be bent into the shape of a square, then each side of the square will be x/4 inches long (since a square has 4 equal sides). Therefore, the area of the square = (x/4)^2 = x^2/16 sq.inches.

The remaining piece of the wire is 5-x inches long and is to be bent into the shape of a circle. The circumference of the circle is 5-x inches (since it uses the remaining wire), therefore the radius of the circle is (5-x)/(2*Pi) inches. Therefore, the area of the circle = Pi*((5-x)/(2*Pi))^2 = (25 - 10x + x^2)/(4*Pi) sq.inches.

The total area made up by the square and the circle is the sum of their areas, therefore the function representing the total area f(x) = x^2/16 + (25 - 10x + x^2)/(4*Pi) sq.inches.

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Answer:

Thus, the expected value of points for Derek and Mia are [tex]\dfrac{-1}{9}[/tex] and [tex]\dfrac{1}{9}[/tex] respectively.

Step-by-step explanation:

Number of green marbles = 2 and Number of Yellow marbles = 1

Then, total number of marbles = 2+1 = 3

A person selects two marbles one after another after replacing them.

So, the probabilities of selecting different combinations of colors are,

[tex]1.\ P(GG)=P(G)\times P(G)\\\\P(GG)=\dfrac{2}{3}\times \dfrac{2}{3}\\\\P(GG)=\dfrac{4}{9}[/tex]

[tex]2.\ P(GY)=P(G)\times P(Y)\\\\P(GY)=\dfrac{2}{3}\times \dfrac{1}{3}\\\\P(GY)=\dfrac{2}{9}[/tex]

[tex]3.\ P(YG)=P(Y)\times P(G)\\\\P(YG)=\dfrac{1}{3}\times \dfrac{2}{3}\\\\P(YG)=\dfrac{2}{9}[/tex]

[tex]4.\ P(YY)=P(Y)\times P(Y)\\\\P(YY)=\dfrac{1}{3}\times \dfrac{1}{3}\\\\P(YY)=\dfrac{1}{9}[/tex]

Now, we have that,

If two marbles are of same color, then Mia gains 1 point and Derek loses 1 point.

If two marbles are of different color, then Derek gains 1 point and Mia loses 1 point.

Then, the expected value of points for Derek is,

[tex]E(D)= (-1)\times \dfrac{4}{9}+1\times \dfrac{2}{9}+1\times \dfrac{2}{9}+(-1)\times \dfrac{1}{9}\\\\E(D)= \dfrac{-5}{9}+\dfrac{4}{9}\\\\E(D)=\dfrac{-1}{9}[/tex]

And the expected value of points for Mia is,

[tex]E(M)= 1\times \dfrac{4}{9}+(-1)\times \dfrac{2}{9}+(-1)\times \dfrac{2}{9}+1\times \dfrac{1}{9}\\\\E(M)= \dfrac{5}{9}-\dfrac{4}{9}\\\\E(M)=\dfrac{1}{9}[/tex].

Thus, the expected value of points for Derek and Mia are [tex]\dfrac{-1}{9}[/tex] and [tex]\dfrac{1}{9}[/tex] respectively.

Answer: P(GG)= 4/9

P(GY)= 2/9

P(YG)= 2/9

P(YY)= 1/9

Derek, E(X) = -1/9

Mia, E(X) = 1/9

Step-by-step explanation: just did it on edge

The series is convergent, but the number of terms needed to find the sum to a specific accuracy cannot be determined.

To determine the convergence of the series sum_(n=1)^(infinity) (-1)^(n+1)/( n^7), we can use the Alternating Series Test. The Alternating Series Test states that if the terms of a series alternate in sign and decrease in absolute value, then the series is convergent. In this case, the terms of the series alternate in sign and decrease as n increases, so the series is convergent.

To find the number of terms needed to achieve a sum with an error less than 0.00005, we need to use the Remainder Estimation Theorem. However, this theorem requires that the terms of the series decrease in absolute value, which is not the case in this series. Therefore, we cannot determine the number of terms needed to reach the desired accuracy.

Overall, the series is convergent, but we cannot determine the number of terms needed to reach a specific accuracy.

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Final Answer:

The standard form of the equation of the hyperbola with vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15) is  (x - 30)^2 / 1600 - (y + 15)^2 / 81 = 1

Explanation:

To write the standard form of the equation of a hyperbola with the given vertices and a focus, we'll follow these steps:

1. Determine the center of the hyperbola.
2. Calculate the distance between the vertices and the center to find the length of the transverse axis (2a).
3. Calculate the distance between a focus and the center to find the focal distance (c).
4. Use the relationship c^2 = a^2 + b^2 to determine the length of the conjugate axis (2b).
5. Write the standard form equation based on the orientation of the hyperbola.

Step 1: Determine the center of the hyperbola.
The center of the hyperbola is the midpoint of the line segment joining the two vertices. Since the vertices are at (-10, -15) and (70, -15), the center (h, k) can be found as follows:

h = (-10 + 70) / 2 = 60 / 2 = 30
k = (-15 + (-15)) / 2 = -30 / 2 = -15

So, the center of the hyperbola is at (30, -15).

Step 2: Calculate the length of the transverse axis (2a).
The distance between the vertices is the length of the transverse axis. The vertices are 80 units apart because they are at (-10, -15) and (70, -15). This means:

2a = 80
a = 40

Therefore, the length of the semi-transverse axis a is 40 units.

Step 3: Calculate the focal distance (c).
The focal distance is the distance between the center and one of the foci. We were given one focus at (-11, -15). Since the center is at (30, -15), the focal distance c is:

c = |30 - (-11)| = |30 + 11| = 41

Step 4: Use the relationship c^2 = a^2 + b^2 to determine b.
We know that a = 40 and c = 41. Plugging these values into the relationship gives us:

41^2 = 40^2 + b^2
1681 = 1600 + b^2
b^2 = 1681 - 1600
b^2 = 81
b = 9

Therefore, the length of the semi-conjugate axis b is 9 units.

Step 5: Write the standard form equation.
Since the hyperbola is horizontal (the vertices have the same y-coordinate), the standard form of its equation is:

(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1

Plugging in the values for h, k, a, and b, we get:

(x - 30)^2 / 40^2 - (y + 15)^2 / 9^2 = 1

Simplify further by squaring the values of a and b:

(x - 30)^2 / 1600 - (y + 15)^2 / 81 = 1

This is the standard form of the equation of the hyperbola with vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15).

The range in miles is 4.72 mile

mile, any of various units of distance, such as the statute mile of 5,280 feet (1.609 km). It originated from the Roman mille passus, or “thousand paces,” which measured 5,000 Roman feet.

Given : range= 8320 yards

1 mile= 5280 feet

3 feet= 1 yard

Now,

8320yards X 3ft = 24,960

Now,  divide that by 5,280ft in a mile

= 24960/5280

= 4.72 miles

Hence, range is 4.72 miles.

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Final answer:

To convert the artillery piece's range of 8320 yards to miles, you multiply by 3 to change yards to feet and then divide by 5280 to convert feet to miles, resulting in a range of approximately 4.727 miles.

Explanation:

To find the artillery piece's range in miles, starting with its range in yards, we need to use unit conversion factors. Knowing that 1 mile equals 5280 feet and 3 feet equals 1 yard, we can set up a conversion to calculate the distance in miles.

Steps to Convert Yards to Miles:

For an artillery range of 8320 yards:

When you divide 24960 by 5280, you get 4.727 miles (rounded to three decimal places).