The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.


2 0, 1, 4
3 1, 2, 6
4 1, 3, 7
5 1, 1
6 5
Key: 3|2 means 3.2


What is the mean, and what does it tell you in terms of the problem?

Answer: A

Step-by-step explanation :

HE ASKED YOU ABOUT AN EQUALTULAR ( TO EQUALED AND OPPSITE ANGLE )

Answer:

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

(Sum of first 5 quizzes) / 5 quizzes = 8

Sum of 1st 5 quizzes = 8 x 5 = 40

let x = score on the 8th quiz

(40 + 7 + 5 + x) / 8 = 7.5

52 + x = (7.5)(8) = 60

x = 60 - 52 = 8

Answer:

I think the answer is 33?

The values of the variables, x and y in the angles formed by the parallel lines that have a common transversal are;

x = 4°, y = 10°

11. x = 9°, y = 12°

12. x = 14°, y = 5°

13. x = 8°, y = 11°

14. x = 16°, y = 23°

15. x = 9°, y = 13°

Parallel lines are lines that maintain the same distance from each other along their lengths.

From the figure, we get;

(29·x - 3) and (15·x + 7) are linear pair angles, therefore;

(29·x - 3) + (15·x + 7) = 180°

44·x + 4 = 180

x = (180 - 4)/44 = 4

x = 4°

(15·x + 7) and (13·y - 17) are same side exterior angles between parallel lines, therefore;

(15·x + 7) + (13·y - 17) = 180°

(15×4 + 7) + (13·y - 17) = 180°

67 + 13·y - 17 = 180°

50 + 13·y = 180

13·y = 180 - 50 = 130

y = 130 ÷ 13 = 10

y = 10°

11. (18·x - 44)° and  (8·x - 10)° are same side exterior angles, therefore;

(18·x - 44)° +  (8·x - 10)° = 180°

26·x - 54 = 180

x = (180 + 54)/26 = 9

x = 9°

(8·x - 10)° and (13·y - 38)° are linear pair angles, therefore;

(8·x - 10)° + (13·y - 38)° = 180°

(8 × 9 - 10)° + (13·y - 38)° = 180°

62 - 38 + 13·y = 180

13·y = 180 - (62 - 38) = 156

y = 156 ÷ 13 = 12

y = 12°

12. (9·x - 2)° and (5·x + 54)° are corresponding angles, therefore;

(9·x - 2)° = (5·x + 54)°

(9·x - 2)° = (5·x + 54)°

9·x - 5·x = 54 + 2 = 56°

4·x = 56°

x = 56° ÷ 4 = 14°

x = 14°

(9·x - 2)° and (10·y + 6)° are linear pair angles, therefore;

(9·x - 2)° + (10·y + 6)° = 180°

(9 × 14 - 2)° + (10·y + 6)° = 180°

124 + 6 + 10·y = 180

10·y = 180 - 130 = 50

y = 50 ÷ 10 = 5

y = 5°

13. The angle to which the angle (8·x - 1)° is an alternate interior angle is a corresponding angle to the angle (11·x - 25)°, therefore;

(8·x - 1)° is congruent to angle (11·x - 25)°

(8·x - 1)° = (11·x - 25)°

11·x - 8·x = 25 - 1 = 24

3·x = 24

x = 24 ÷ 4 = 8

x = 8°

Angles (15·y - 48)° and (8·x - 1)° are linear pair angles, therefore;

(15·y - 48)° + (8·x - 1)° = 180°

(15·y - 48)° + (8 × 8 - 1)° = 180°

(15·y - 48)° + 63° = 180°

15·y + 15° = 180°

15·y = 180° - 15° = 165°

y = 165° ÷ 15 = 11°

y = 11°

14· The angle (4·x + 4)° and (7·x - 44)° are alternate exterior angles, therefore;

(4·x + 4)° = (7·x - 44)°

7·x - 4·x = 44° + 4° = 48°

3·x = 48°

x = 48° ÷ 3 = 16°

x = 16°

The vertical angle to angle 39° is a linear pair angle to the angle (8·y - 43)°

Therefore;

