A sample of n = 5 scores has m = 20 and s2 = 4. what is the sample standard deviation?

The distance between points  J(-3,2) and K(9,2) is 12 units.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

The given points are

J(-3,2) and K(9,2)

[tex]x_{1} =-3\\\\x_{2} =9\\\\y_{1} =2\\\\y_{2} =2[/tex]

According to given question we have

By the use of distance formula we have

[tex]\sqrt{(x_{2} -x_{1} )^{2}+ (y_{2} -y_{1} )^{2}} \\\\=\sqrt{(9 -(-3) )^{2}+ (2 -2 )^{2}}\\\\=\sqrt{(12 )^{2}}\\\\=12[/tex]

Therefore, the distance between points  J(-3,2) and K(9,2) is 12 units.

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Distance between is missing in question

The average time in two races must be less than 7 minutes.

Given,

Runner's times in three races = 6.9 minutes, 6.6 minutes, 6.5 minutes.

Runner will run two more races.

The average time of all five races = less than 6.8 minutes

We have to find the average time needed in the two races:

Now,

(6.9 + 6.6 + 6.5 + x + y) / 5 < 6.8

Here, x and y are the time in two races.

Let's assume the average as 6.5 which is less than 6.8.

Then,

(6.9 + 6.6 + 6.5 + x + y) / 5 = 6.5

(6.9 + 6.6 + 6.5 + x + y) = (6.5 × 5)

x + y = (6.5 × 5) - (6.9 + 6.6 + 6.5)

x + y = 32.5 - 20

x + y = 12.5

Now, we have to find the average of two races:

That is, (x + y) / 2 = 12.5 / 2 = 6.25.

Above is a solution required by an assumption. By this solution we came to know that the average of two races must be less than 7 minutes.

So, let's conclude like:

The average time in the two races must be less than 7 minutes.

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Answer:

x = 6

Step-by-step explanation:

From the above diagram, we can deduce that:

5x + (x + 54) = 90 (Sum of Acute Angles)

Now, we can solve for x using this equation.

[tex]5x + (x + 54) = 90 \\ 6x + 54 = 90 \\ 6x + 54 - 54 = 90 - 54 \\ 6x = 36 \\ x = \frac{36}{6} \\ x = 6[/tex]

The line segment BC has a length of 13 units.

In this question we know the locations of the two ends of a line segment. The procedure consists in calculating the vector behind the line segment and later determing its magnitude by Pythagorean theorem. If we know that B(x, y) = (8, - 7) and C(x, y) = (- 4, - 2), then the length of the line segment BC is:

BC = (- 4, - 2) - (8, - 7)

BC = (- 12, 5)

BC = √[(- 12)² + 5²]

BC = 13

The line segment BC has a length of 13 units.

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The cone has a volume of (D) 288in3.

To find the volume:

Given:

Formula:

The Pythagorean theorem is used to calculate height.

The volume of the cone:

Therefore, the volume of the cone is (D) 288in³.

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The complete question is given below:
Right triangle ABC, shown, has a vertical leg 6 inches long and a hypotenuse 10 inches long. If the triangle was rotated 360 degrees around the vertical leg to form a right circular cone, what would be the volume of this cone, in cubic inches?

A. 32

B. 96

C. 128

D. 288

E. 384

Answer: h=3V/a^2

Step-by-step explanation:

V=1/3a^2h

V=1/3 * a^2 * h

V*3=3*1/3 * a^2 * h

3V=a^2 * h

h=3V/a^2

Answer:

264 square ft

Step-by-step explanation:

8*33=264

The value of the inequality is a x ≥2 or x ≤ -2.

According to the statement

We have to find that the value in the inequality.

So, For this purpose, we know that the

Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

From the given information:

7x-14 ≥0 or 4x+5 ≤ -3​

The value of the inequality is a :

7x-14 ≥0 or 4x+5 ≤ -3​

x ≥14/7 or x ≤ -3​-5/4

x ≥2 or x ≤ -8/4

x ≥2 or x ≤ -2.

So, The value of the inequality is a x ≥2 or x ≤ -2.

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To solve the equation, multiply both sides by 5/3. The solution is b = -10/3.

A linear equation is an equation of which the highest degree of its variables is 1.

Steps to solve linear equations:

The given problem:

Solve 3/5 b = -2

Notice that the variable, b, is already isolated on the left side.

Multiply both sides by 5/3:

3/5 b . 5/3 = -2 . 5/3

b = -10/3 (solved)

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From calculating the percentages we can say that 43 more students went on Friday than Saturday.

Percentage is defined as quantity per hundred. Percentage is calculated by dividing the given number by the total number and multiplying it by 100.

