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Hence, the standard deviation of the given data is 7 .

10 28 13 18 29 30 22 23 25 32

Here is the total number of observations n are 10

total= 10 +28+ 13+ 18+ 29+ 30+ 22+ 23+ 25+ 32 = 230

mean  (μ) = total/n

         = 230/10

         = 23

         Xi                 Xi-μ                    (Xi-μ)²

         10           10-23=-13                   169

         28           28-23=5                      25

          13           13-23=-10                   100

          18           18-23=-5                      25

          29           29-23=6                      36

          30          30-23=7                       49

           22         22-23=-1                         1

            23         23-23=0                        0

           25          25-23=2                         4

            32          32-23=9                       81

Use the formula to calculate the standard deviation.

√1/n*∑   (Xi-μ)² =√1/10*490

                        = √49

                         =7

Hence, the standard deviation of the given data is 7 .

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Yes , the equation 3x² + 11x + 10 = 0 is a quadratic equation and the roots are x = -5/3 and x = -2

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c = 0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the equation be represented as A

Now , the value of A is

3x² + 11x + 10 = 0   be equation (1)

Now , the equation is of the form ax² + bx + c = 0 , where the value of a = 3 , b = 11 and c = 10

So , the coefficient a is has the variable x² and equation 3x² + 11x + 10 = 0 is a quadratic equation

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

Substituting the values in the equation , we get

x = [ -11 ± √ ( ( 11 )² - 4 ( 3 ) ( 10 ) ) ] / 2 ( 3 )

On simplifying the equation , we get

x = [ -11 ± √ ( 121 - 120 ) ] / 6

x = ( -11 ± 1 ) / 6

So , the two roots of the equations are

x = ( -11 - 1 ) / 6 and

x = ( -11 + 1 ) / 6

x = -2 and

x = -5/3

Therefore , the values of x are -5/3 and -2

Hence , the roots of the quadratic equations are -5/3 and -2

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Using the ratio we know that before the weekend started, she could have won as many as 164 games.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.

A proportion is an equation that sets two ratios at the same value.

For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

So, let n be the number of victories so that:

n/2n = 1/2 and n+3/2n+4 > 503/1000

Now, cross multiply as follows:

1000n + 3000 > 1006n + 2012

n < 988/6 = 164 4/6 = 164 2/3

Therefore, using the ratio we know that before the weekend started, she could have won as many as 164 games.

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Answer:

Let,

length of rectangle ( L) =9cm

breadth of rectangle (b) =4cm

Area of rectangle=L×b

=9×4

=36cm^2

Step-by-step explanation:

The base is the length of one of the triangle's sides, and the height is the distance from that side to the triangle's opposite corner.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.

Here,

The base of the triangle is the length of one of its sides, and the height is the distance from that side to the triangle's opposite corner.

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Answer:

1st and 3rd 4th

graph of f(x) = x² - 12x-45 has an x-intercept at x = -3

-3 is a zero of the function f(x) = x²-12x- 45

x + 3 is a factor of x² - 12x-45

Steps:

other solution is (x - 15) or x = 15

x² - 12x-45

2 numbers that when multiplied give -45 & when added give -12 are -15 & 3

(x-15) (x+3)

"zero" is a fancy way for asking for the answer or root

imaginary number is i which is √-1 so

if you have √-9 = √9 * √-1 = 3i

if you have √-20 = √4 * √-1 * √5 = 2i√5

.

Answer:

x=12

Step-by-step explanation:

3x+7 = 5x-17

-2x=-24

x=12

Hope this helps you can thank me if this helps and 5 star if you dont mind :)

Answer:

x=12

Step-by-step explanation:

The two sides must be equal in length

3x+7 = 5x-17

Subtract 3x from each side

3x-3x+7 = 5x-3x-17

7 = 2x-17

Add 17 to each side

7+17 = 2x-17+17

24 = 2x

Divide each side by 2

24/2 = 2x/2

12 =x

Yes, the isosceles triangles are equal to 180 degrees.