39 + 8·y - 43 = 180°

8·y  = 180 + 43 - 39 = 184

y = 184 ÷ 8 = 23

y = 23°

15. The diagram indicates that the angles (15·x - 26)° and (12·x + 1)° are congruent, therefore;

(15·x - 26) = (12·x + 1)

(15·x - 12·x) = (26 + 1)

3·x = 27

x = 27 ÷ 3 = 9

x = 9°

The vertical angle to (2·x + 1) is therefore;

12·x + 1 = 12 × 9 + 1 = 109

The angle sum property indicates that we have;

28° + 109° + (4·y - 9)° = 180°

(4·y - 9)° = 180° - (28° + 109°) = 43°

(4·y - 9)° = 43°

(4·y)° = 43° + 9° = 52°

y = 52°/4 = 13°

y = 13°

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The solution of the given statement will be inequality c > -60.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.

We have been given the statement "number c divided by 3 is greater than -20".

As per the given statement, we can represent this algebraic form with inequality as:

⇒ c / 3 > -20

Inequality by multiplying both sides of the inequality by 3:

⇒ 3 × c / 3 > 3 × -20

⇒ c > -60

Thus, the solution of the given statement will be inequality c > -60.

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The question seems to be incomplete the correct question would be

Find the solution if a number c divided by 3 is greater than -20.

Answer:

52°

Step-by-step explanation:

This is an equilateral triangle. Therefore all the sides and angles are equal to each other.

We know that,

the sum of the interior angles in a triangle is 180° and in equilateral triangles each angle measured 60° ( 180°/3 ).

Accordingly,

x + 8 = 60

Subtract 8 from both sides.

x = 60 - 8

x = 52°

By using the formula of acceleration, it can be calculated that

Time taken by an earthworm  to accelerate from a speed of 0.01 m/s to 0.02 m/s over a distance of 0.9 m is 59.88 s

What is acceleration?

At first, it is important to know about velocity

Distance travelled by a body per unit interval of time in a particular direction is called Velocity

The rate of change of velocity is called acceleration.

Acceleration is a vector quantity as the direction is taken into account.

Initial velocity of earthworm (u)= 0.01 m/s

Final velocity of earthworm (v) = 0.02 m/s

Distance (s) = 0.9 m

We know,

[tex]v^2 = u^2 + 2as\\0.02^2 = 0.01^2 + 2 \times a \times 0.9\\0.02^2 - 0.01^2 = 1.8a\\(0.02 + 0.01)(0.02 - 0.01) = 1.8a\\a = \frac{0.03 \times 0.01}{1.8}\\a = 0.000167 \ ms^{-2}[/tex]

Again,

v = u + at

0.02 = 0.01 + 0.000167[tex]\times[/tex] t

t = [tex]\frac{0.02 - 0.01}{0.000167}[/tex]

t = 59.88 s

Time taken by an earthworm  to accelerate from a speed of 0.01 m/s to 0.02 m/s over a distance of 0.9 m is 59.88 s

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In the given equation [12.5x + 5y = C] the constant C is always 50 with different given values of x and y.

So, the values of C are:

Calculate as follows:

(A) When x = -2 and y = 15.

(B) When x = 0 and y = 10.

(C) When x = 2 and y = 5.

(D) When x = 4 and y = 0.

Therefore, in the given equation [12.5x + 5y = C] the constant C is always 50 with different given values of x and y.

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To make a square using the method of completing the square.

[ (a + b)² = a² + 2ab + b² ]

[ (a - b)² = a² - 2ab + b² ]

x² - 13x + 31 = 0

(x - 13/2)² + (293/4) = 0

The number added to complete the square is 293/4.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

x² - 13x + 31 = 0

To make a square using the method of completing the square.

[ (a + b)² = a² + 2ab + b² ]

[ (a - b)² = a² - 2ab + b² ]

x² - 2 x (13/2)x + (13/2)² - (13/2)² + 31 = 0

(x - 13/2)² + 169/4 + 31 = 0

(x - 13/2)² + (293/4) = 0

Thus

The number added to complete the square is 293/4.

