The following data represents the age of 30 lottery winners.
20 25 28 33 34 36
37 40 40 41 42 43
47 50 50 51 51 52
53 53 54 55 56 57
62 68 68 70 76 82
Complete the frequency distribution for the data.
Age Frequency
20-29
30-39
40-49
50-59
60-69
70-79
80-89

Answer:28%

Step-by-step explanation:

Answer:

Уравнение 1 + tan(a) * tan(b) = (cos(a + b))/(cos(a) + cos(b)) может быть упрощено, используя тождество tan(a) * tan(b) = (sin(a) * sin(b))/(cos(a) * cos(b)) и тождество sin(a + b) = sin(a) * cos(b) + cos(a) * sin(b). Однако дальнейшее упрощение может быть невозможным, поскольку уравнение уже в довольно простой форме.

Answer:

 x = 1/2. 

Step-by-step explanation:

Hope this helps!

The value of the missing side assuming that all the intersecting sides meet at right angles would be = 6ft.

From the diagram above, the length and the width of one side of the figure is given as;

Length = 13 ft

width = 16 ft

This is supposed to be the same for the other missing side length and width ;

That is ;

width = 11 + 5 = 16 ft

Length = 13 = 7 + ?

Make ? that subject of formula;

? = 13-7 = 6 ft

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Answer:

y = - x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (- 3, 1) and (x₂, y₂ ) = (2, - 4) ← 2 points on the line

m = [tex]\frac{-4=1}{2-(-3)}[/tex] = [tex]\frac{-5}{2+3}[/tex] = [tex]\frac{-5}{5}[/tex] = - 1

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = - x - 2 ← equation of line

Answer:

11 words

Step-by-step explanation:

Thera are 56 words shared equally among 7 lines

Therefore there are 56/7 = 8 words per line

On the last line by adding 3 words, there will be 8 + 3 = 11 words

We can show that any field IF is a vector space over itself, with the field addition used as vector addition and the field multiplication used as scalar multiplication.

A field is a set of elements, denoted by IF, that satisfies the following axioms:

Commutativity of addition

Associativity of addition

Existence of additive identity

Existence of additive inverse

Commutativity of multiplication

Associativity of multiplication

Distributivity of multiplication over addition

Existence of multiplicative identity

Existence of multiplicative inverse

Given these axioms, we can show that IF is a vector space over itself.

Closure under addition: For any a, b in IF, their sum a + b is also in IF.

Commutativity of vector addition: For any a, b in IF, a + b = b + a.

Associativity of vector addition: For any a, b, c in IF, (a + b) + c = a + (b + c).

Existence of additive identity: The additive identity 0 in the field IF can also be used as the additive identity in the vector space.

Existence of additive inverse: For any a in IF, its additive inverse -a in the field IF can also be used as the additive inverse in the vector space.

Distributivity of scalar multiplication over vector addition: For any a in IF and any u, v in IF, a * (u + v) = a * u + a * v.

Distributivity of scalar multiplication over field addition: For any a, b in IF and any u in IF, (a + b) * u = a * u + b * u.

Existence of multiplicative identity: The multiplicative identity 1 in the field IF can also be used as the multiplicative identity in the vector space.

Therefore, we have shown that any field IF is a vector space over itself, with the field addition used as vector addition and the field multiplication used as scalar multiplication.

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let's say segment A(1 , 4) through B(6 , 14) gets partitioned by point C

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(1,4)\qquad B(6,14)\qquad \qquad \stackrel{\textit{ratio from A to B}}{2:3} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(1,4)=2(6,14)[/tex]

[tex](\stackrel{x}{3}~~,~~ \stackrel{y}{12})=(\stackrel{x}{12}~~,~~ \stackrel{y}{28}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{3 +12}}{2+3}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{12 +28}}{2+3} \right)} \\\\\\ C=\left( \cfrac{ 15 }{ 5 }~~,~~\cfrac{ 40}{ 5 } \right)\implies C=(3~~,~~8)[/tex]

According to the information, it can be inferred that Rebecca spent 31 minutes and 25 seconds on her phone from Monday to Thursday

To calculate the time Rebecca spent on her phone from Monday through Thursday we must add the number of minutes (and seconds) she used her phone during this period. For this we must rely on the information in the table:

According to the table, Rebecca made two calls each day, and each call was delayed:

Monday

call 1: 2 minutes 15 seconds

call 2: 4 minutes 23 seconds

Tuesday

call 1: 5 minutes 53 seconds

call 2: 1 minute 20 seconds

Wednesday:

call 1: 6 minutes 40 seconds

call 2: 3 minutes

Thursday:

call 1: 4 minutes 12 seconds

call 2: 3 minutes 42 seconds

Based on the above, we need to add the time in minutes and seconds and then calculate how much time in total she used her phone:

So finally we must divide the number of seconds into 60 (number of seconds that a minute has) and calculate how many minutes they are:

205 / 60 = 3.4

This equates to 3 minutes and 25 seconds. In total, Rebeca spent 31 minutes and 25 seconds on her phone from Monday to Thursday.