We know that isosceles triangles are triangles which have two equal sides. Since the sides are equal, they subtend equal angles as well.

However, the two equal angles subtended by the equal sides and one more angle which is subtended by the third side of the isosceles triangle all add up to a total of 180 degree as we know that the sum of all the angles of a triangle is always equal to 180 degrees.

Hence we can conclude that the isosceles triangles are also equal to 180 degrees like every other triangle.

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898 integers in that range excluding 100 and 999

There are 900 integers between 100 and 999, inclusive.

Numbers between 999 and 100 inclusive:  999 - 99 = 900

If you want to know the number of integers between 100 and 999, but not including either 100 or 999, then there are 898 integers in that range.

What is an integers number:

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a set of integers that consists of the following:

Positive Numbers: If a number is greater than zero, it is considered positive. For instance, 1, 2, 3, etc.

Negative numbers are those that are less than zero. For instance: 1, 2, 3, etc.

Zero is described as being neither a positive nor a negative number. A whole number, that is.

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We need to draw all sides of the triangle equal in order to make a SSS triangle because we know that the SSS triangle has all 3 sides equal.

Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.

We u can move, flip, twist, and turn these triangles to produce the same effect.

When relocated, they are parallel to one another.

Two triangles are deemed similar by the SSS test for triangle resemblance if their third sides are proportionate to one another.

Therefore, we need to draw all sides of the triangle equal in order to make a SSS triangle because we know that the SSS triangle has all 3 sides equal.

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The value of radius of the merry-go-round will be 6 feet.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circular objects for example our bike wheel.

The longest line which can be drawn inside the circle will be the diameter.

The perimeter of the circle = 2πr where r is the radius of the circle.

The Merry cover on the round in 3 seconds thus, to cover the 2πr path it takes 3 seconds.

2πr/3 = 12.56

2πr = 37.68

r = 5.996 ≈ 6 feet.

Hence "The value of the radius of the merry-go-round will be 6 feet".

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By combining the mother's as well as father's heights in inches, you may determine the midparental height. For boys, measure 5 inches longer; for girls, measure 5 inches shorter. multiply by two.

However, a number of calculations can offer a reliable approximation of a child's growth. Here is a common illustration:

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five plus eight times nine

The length of the guy wire, to the nearest foot, is 201 ft.

Refer to the diagram attached below for the given information

We have two similar right triangles, ΔABE and ΔCDE.

CD = 11 ft

DE = 4 ft

BD = 32 ft

Length of the guy wire (AE)

Since ΔABE ~ ΔCDE, therefore,

AB/CD = BE/DE (proportional sides)

Plug in the values:

AB/11 = (32 + 4)/2

AB/11 = 36/2

Cross multiply:

AB = (36 × 11)/2

AB = 198 ft

Apply Pythagorean Theorem to find AE:

AE = √(AB² + BE²)

AE = √(198² + 36²)

AE = 201 ft (nearest foot)

Therefore, the length of the guy wire, to the nearest foot is 201 ft.

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We have two similar right triangles, ΔABE and ΔCDE.

CD = 11 ft

DE = 4 ft

BD = 32 ft

Length of the guy wire (AE)

Since ΔABE ~ ΔCDE, therefore,

AB/CD = BE/DE (proportional sides)

AB/11 = (32 + 4)/2

AB/11 = 36/2

AB = (36 × 11)/2

AB = 198 ft

AE = √(AB² + BE²)

AE = √(198² + 36²)

AE = 201 ft (nearest foot)

The x and y intercept of y=3x-15 is X intercept  is 5, Y interceptis -15

To find X intercept substitute y=0

y=0

0=3x-15

3x=15

x=15/3

x=5

X intercept  is 5 line cuts at (5,0)

To find Y intercept substitute x=0

y=3(0)-15

y=-15

Y interceptis -15 line cuts at  (0,-15)

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In Parallelogram: Area = base x height(perpendicular distance).

In rectangle: Area = base x height.

Parallelogram:

A parallelogram is a particular sort of polygon. It's a quadrilateral in which the opposite side pairs are parallel to one another.