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Using polar coordinates, volume of the given solid is, 32√3π.

What is volume of solid?

An object's space requirement is expressed in terms of its volume. The amount of unit cubes required to completely fill the solid is how much it weighs. We have a total of 30 unit cubes in the solid, so the volume is as follows: 2 units 3 units 1 unit Equals 30 cubic units

We have to find the volume of the solid Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4 using polar coordinates.

So, the volume is

[tex]2\int\limits\int\limits_D {\sqrt{16-x^2-y^2} } \, dA[/tex]

[tex]2\int\limits^2^\pi _0 {\int\limits^4_2 {\sqrt{16-r^2} } rdrdtheta[/tex]

[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(16-r^2)_2^4 } \, dtheta[/tex]

[tex]2\int\limits^2^\pi _0 {(-\frac{1}{3})(-2\sqrt{3}) } \, dtheta[/tex]

[tex]\int\limits^2^\pi _0 {16\sqrt{3} } \, dtheta[/tex]

[tex]32\sqrt{3}\pi[/tex]

Hence, the volume of the given solid using polar coordinates is, [tex]32\sqrt{3}\pi[/tex].

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The linear equation in the slope-intercept is:

y = (-1/5)*x  - 26/5

And it can be written as:

y = (-1/5)*(x + 1) - 5

We can write the equation for line L as:

y = a*x +b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the product between the slopes is equal to -1.

So if we want our line to be perpendicular to y= 5x, then we must have:

a*5 = -1

a = -1/5

So our line is something like:

y = (-1/5)*x + b

And the line passes through (-1, -5), replacing these values:

-5 = (-1/5)*-1 + b

-5 = 1/5 + b

-5 - 1/5 = b

-26/5 = b

The linear equation is:

y = (-1/5)*x  - 26/5

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The factors of 6x²y-10xy+15x-25​ are (3x-5)(2xy+5).

According to the question,

We have the following expression:

6x²y-10xy+15x-25​

In this expression, we can not use any identity to solve it further.

Now, in order to find the factors of this expression, we will find the common terms from the first two terms and one common factor from the last two terms.

Taking 2xy as a common factor from first two terms and 5x as a common factor from the last two terms:

2xy(3x-5)+5(3x-5)

Taking (3x-5) as a common factor from the above expression:

(3x-5) (2xy+5)

Hence, the factors of 6x²y-10xy+15x-25​ are (3x-5)(2xy+5).

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The fifth term of the geometric progression is -0.125 and the sum of the first 20 terms is  [tex]\frac{4}{3}(\frac{1-2^{20} }{2^{20} }) }[/tex]

A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio.

All terms of a geometric progression have a common multiple called the common ratio.

if a = -2, which is first term

r = -0.5 which is common ration,

Then fifth term = a[tex]r^{4}[/tex]

substitute a and r into the above equation, you have

fifth term = (-2)([tex](-0.5)^{4}[/tex] = - 0.125

sum of G.P when the common ratio is less than 1, we have

[tex]\frac{a(1 - r^{n} )}{1 - r}[/tex]

where n = number of terms = 20

sum = [tex]\frac{-2(1 - (-0.5)^{20}) }{1--0.5}[/tex] =  [tex]\frac{4}{3}(\frac{1-2^{20} }{2^{20} }) }[/tex]

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Answer: Let us assume speed of jet in still air =x

speed of wind =y

Jet flying against the wind

Relative speed of the jet = speed of jet in still air -speed of the wind=x-y

distance covered =3426

time =6 hours

distance = speed * time

3426=(x-y)*6

x-y =3426/6

x-y=571——(1)

Jet flying with the wind

Relative speed of the jet = speed of jet in still air +speed of the wind=x+y

distance covered =4026

time =6 hours

distance = speed * time

4026=(x+y)*6

x+y =4026/6

x+y=671———-(2)

solving 1 and 2 we get

x+y=671

x-y=571

x=621

y=50

speed of jet in the still air =x= 621 miles per hour

Step-by-step explanation:

The maximum number of guests that can fill all the standard rooms is twice the number of the standard rooms

Information from the question

each standard room can fill 2 guests

the maximum number of guests that all standard rooms can accommodate = ?

