A dance group of 17 teenagers had a mean mass of 44.5kg. to enter a competition there needs to be 18 people in the group with an average mass of 44.4kg or less. what is the maximum mass that the 18th person could be

The angle of depression, at which Tom threw the paper is 14.93°

In this question,

Tom throws a paper from a height of 4 feet, and it lands 15 feet from the car.

We need to find the angle of depression, at which he threw the paper.

Consider the following diagram.

Let the θ be the angle of depression, at which he threw the paper.

Consider the tangent of angle θ.

⇒ tan(θ) = 4/15

⇒ θ = [tex]tan^{-1}(\frac{4}{15} )[/tex]

⇒ θ = 14.93°

Therefore, the angle of depression, at which Tom threw the paper is 14.93°

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The equation of a line with slope = 0 and y-intercept = (0,-2) is: y = -2

Now,

Given:

To find: Equation of the line

Finding:

Now, we know that the slope-point form method to find the equation of a line, requires only two things: slope of the line and coordinates of the y-intercept.

The equation so given by the method: y = mx + c, where

m = slope of the line

c = y-intercept

On substituting the given values in the above equation, we get:

=> y = 0x - 2, which the required equation of the line.

Hence, The equation of a line with slope = 0 and y-intercept = (0,-2) is: y = -2.

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The required simplified value of the quantity is  1 / 81. Option A is correct.

Given that,
To determine the simplified value of the quantity one-third raised to the second power times one-third raised to the zero power end quantity all raised to the second power.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
According to the question,
= [(1 / 3)² + ( 1 / 3)⁰]²
Simplification,
= (1 / 3)²°²
= (1 / 3)⁴
= 1⁴ / 3⁴
= 1 / 81  (since 3⁴ = 81)

Thus, the required simplified value of the quantity is  1 / 81. Option A is correct.

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Step-by-step explanation:

$2.88 per pound

so, then how much for e.g. 2 pounds ?

right : the price for 1 pound plus 1 pound = 2×$2.88 = $5.76

and so on.

therefore, 3.9 pound cost :

3.9 × $2.88 = $11.232 ≈ $11.23

Answer:

11.232

Step-by-step explanation:

3.9×2.88=11.232

The value of the variable k must equal to - 2 such that the line segment MS is perpendicular to the line segment OP.

According to analytical geometry, two lines are perpendicular to each other if the product of their slopes are equal to - 1. Slopes can be determine by secant line formula:

m₁ = (5 - 8) / [- 2 - (- 6)]

m₁ = - 3 / 4

m₂ = [(k - 2) - (- 20)] / [13 - (k + 3)]

m₂ = (k + 18) / (10 - k)

(- 3 / 4) · [(k + 18) / (10 - k)] = - 1

(- 3 / 4) · (k + 18) = - (10 - k)

- 3 · (k + 18) = - 4 · (10 - k)

- 3 · k - 54 = - 40 + 4 · k

7 · k = - 54 + 40

7 · k = - 14

k = - 2

The value of the variable k must equal to - 2 such that the line segment MS is perpendicular to the line segment OP.

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Using algebraic expression and equation, each pen costs 14 cents while each pencil costs 3 cents.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

Given that the pens cost 11 cents more than the pencils, we can express this as:

x = 11 + y

where x = cost of each pen (cents)

y = cost of each pencil (cents)

If Lin ordered 250 pens and 250 pencils and the total order costs $42.50, we can express that as:

250x + 250y = $42.50

Substitute the value of x in this equation and solve for y.

250x + 250y = $42.50

250(11 + y) + 250y = 4250 cents

2750 + 250y + 250y = 4250

500y = 1500

y = 3

cost of each pencil = 3 cents

x = 11 + y

x = 11 + 3

x = 14

cost of each pen = 14 cents

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answer:

5

explanation:

(5*5) + 3=28

(7*5) - 7= 28

The expression that shows the number of books he sold on Thursday is x + 9 = 27; 18 books

The given parameters are

Friday sales = 27

Friday sales = 9 more than the number of books he sold on Thursday.