Area = base x height(perpendicular distance)

Rectangle:

Area = base(length) x height(width).

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Answer:

9.6

Step-by-step explanation:

What is the mean of the following data set 4 8 11 12 13?

Mean: is the average of values so:

(4 + 8 + 11 + 12 + 13) / 5 = 9.6

The three methods to find the mean are arithmetic, geometric and harmonic .

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Answer:

11111111111111111111

Answer:

first one and second one

Step-by-step explanation:

x + y is lesser or equal to 20

20 being the max amount of hours he can work in one week and x and y being hours he works

second one because they can earn at least 300 dollars, not less than, but x+Y must still be less than 20 though

Answer:

I think 11 trips to New York because it's a popular tourist attraction.

The triangles are congruent if all three sets of comparable sides are present. The side-side-side shortcut is a congruence technique (SSS).

Triangles are considered congruent by SAS if their two sides match up with their corresponding two sides on the other triangle, and if their included angles match up in both triangles.

We can prove two triangles, either by SSS or SAS by simply taking two triangles and checking whether the sides and the angles of the corresponding triangles are congruent or not.

By simply comparing it on the basis of their sides and angles we can easily prove the corresponding triangles by SSS or SAS.

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A triangle AAA does not satisfy congruence theorem. Triangle denoted by AAA refers a triangle having three equal side lengths and three equal angles.

Congruence theorem is developed based on two triangles which have equal corresponding side lengths and equal corresponding angles.

there are four criteria in where one or more criteria needed to satisfy. if two triangles have all three equal side lengths and equal corresponding angles then they satisfy congruence theorem. if two triangles have 2 equal side lengths and angle between sides are equal, they satisfy congruence theorem. If two triangles have equal two angles along

with equal similar side length, they satisfy congruence theorem.

hence, the triangle mentioned in the question is not congruent.

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Answer:

FALSE

Step-by-step explanation:

The angles can be the same, but the lengths of the sides can differ.

The median is the exact middle number in a sequence or set of numbers.

Steps to find the median is given below:

Finding the Median in an Odd Set of Numbers:

Step 1: Sort your set of numbers from least to greatest. If they're scrambled, line them up, starting with the lowest number and ending with the highest number.

Step 2: Find the number that is exactly in the middle. This means that the median number has the same amount of numbers in front of it as it does behind it.

Finding the Median in an Even Set of Numbers

Step 1: Sort out your set of numbers from least to greatest. An even set of numbers is going to have two numbers exactly in the middle.

Step 2: Find the average of the two numbers in the middle. If 2 and 3 are both in the middle, so you need to add 2 and 3, then divide the sum by 2. The formula for finding the average of two numbers is (the sum of the two middle numbers) ÷ 2.

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Answer:

Step-by-step explanation:

you can use the zero-product property to find the roots of a factored equation. After you factor a polynomial into its different pieces, you can set each piece equal to zero to solve for the roots with the zero-product property.

The approximate area of the rectangle as per the options will be equal to 15 square units. Hence, option B is correct.

An object's area is how much space it takes up in two dimensions. It is the measurement of the amount of unit squares which completely encompass the surface of a compact figure.

The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given information in the question,

Let the length is given as, l = √24 and,

The width is given as, w = √10

Use the formula of area of rectangle,

A = lw

A = √24 × √10

A = 4.89 × 3.16

A = 15.45 ≈ 15 square units.

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Answer:

Step-by-step explanation

In the first equation

x=17-4y

In the second equation

We clear "x"

y=x-2

x=y+2

We ecuate "x"

x=17-4y=y+2

17-4y=y+2

15=5y

y=3

we substitute to find "x"

x=17-4y=17-4(3)=5

Yes, 5 is the high standard deviation which is considered very good.

85 persons responded to my survey about their capacity to carry out specific duties.

The responses are rated on a Likert scale of 1 to 5:

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Answer: 56 miles per hour

Step-by-step explanation:

45 minutes = 0.75 hour

3 hours and 45 minutes = 3.75 hours

Takes 210 divided by 3.75 = 56 miles per hour