The problem is solved by multiplication

each standard room (1) = 2 guests

all standard rooms = ?

cross multiplying

? * 1 = 2 * all standard rooms

? = all standard rooms times two

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The range of the function is y ≤ 3.

The set of a function's potential output values is known as its range.

Given, the graph of the function.

The range of a function is the set of values of y the function can take.

The maximum y value of the function is 3, and the graph is going down both sides infinitely.

Therefore, the range of the function is y ≤ 3.

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The exact arc length of f(x)=√2x+1 is 4.5.

The arc length is the separation between two points along a curve segment. The arc length of a function f(x) is given by the formula,

[tex]L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx[/tex]

Where f'(x) is derivative of function f(x). The arc length is, to put it simply, the distance that passes across the curved line of the circle that forms the arc. It should be noted that the arc's length is greater than the separation of its ends along a straight line.

Finding the arc length of f(x)=√2x+1 0≤x≤4, using the formula,

First finding the derivative of function,

[tex]f'(x)=\frac{d(\sqrt{2x+1})}{dx} \\\\=\frac{2}{2\sqrt{2x+1}} \\\\=\frac{1}{\sqrt{2x+1}}[/tex]

Now, putting the derivative of function f(x) in the formula of arc length L,

[tex]L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+(\frac{1}{\sqrt{2x+1}})^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+\frac{1}{2x+1}}}\\\\L=\int\limits^4_0 {\sqrt{\frac{2x+1+1}{2x+1}}}\\L=\int\limits^4_0 {\sqrt{\frac{1}{2x+1}}}\\\approx4.5[/tex]

Therefore, the exact arc length of f(x)=√2x+1 is 4.5.

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-4 2/3 ,-3 2/3, -1 2/3 2/3

The expression used to find the width using division is:

W = A/L

We know that for a rectangle of width W and length L, we know that the area is given by the product between these two dimensions, then:

A = L*W

We want a expression using division that can be used to find the width, so, suppose we know the values of the area and the length, the we can divide both sides by L to get:

A/L = W

This expression gives the width.

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Answer:

103 N

Step-by-step explanation:

we use the equation: w = mg

where m is mass, W is weight and g is gravitational field strength

w = ?

m= 10.5 kg

g = 9.81 ms‐² (for earth)

so,

w = 10.5 × 9.81

w = 103.005

w ≈ 103 Newtons

Answer:

Figure A was translated right 4 units and up 2 units

Answer:

Here,

Let the age of Adam be x

and ,Brian be y

so,x=y+20.........eqn 1

and ,2(y+2)=x

or,2y+4=x......eqn 2

Now ,

subtracting eqn1 and eqn 2

so, x=y+20

x=2y+4

- - -

______________

0 = -y+16

so,y=16 and x=y+20 =16+20=36 .

so Adam is 36 years old and brian is 16.

The standard score (z-score) of the given sample mean is equal to 7.11

A standard score is also referred to as a z-value or z-score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

Mathematically, the standard score of a given sample mean can be calculated by using this formula:

[tex]Z=\frac{\bar{x}\;-\;\mu}{ \frac{\delta}{n} }[/tex]

Where:

Where:

Substituting the given parameters into the formula, we have;

Standard score, z = (30 - 31)/(9/64)

Standard score, z = -1/0.140625

Standard score, z = 7.11

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The cost of topsoil per ton would be $48.

The cost of pea gravel per ton is  $20.

The cost of mulch per ton is $479.

What is the linear equations in two variable?

A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equation.

We have,

7 tons of topsoil, 6 tons of mulch, and 3 tons of pea gravel for $3270.

5 tons of topsoil, 5 tons of mulch, and 5 tons of pea gravel for $3015.