Note: This information is incomplete. Here is the complete information:

Monday

call 1: 2 minutes 15 seconds

call 2: 4 minutes 23 seconds

Tuesday

call 1: 5 minutes 53 seconds

call 2: 1 minute 20 seconds

Wednesday:

call 1: 6 minutes 40 seconds

call 2: 3 minutes

Thursday:

call 1: 4 minutes 12 seconds

call 2: 3 minutes 42 seconds

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Answer:

(x + 1)^2 + (y + 5)^2 = 169

Step-by-step explanation:

The equation of a circle centered at (h,k) with radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

To find the equation of the circle, we first need to find the center and the radius.

Given that the circle is centered at (-1,-5), h = -1 and k = -5.

Next, we need to find the radius. To do this, we use the point (0,-18) that lies on the circle and use the distance formula:

r = sqrt[ (0-(-1))^2 + (-18-(-5))^2 ] = sqrt[ 1^2 + (13)^2 ] = sqrt[1 + 169] = sqrt[170] = 13

So, the equation of the circle is:

(x + 1)^2 + (y + 5)^2 = 13^2

Therefore, the equation of the circle centered at (-1,-5) that passes through (0,-18) is:

(x + 1)^2 + (y + 5)^2 = 169

Therefore , the solution of the given problem of angle comes out to be sin α = 0.20 is between 10º and 1 and cos α = 0.32 is between 70º and 75º.

An angle, according to Euclidean geometry, is a shape comprised of two rays, referred as the angle's extremity, which meet at a vertex in the center. When two rays are combined, the surfaces on which they are focused may take on an angle. A plane collision also produces an angle. Dihedral angles are the name given to them. Angles are the shapes that two rays or lines with similar terminations can take in plane geometry.

Here,

a) he closest value to 0.32 is the cosine of 71.8º, which is approximately equal to 0.32.

Therefore, the angle α that satisfies

=>cos α = 0.32 is between 70º and 75º.

b) To find the value of the angle α that satisfies sin α = 0.20, it is necessary to look in the table of sine values ​​for angles of 0º, 30º, 45º, 60º and 90º, and find the closest value to 0.20.

The closest value to 0.20 is sine 11.5º, which is approximately equal to 0.20.

Therefore, the angle α that meets

=> sin α = 0.20 is between 10º and 1

Therefore , the solution of the given problem of angle comes out to be sin α = 0.20 is between 10º and 1 and cos α = 0.32 is between 70º and 75º.

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Answer: 3

Step-by-step explanation:

      The line y = 3x + 7 has a slope of 3. Slope-intercept form equations have a slope of m when written as y = mx + b. See the attached picture for more information.

y = mx + b ➜ y = 3x + 7 ➜ y = 3x + 7 ➜ 3

Answer:

Step-by-step explanation:

The ratio at which the y-value varies when the x-value changes is shown by a line's slope. The coefficient of x in the equation y = 3x + 7 is 3, therefore y rises by 3 units for every unit increase in x. The slope is thus 3. This indicates that the line will climb 3 units along the y-axis for every unit you move to the right along the x-axis.

The computed mean is 18.8 and it is more than 32.1 than the actual mean.

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.

The mean of the data is given as:

x' = ∑x / n

∑x = 29 + 13 + 6 + 45 + 1 = 94

x' = 94 / 5 = 18.8

The difference between the actual mean and the calculated mean is:

D = 50.9 - 18.8

D = 32.1

Hence, the computed mean is 18.8 and it is more than 32.1 than the actual mean.

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B. Theorem is the term that refer to true statements.

According to the definitions of the terms we have:

A confirmed factual assertion is referred to as a theorem.

• Proposition: A truthful assertion that's less significant but nonetheless intriguing.

• Lemma: A true statement that serves as an example of another true statement.

significant theorem that aids in the validation of other findings).

• Corollary: A true statement that can be inferred directly from a premise or theorem.

• Proof: The justification for why a claim is accurate.

• Conjecture: An assertion that is deemed true but for which there is no supporting evidence. (An assertion that is being put forth as being true).