Let the number of books he sold on Thursday be x

So, we have

Friday = 9 + x

This gives

27 = 9 + x

Rewrite as

x + 9 = 27

Solve

x = 18

Hence, the expression that shows the number of books he sold on Thursday is x + 9 = 27; 18 books

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Answer:

(2x2x2)*(2x2x2x2x2) so 8x32 = 256

Step-by-step explanation:

Answer: Simplify  {2}^{3}2

3

  to  88.

8x\times {2}^{5}

8x×2

5

2 Simplify  {2}^{5}2

5

  to  3232.

8x\times 32

8x×32

3 Simplify.

256x

Step-by-step explanation: hope this helps!!!!

[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]

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

[tex]\textsf{Parallel lines have the same slope, thus:}[/tex]

[tex].\qquad\bullet\sf{Slope\:of\:the\:line\:that's\:parallel\:to\:the\:given\:line: \dfrac{1}{3}}[/tex]

[tex]\textsf{Next, we'll apply the \textbf{Point-Slope Formula:}}[/tex]

[tex].\qquad\bullet\sf{y-y_1=m(x-x_1)}[/tex]

[tex]\textbf{\underline{Setting the values:}}[/tex]

[tex].\qquad\bullet\sf{y_1=2}\\.\qquad\bullet m=1/3\\.\qquad\bullet x_1=6}}[/tex]

[tex]\textbf{\underline{Plugging in the values:}}[/tex]

[tex].\qquad\bullet\sf{y-2=\dfrac{1}{3} (x-6)}\\\\.\qquad\bullet y-2=\dfrac{1}{3}x-2}\\\\.\qquad\bullet y=\dfrac{1}{3} x}[/tex]

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

[tex]\large\overbrace{\underbrace{\textsf{\textbf{Reflection - RoSe}}}}^\star_\star[/tex]

Answer:11.25

Step-by-step explanation: first subtract 12 from both sides then you would have 3.2x=36

and then divide both sides by 3.2 which is x=11.25

Answer: x=11.25

Step-by-step explanation: 48-12> 36> 3.2x=36> divide 36 by 3.2> x= 11.25

Hope this helped

Answer:

400 ml of lemon juice

Step-by-step explanation:

We know that there are 700 ml of salad dressing, and the ratio of lemon juice to vinegar is 4:3. We know that therefore, there are 7 equal parts. To find how many ml are in one part, we divide 700 by 7, which gives us 100. Then we can multiply that answer by 4 to find how many ml of lemon juice and 3 to find how many ml of vinegar.

100 x 4 = 400

Therefore, Vicky uses 400 ml of lemon juice.

Answer:50 pounds a month

Step-by-step explanation:400 divided by 8=50pounds

Answer:

You substitute the x with the number.

8(3)+5=29 so 8*3 is 24 + 5 is 29

Step-by-step explanation:

Answer:

2x² - 25x + 90

Step-by-step explanation:

→ Replace every x in 2x² + 5x + 15 with -x + 5

2 × ( -x + 5 )² + 5 ( -x + 5 ) + 15

→ Simplify

2 ( x² - 10x + 25 ) - 5x + 25 + 15

→ Expand

2x² - 20x + 50 - 5x + 40

→ Simplify

2x² -25x + 90

[tex]\frac{12}{5}[/tex] = [tex]2\frac{2}{5}[/tex] revolutions per second is the unit rate.

An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.

1) Convert mixed fractions into fractions.

[tex]6\frac{2}{5}[/tex] = [tex]\frac{((6*5) + 2)}{5}[/tex] = [tex]\frac{32}{5}[/tex]

[tex]2\frac{2}{3}[/tex] = [tex]\frac{((2*3) + 2)}{3}[/tex]  =  [tex]\frac{8}{3}[/tex]

2) [tex]\frac{32}{5}[/tex] ÷ [tex]\frac{8}{3}[/tex] ; where [tex]\frac{32}{5}[/tex] is the 1st fraction and [tex]\frac{8}{3}[/tex] is the 2nd fraction

a) Find the second fraction's reciprocal:

  From [tex]\frac{8}{3}[/tex] to [tex]\frac{3}{8}[/tex]

b) Multiply the first fraction by the second fraction's reciprocal, which is 32/5, 5/3, or (5/3), to get 96/40.

c) Simplify the fraction.

Divide 96 / 40 by 4 to get 24/10.