From the survey we can see that 550 students were supposed to go on Friday. But it is given that 18 percent students did not go to the festival.

Number of students who went = 550 - (18% of 550 )

Therefore students = 550 - 99 =451 students

Again from the survey we can see that 480 students were supposed to go on Saturday . But it is given that 15 percent students did not go to the festival.

Number of students who went =480 - (15% of 480 )

Therefore students = 480 - 72 = 408 students

Therefore the number of more students who went on Friday than Saturday is 451-408 = 43 students

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Answer: 3 groups of 5 = 5 + 5 + 5 = 15. 5 groups of 3 = 3 + 3 + 3 + 3 + 3 = 15. 3 groups of 5 has the same answer as 5 groups of 3! So, 3 x 5 = 5 x 3. This means that when you multiply 2 numbers, the order of the numbers (which number is first and which is second) does not matter, the answer will still be the same. Multiplication Terms

Step-by-step explanation: I hopes this helps.

Answer:

Step-by-step explanation:

a)

Peter now = x years old

John now = y years old

Five years ago

y-5 = 2(x-5)

y-5 = 2x-10

y = 2x-5

b)

x+y=28

y=28-x

Therefore

2x-5 = 28-x

3x = 33

x = 11

y = 28 - (11)

y = 17

Therefore

In three years time John will be:

17 + 3 = 20

c)

y-5 = 2x-10

Lefthand side:

(17)-5 = 12

Righthand side:

2(11)-10=22-10=12

Therefore 

Lefthand side =Righthand side

YAY!

Answer:

b

Step-by-step explanation:

(x-8)(x+2)= x^2 - 6x - 16

Answer: 801.2

Step-by-step explanation:

Answer:

[tex]xy^2+2x-4y^2[/tex][tex];-58[/tex]

Step-by-step explanation:

First, align the same terms next to each other so that combining like terms will be easier.

Remember like terms have the same variables and powers. To combine like terms, all you have to do is add/subtract the coefficients (the numbers in from of the variables).

[tex]2xy^{2} +2xy^{2} -3xy^{2} +3x-x-4y^{2}[/tex]

[tex]2xy^{2} +2xy^{2} -3xy^{2} =xy^{2}[/tex]

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

And [tex]-4y^{2}[/tex] stays the same because there is no term that has [tex]y^{2}[/tex].

So, we have [tex]xy^{2} +2x-4y^{2}[/tex].

Now to evaluate for x= -2 and y= -3 you have to plug them into the simplified expression.

[tex](-2)(-3)^{2} +2(-2)-4(-3)^{2}[/tex]

According to PEMDAS we first solve the exponents: [tex](-2)(9) +2(-2)-4(9)[/tex]

Then we multiply:

[tex](-18) +(-4)-36[/tex]

Add/subtract:

-58

Answer:

Each side is 2 centimeters.

Hope this helps :)

Step-by-step explanation:

A square has sides that are all equal. So in this case the area is 4 square centimeters, and in order to find that we had to multiply 2 sides in which they are equal to each other. All the sides were 2 centimeters. We get 2 sides and multiply to get the area of the square chip.

2 cm × 2cm = 4 square centimeters

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

Explanation:

The ratio 3:5 is equivalent to 3x:5x after multiplying both parts by x.

Jess has 3x dollars and Marie has 5x dollars

3x+5x = 64

8x = 64

x = 64/8

x = 8

Therefore,

The ratio 24:40 reduces to 3:5 after dividing both parts by the GCF 8.

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

Another way to solve:

m = amount Marie has

64-m = amount Jess has

3/5 = (64-m)/m

3m = 5(64-m)

3m = 320-5m

3m+5m = 320

8m = 320

m = 320/8

m = 40 dollars is the amount Marie has

61/100 is the equivalent fraction for the given decimal number.

A decimal number then has two components: a whole number part and a fractional part. The decimal place value system for the whole part of a decimal number is the same as the whole number value system. However, we get the fractional part of the decimal number as we move toward the right after the decimal point.

A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken.  The number below the line is called the denominator.  It shows the total number of equal parts the whole is divided into or the total number of the same objects in a collection.

for converting a decimal into a fraction we need to multiply and divide the decimal by the 10^n where n is the number of digits after the decimal.

61/100 is the equivalent fraction for the given decimal number.

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Answer:

the approximate value should be 2.83

Answer:68.48

Step-by-step explanation:a²+b²=c²  a=60 b=33 so 60²+33²=4689 and take the square root of that which equals 68.48

Answer:

Explanation ↓

Step-by-step explanation:

The origin is the rotation’s set point unless expressed otherwise. In a coordinate plane, when the point (x, y) is revolved in a 90-degree clockwise directive, the projected vision will have a coordinate of (y, -x).