Let,

cost of topsoil per ton = x

cost of pea gravel per ton = x - 28

cost of mulch per ton = m

7x + 6m + 3(x - 28)  = 3270

7x + 6m + 3x - 84  = 3270

10x + 6m = 3270 + 84

10x + 6m = 3354 -------------(i)

5x + 5m + 5(x - 28)  = 3015

5x + 5m + 5(x - 28)  = 3015

10x + 5m = 3015 - 140

10x + 5m = 2875 -----------(II)

Subtracting equation (II) from (I), we get

   10x + 6m = 3354

-   10x + 5m = 2875

Solving we get

       m = 479

Put m = 479 in equation(I), we get

           10x + 6m = 3354

           10x + 6(479) = 3354

           10x = 480

              x = 480/10

              x = 48

Hence,

The cost of topsoil per ton would be = x = $48.

The cost of pea gravel per ton = x - 28 = 48 - 28 = $20.

The cost of mulch per ton = m = $479.

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If lliot and Jack share some money in the ratio . 8:5 Elliot got £21 more than Jack. The amount that Elliot received is £56.

Given data;

Sharing ratio 8:5

Amount Elliot got = 21

In order to determine  the amount that Elliot received we need to formulate and equation and then use the formulated equation to find the amount received.

Equation

21 × 8 ÷ (8-5)

Hence,

£21 × 8 ÷ (8-5)

£168 ÷ 3

=  £56

Therefore Elliot received £56.

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1) The probability that a randomly chosen penny weighs less than 2.4 grams is; 0.00621.

2) The probability that the mean weight of 15 pennies is less than 2.4 grams is; 0

The central limit theorem in statistics tells us that the sampling distribution of the mean will usually be normally distributed, provided that the sample size is large enough.

We are given the following parameter;

Population mean; μ = 2.4 grams

Standard deviation; σ = 0.04 grams

1) The probability that a randomly chosen penny weighs less than 2.4 grams is: P(X < 2.4)

Formula for z-score is;

z = (X - μ)/σ

z = (2.4 - 2.5)/0.04

z = -2.5

The p-value from z-score calculator is; p = 0.00621.

2) The standard deviation for these 15 pennies will now be;

σ' = 0.04/√15

σ' = 0.0103

The probability that the mean weight of 15 pennies is less than 2.4 grams is expressed as;

P(X' < 2.4)

z = (2.4 - 2.5)/0.0103

z = -9.709

The p-value from z-score calculator is; p = 0

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Answer:

no

Step-by-step explanation:

the percentage has nothing to do with how many of them there are, forgive me if im wrong

The exact number of books on the shelf cannot be determined based on the information given.

An expression is a grouping of one or more mathematical or logical operators, operands (values, variables, or other expressions), and brackets in mathematics and computer programming that denote a computation that can be evaluated to generate a value.

We know that between 50 and 100 books are stored on a shelf, so let's assume the number of books is some integer value between 50 and 100, inclusive. Let's call this value "n".

Exactly 20% of the books are textbooks, which means there are 0.2n textbooks on the shelf.

Exactly one-seventh of the books are novels, which means there are (1/7)n novels on the shelf.

We know that n, 0.2n, and (1/7)n are all integers because they represent whole numbers of books. We can write this as:

n = a

0.2n = b

(1/7)n = c

where a, b, and c are integers.

From the second equation, we know that 0.2n is a multiple of 1/10. From the third equation, we know that n is a multiple of 7. Therefore, we can rewrite these equations as:

n = 10b

n = 7c

Since n is equal to both 10b and 7c, we know that n must be a multiple of the least common multiple of 10 and 7, which is 70.

So, n must be a multiple of 70, and therefore must be one of the integers 50, 70, or 90. However, we cannot determine which of these three values is the correct one based on the information given, because all three satisfy the conditions in the problem:

If n=50, then 20% of the books (i.e., 10 books) are textbooks, and 1/7 of the books (i.e., 7.14 books, which we round down to 7) are novels.

If n=70, then 20% of the books (i.e., 14 books) are textbooks, and 1/7 of the books (i.e., 10 books) are novels.

If n=90, then 20% of the books (i.e., 18 books) are textbooks, and 1/7 of the books (i.e., 12.86 books, which we round down to 12) are novels.

Therefore, the exact number of books on the shelf cannot be determined based on the information given.

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