Divide 24/10 by 2, and the result is 12/5. The 96/40 simple fraction

[tex]\frac{12}{5}[/tex] = [tex]2\frac{2}{5}[/tex] revolutions per second is the unit rate.

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Answer: 40

Step-by-step explanation:

ok, so the unknown number is x

2/5(x)=16

multiply by the reciprocal, which is 5/2 to cancel out the 2/5

so your new equation is x=16*5/2

you should get 40

a) Yes, by multiplying both sides by 1/8.

b) The inequality is false, thus, there is nothing to solve.

Yes, you can.

There is a property that says that if you perform the same operation (multiplicating by 1/8 in this case) in both sides, then the truth value of the inequality does not change.

8m > -1/10

So,  if we multiply both sides by 1/8, we will get:

8m/m > -1/(10*8)

m > -1/80

The inequality is solved.

There is nothing to really solve here, as you can see, the inequality says that a negative number is larger than a positive number, so the inequality is clearly false, and thus, there is nothing to solve.

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Triangle DEF was rotated 90 degrees about the origin to form congruent triangle LMN. Hence, EF ≅ MN.

Two triangles are said to be congruent if they have the same shape and their corresponding sides are also equal. Therefore, their corresponding angles would also be congruent.

Rotation, reflection and translation produces congruent triangles.

Hence:

Triangle DEF was rotated 90 degrees about the origin to form congruent triangle LMN. Hence, EF ≅ MN.

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Answer:

Multiply 2 by 9, and then 2 by 11, and add it up all together. 18+22=40

Step-by-step explanation:

ΔABC ≅ ΔDBC under angle-side-angle (ASA) condition.

So,

To prove:  ΔABC ≅ ΔDBC

Then, ΔABC ≅ ΔDBC under angle-side-angle (ASA) condition.

(Refer the table shown below)

Therefore, ΔABC ≅ ΔDBC under angle-side-angle (ASA) condition.

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Answer:

F

Step-by-step explanation:

La respuesta es f porque la tasa vigente en el lado x es por 2 y la tasa vigente en el lado y es por 12.

The division of given rational expression [tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12}[/tex] is [tex]\frac{3(x-2)}{4(x+3)}[/tex] provided x ≠ -3

In this question,

we have been given a complex rational expression [tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12}[/tex]

We need to find the division of given rational expression.

We rewrite given rational expression as,

[tex]\frac{\frac{3x-6}{12x-24}}{\frac{x^2+5x+6}{3x^{2} -12}}\\\\\\= \frac{3x-6}{12x-24}\times \frac{3x^2-12}{x^2+5x+6}[/tex]

First we simplify the quadratic expression x² + 5x + 6

x² + 5x + 6

= x² + 3x + 2x + 6

= x(x + 3) + 2(x + 3)

= (x + 3)(x + 2)

And the simplified form of quadratic expression 3x² - 12 would be,

3x² - 12

= 3(x² - 4)

= 3(x² - 2²)

= 3(x + 2)(x - 2)

So, the given rational expression would be,

[tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12} \\\\\\ = \frac{3x-6}{12x-24}\times \frac{3x^2-12}{x^2+5x+6}\\\\\\=\frac{3(x-2)}{12(x-2)}\times \frac{3(x+2)(x-2)}{(x+3)(x+2)}[/tex]

[tex]\\\\=\frac{3}{12}\times \frac{3(x-2)}{(x+3)}\\\\\\=\frac{3(x-2)}{4(x+3)}~~~~~~~~~~~~~(provided~~x\neq -3)[/tex]

Therefore, the division of given rational expression [tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12}[/tex] is [tex]\frac{3(x-2)}{4(x+3)}[/tex] provided x ≠ -3

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Answer: h=60 feet

Step-by-step explanation:

h=4+60t-16t²

h(2)=4+(60)(2)-(16)(2)²

h(2)=4+120-(16)(2)(2)

h(2)=124-64

h(2)=60 feet

The equation of the line for given values is y = -5x - 7.

When you know the slope of the line to be investigated and the provided point is also the y intercept, you may utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

The standard equation of straight line is y = mx + c.

Given m = -5 and y - intercept is -7

So, the equation of the line becomes y = -5x - 7

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Answer:26105 rounded

Step-by-step explanation: if not rounded 26104.754