If the original quantity is 20 and the new quantity is 16 ​, what is the percent​ decrease?

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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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]

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

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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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:

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: The trigonometric identity for the tangent of a sum of angles can be used to simplify the expression:

tan (480° + 300°) = (tan 480° + tan 300°) / (1 - tan 480° tan 300°)

Using the identity for the tangent of half an angle, the tangent of 480° can be expressed as follows:

tan 480° = tan (450° + 30°) = (tan 450° + tan 30°) / (1 - tan 450° tan 30°) = (1 + tan 30°) / (1 - tan 30°) = (1 + √3/3) / (1 - √3/3) = (1 + √3) / (√3 - 1)

Using the identity for the sine and cosine of a multiple of 30°, the tangent of 300° can be expressed as follows:

tan 300° = tan (30° * 10) = tan 30° / (1 - tan 30°) = √3 / (1 - √3) = √3 / (-1 - √3)

Plugging these values back into the expression for tan (480° + 300°), we get:

tan (480° + 300°) = (tan 480° + tan 300°) / (1 - tan 480° tan 300°) = ( (1 + √3) / (√3 - 1) + √3 / (-1 - √3) ) / (1 - (1 + √3) / (√3 - 1) * √3 / (-1 - √3) )

Expanding the denominator and simplifying, we get:

tan (480° + 300°) = ( (1 + √3) / (√3 - 1) + √3 / (-1 - √3) ) / ( (√3 - 1) / (-1 - √3) - (1 + √3) / (-1 - √3) )

Using the identity for the sine and cosine of a sum of angles, the sine and cosine of 480° + 300° can be expressed as follows:

sin (480° + 300°) = sin 480° cos 300° + cos 480° sin 300°

Finally, using the identity for the tangent of an angle in terms of sine and cosine, we get:

tan (480° + 300°) = sin (480° + 300°) / cos (480° + 300°) = sin 780° / cos 780°

The other trigonometric functions in the expression can be simplified using similar techniques, but the final result may be complex. However, it can be verified that the expression is equal to 3/2 by using a calculator or numerical methods.

Step-by-step explanation:

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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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:

Answer:28%

Step-by-step explanation:

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:

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!

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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The p-value (rounded to four decimal places) is 0.2709.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

p = 477/1000 = 0.477

p = 0.48

n = 1000

Now,

The test statistic for a hypothesis test for a proportion is given by:

z = (pi - p) / sqrt(p * (1 - p) / n)

where p is the sample proportion, p is the hypothesized proportion under the null hypothesis, n is the sample size, and sqrt is the square root function.

Substituting these values into the formula, we get:

z = (0.477 - 0.48) / sqrt(0.48 * 0.52 / 1000) ≈ -0.61

We find that the area to the left of z = -0.61 is approximately 0.2709 This means that the probability of getting a test statistic as extreme or more extreme than -0.61, assuming the null hypothesis is true, is 0.2709

Therefore, by probability the answer will be 0.2709

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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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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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The linear function that models this scenario is given as follows:

y = -0.25x + 13.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Bridget has 13 gallons of gasoline to use for her lawnmowing business, hence the intercept b is given as follows:

b = 13.

From the graph, when x increases by 20, y decays by 5, hence the slope m is given as follows:

m = -5/20

m = -0.25.

Hence the function is given as follows:

y = -0.25x + 13.

The problem is given by the image presented at the end of the answer.

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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

Answer:

The First question's answer is AngleW = 77 degrees

The Second question's answe is x = 2

Step-by-step explanation:

First Question:

AngleW = 7x

AngleY = 6x + 11

Since Opposite Angles in a parallelogram are equal,

AngleW = AngleY

or

7x = 6x + 11

7x - 6x = 11

x = 11

Now that we know the value of x, we can find the value of angleW

AngleW = 7x

AngleW = 7(11)

Angle W = 77

Second Question:

LN = 20

UN = 5x

Since LN and KM are diagonals of the parallelogram, they bisect each other at point of contact, so, UN = 1/2LN

or

5x=1/2 × 20

5x = 10

x = 2

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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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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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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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).

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:

no it can not so false boiiiiiiiii

Step-by-step explanation:

I think it’s false, maybe

Answer:

A: 5

Step-by-step explanation:

Using the side-splitter theorem (parallel lines and similar triangle ratios).

[tex]\frac{16}{4x} = \frac{28}{35}[/tex]

Through cross mutliplying, we get 112x = 560

x = 5

The number of hours of television watched and the number of hours of exercise, correct to three decimal places is 3.940.

A decimal is any number expressed in base-10 notation, which includes a decimal point and the numbers 0 through 9. Decimals are used to represent fractions, numbers that are not whole numbers, and numbers that are exceptionally large or tiny.

To calculate the correlation coefficient between hours of television watched and hours of exercise, we will use the formula

r = (∑xy − (∑x)(∑y) / n) /[tex]\sqrt{((2x-x/n)(2y-2/n))}[/tex]

where x is the number of hours of television watched and y is the number of hours of exercise.

Given the data provided, we have

x = 3, 14, 21, 28, 43

y = 38, 27, 36, 15, 30

Therefore,

∑x = 3 + 14 + 21 + 28 + 43 = 109

∑y = 38 + 27 + 36 + 15 + 30 = 156

∑xy = (3)(38) + (14)(27) + (21)(36) + (28)(15) + (43)(30) = 1291

∑x2 = 32 + 142 + 212 + 282 + 432 = 4552

∑y2 = 382 + 272 + 362 + 152 + 302 = 4644

n = 5 (number of members surveyed)

Substituting these values into the formula, we get

r = (1291 − (109)(156) / 5) /[tex]\sqrt{(4552-(109)2/5)(4644-(156)2/5)))}[/tex]

r = (1291 − 17784 / 5) /[tex]\sqrt{(4552-10902/5)(4644-24336/5)}[/tex]

r = (-16493 / 5) / [tex]\sqrt{(3456)(2036)}[/tex]

r = -3298.6 / [tex]\sqrt{695936}[/tex]

r = -3298.6 / 835.2

r = -3.94

Rounded to the nearest thousandth, r = -3.940.

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