• Axiom: A fundamental presumption regarding a mathematical scenario. (a premise we take to be true)

Hence, B. Theorem is the term that refer to true statements.

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Answer: To use synthetic division to find f(3), we will divide the polynomial 9v² - 28v + 19 by v - 3.

Here's the process:

| 9 -28 19|

v-3|____________|

9(3)² - 28(3) + 19

| 9 -84 57|

0 -96 38

So, f(3) = 9(3)² - 28(3) + 19 = 9(9) - 28(3) + 19 = 81 - 84 + 19 = -4 + 19 = 15.

So f(3) = 15.

Step-by-step explanation:

The area and perimeter of the shape is 4.65cm² and 9.5cm

Perimeter of a triangle = a + b +c , where a, b and c are the three different sides of the triangle. Area of a triangle = 1/2 b × h; where b is the base and h is the height of the triangle.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

Perimeter of the triangle = 3.2+ 2.0+4.3

= 9.5cm

The area of the triangle = ½bh

= 1/2 ×3.1 × 3

= 4.65 cm²

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The composition of functions f and g is:

(f o g) =6x^2 + 15x + 2

Here we have two known functions:

f(x) = 3x + 2

g(x) = 2x^2 + 5x

We want to find the composition:

(f o g)

That just means that we need to evaluate function f(x) in x = g(x), we wikk get:

(f o g) = 3*g(x) + 2

Now we can replace g(x) there to get:

(f o g) = 3*(2x^2 + 5x) + 2

          = 6x^2 + 15x + 2

That is the composition.

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Considering the expression c^n = d, for n > 1, the number c is the nth root of number d.

The expression for this problem is defined as follows:

c^n = d

To obtain the number that is the nth root to the other, an expression representing the nth root in the problem must appear.

The expression representing the nth root can appear isolating the variable c, as follows:

[tex]c = \sqrt[n]{d}[/tex]

Hence the number c is the nth root of number d.

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Answer:

no it can not so false boiiiiiiiii

Step-by-step explanation:

I think it’s false, maybe

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{12}-\underset{x_1}{4}}} \implies \cfrac{ -6 }{ 8 } \implies - \cfrac{3 }{ 4 }[/tex]

Step-by-step explanation:

The two adjacent vertices of the triangle are A(5; 3) and B(7; 7), and one point on the opposite side is P(-2; 9). To find the coordinates of the third vertex, we need to find the midpoint of AB and extend it to P.

The midpoint of AB can be calculated by finding the average of their x-coordinates and y-coordinates:

C = ((A_x + B_x)/2, (A_y + B_y)/2) = ((5 + 7)/2, (3 + 7)/2) = (6, 5)

Next, we can use the midpoint C and point P to find the slope of the line connecting them:

m = (P_y - C_y) / (P_x - C_x) = (9 - 5) / (-2 - 6) = 4 / -8 = -0.5

Since the slope of a line perpendicular to this one is -2, we can use the midpoint C and the slope to find the equation of the line connecting C and the third vertex D:

y - C_y = -2 (x - C_x)

y - 5 = -2 (x - 6)

Expanding and solving for x, we get:

y = -2x + 17

Substituting the y-coordinate of P (-2) into this equation:

-2 = -2x + 17

Solving for x:

x = 7.5

Finally, we can use the x-coordinate to find the y-coordinate:

y = -2x + 17 = -2 * 7.5 + 17 = 5.5

So the third vertex is D (7.5, 5.5).

The vertices of the triangle are A (5, 3), B (7, 7), and D (7.5, 5.5).

Answer:

y = -110x + 1,600

Step-by-step explanation:

Zachary purchased a computer for $1,600 on a payment plan. Four months after he purchased the computer, his balance was $1,160. Five months after he purchased the computer, his balance was $1,050. What is an equation that models the balance y after x months?

1,160 - 1,050 = $110 change from month 5 to 4

Double check if the rate of decrease is steady over time:

1,600 - ($110 * 4 months) = 1,160

1,600 - ($110 * 5 months) = 1,050

This means, Zachary is paying $110 per month for his computer.

SO:

remaining payment plan balance = initial balance - 110 per month

This can be modeled by the algebraic equation:

y = 1,600 - 110x

rearrange right side:

y = -110x + 1,600

Answer:

[tex]y=-110x+1600[/tex]

Step-by-step explanation:

Given information:

Define the variables:

Therefore:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Determine if the equation is linear by calculating the slope between each pair of (x, y) points:

[tex]\implies \text{Slope}\;(m)=\dfrac{1050-1160}{5-4}=-110[/tex]

[tex]\implies \text{Slope}\;(m)=\dfrac{1160-1600}{4-0}=-110[/tex]

As the slope is the same, the equation is linear.