Answer:

Step-by-step explanation:

The x-coordinates form the domain.

We know the x-coordinates of the end points of the line, the first numbers in pair of coordinates:

Also, since both points are closed circles, the endpoints are included.

So the domain is the interval between 0 and 4, both inclusive.

This is shown as:

The matching answer choice is A.

The domain of the function includes all x-values from 0 to 4, including both 0 and 4.

So, the correct answer is option A: {[tex]{x | 0 \leq x \leq 4}\\[/tex]}.

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. In this case, the function begins with a closed circle at (0, 2) and ends with a closed circle at (4, 6), which means that the function is defined at these specific points.

Since the function is a linear function, it represents a straight line.

A linear function is continuous, and it extends indefinitely in both directions.

Therefore, any x-value between 0 and 4 will also be defined by the linear function.

In mathematical notation, we can represent the domain as:

Domain: {x | 0 ≤ x ≤ 4}

This means that the domain of the function includes all x-values from 0 to 4, including both 0 and 4.

So, the correct answer is option A: {[tex]{x | 0 \leq x \leq 4}\\[/tex]}.

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complete question:

A linear function is shown on the graph.

a linear function that passes through the points (0, 2) and (4, 6)

What is the domain of the function?

[tex]{x | 0 \leq x \leq 4}\\{x | 0 < x < 4}\\{y | 2 \leq y \leq 6}\\{y | 2 < y < 6}[/tex]

graph is attached

Answer:

d

Step-by-step explanation:

bc i think it is

To find which number is one thousand times larger than 2.3 x 10², Change 1,000 to Scientific notation and then multiply by (2.3 x 10²).

The correct answer choice option C

This is a method of writing or of displaying real numbers as a decimal number between 1 and 10 followed by an integer power of 10.

which number is one thousand times larger than 2.3 x 10²

1000 to scientific notation

= 10³

2.3 x 10² × 1000

= 2.3 x 10² × 10³

= 2.3 × 10^5

Furthermore, scientific notation helps us to express numbers in decimal number between 1 and 10 followed by an integer power of 10. It also help us to represent numbers in this pattern.

Therefore, to find which number is one thousand times larger than 2.3 x 10², Change 1,000 to Scientific notation and then multiply by (2.3 x 10²).

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All the above data were obtained by entering them in excel format and obtaining it using standard methods.

A low standard deviation shows that the values tend to be close to the mean (also known as the expected value) of the set, whereas a high standard deviation suggests that the values are spread out over a wider range. The standard deviation is a measure of variance or dispersion in statistics. Standard deviation, often known as SD, is most frequently represented in mathematical texts and equations by the lowercase Greek letter (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

For sample size 5, Mean = 117.6 and Standard Deviation = 9.2

For sample size 12, Mean = 103.5 and Standard Deviation = 8.6

For sample size 30, Mean =104.6 and Standard Deviation = 8.7

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The condition for two line segments to be congruent is that they must have equal length.

What is a line segment?

A geometrical figure which is a part of a straight line having two unique endpoints is called a line segment. Each point on the line segment lies within the two given endpoints

Explanation of the fact that for the two given line segments to be congruent, they must have the same length

The given statement is False. Because two line segments are said to be congruent if and only if they have exactly the same length. If we construct a ray shorter than the line segment, then both will never be congruent according to the properties of congruence. So, for these two to become congruent, they must have the same length.

Hence, we obtain that the two line segments are congruent if they have exactly the same length.

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Answer:

[tex]3^{4}[/tex]

Step-by-step explanation:

Because 3x3x3x3

3 multipily by 4 times as it's same number

The value of sin S is = 5/13

Given a right triangle with hypotenuse BD = 13 & BC = 12, Find CD,

By, Pythagoras theorem

BD2 = BC2 + CD2

132 = 122 + CD2

CD2 = 132 - 122

CD2 = 169 – 144

CD2 = 25

CD =  

CD = 5

We know that,

Sin   = opposite side/hypotenuse

Sin S = 5/13

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Hence, these triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

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The correct option is r < 0 for the given inequalities of  p < 0, q > 0, and p + q = r.

For the given inequalities;

p < 0, q > 0, and p + q = r;

As, we know that if p < 0; then it hold the negative value.

And for  q > 0, it have the positive values.

Because -negative(P) was closer to zero than Positive q, let's say p = -10 and q = 5.

p + q = r

Put the values;

r = -10 + 5 = -5,

r = -5

Therefore, r < 0 is the correct condition for the given inequalities.

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Answer:

Step-by-step explanation:

(4x+8)

4(x+2)