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

As the initial purchase price of the computer was $1,600, the y-intercept is 1600.  We have already calculated the slope. Therefore, substitute the found slope and y-intercept into the slope-intercept formula to create an equation that models the balance y after x months:

416 ÷ 100 = 4.16

4.16 ÷ 10 = 0.416

41600 ÷ 1000 = 4.1600 = 4.16

4.16 ÷ 100 = 0.0416

41.6 ÷ 100 = 0.416

When you divide by a power of 10, you move the decimal to the left the number of 0's in the number.

    ÷ 10 and you move the decimal point 1 place to the left

    ÷ 100 and you move the decimal point 2 places to the left

    ÷ 1000 and you move the decimal point 3 places to the left

Answer:

416 / 100 = 4.16

4.16 / 10 = 0.416

41600 / 1000 = 41.6

4.16 / 100 = 0.0416

41.6 / 100 = 0.416

Step-by-step explanation:

When you divide a number by another number, you find out how many times the second number fits into the first one. For example, in the expression 416 / 100, you are finding out how many times 100 fits into 416. The answer is 4.16, meaning 100 fits into 416 4 times with a remainder of 16.

Similarly, in the expression 4.16 / 10, you are finding out how many times 10 fits into 4.16. The answer is 0.416, meaning 10 fits into 4.16 0 times with a remainder of 4.16.

In the expression 41600 / 1000, you are finding out how many times 1000 fits into 41600. The answer is 41.6, meaning 1000 fits into 41600 41 times with a remainder of 600.

In the expression 4.16 / 100, you are finding out how many times 100 fits into 4.16. The answer is 0.0416, meaning 100 fits into 4.16 0 times with a remainder of 4.16.

In the expression 41.6 / 100, you are finding out how many times 100 fits into 41.6. The answer is 0.416, meaning 100 fits into 41.6 0 times with a remainder of 41.6.

The area of the trapezoid with base lengths of 16 cm and 13 cm and the height with 10 cm, is 145 cm²

A trapezoid, also known as a trapezium, is a flat-closed shape having 4 straight sides, with one pair of parallel sides.

Given that, a trapezoid has base lengths of 16 centimeters and 13 centimeters, the height of the trapezoid is 10 centimeters, we are asked to find the area of the trapezoid,

Area of the trapezoid = (sum of the bases) × height / 2

Length of bases = 16 cm and 13 cm

Height = 10 cm

Area of the trapezoid = 16+13 × 10/2

= 145

Hence, the area of the trapezoid with base lengths of 16 cm and 13 cm and the height with 10 cm, is 145 cm²

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The cube root can be estimated in the range:

3 < ∛29 < 4

And the value is ∛29 = 3.1

First we need to find two perfect cubes that bound our number.

We know that:

3*3*3 = 3^3 = 27

4*4*4 = 64

Then:

27 < 29 < 64

∛27 < ∛29 < ∛64

3 < ∛29 < 4

So we have an estimation of the cube root, and it will be closer to 3 than to 4, so we can estimate this as:

∛29 = 3.1

3.1 = 29.7

So it is a good estimation.

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On x-axis where |x|>0 is located at point E on the coordinate plane.

What does a math definition of a coordinate plane mean?

A surface with two dimensions known as the coordinate plane is created by two number lines. The x-axis is the name given to one horizontal number line. The y-axis is the name given to the vertical number line that is the other number line. A place known as the origin is where the two axes collide.

                        To graph points, lines, and other things, we can utilize the coordinate plane. The Y-axis and the X-axis cross to create a two-dimensional plane known as a coordinate plane, also referred to as a rectangular coordinate plane grid.

on x-axis except at the origin

or on x-axis where |x|>0

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It cost $17.82 to buy the papers needed for this reports

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

A long year-end status report for work is 141 pages long. You need to print 18 copies for a meeting next week. Therefore:

Amount of paper printed = 141 pages long * 18 copies = 2538 pages

Paper is sold in reams (500 pages) for $3.51 each. Hence:

Amount spent on papers = 2538 pages * ($3.51 / 500 pages) = $17.82

About $17.82 was spent on papers

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Answer:

8

Step-by-step explanation:

46 = 10b - 34

Move 34 to the other side by adding 34 to each side

80 = 10b

Divide 10 on each side to get b on one side

8 = b