There are 10 participants in the Olympic 100 meter sprint. If first, second, and third place get medals, how many possible outcomes of medal winners are there if Usain Bolt places first?

Answer:

f= 5.2 or 3[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Cot(60) = 3/f

0.58 =3/f

0.58f = 3

f= 5.2 or 3[tex]\sqrt{3}[/tex]

Answer:  [tex]y=\frac{-15}{7}x-\frac{4}{7}[/tex]

Slope: -15/7

y-int:-4/7

Step-by-step explanation:

slope: rise/run

[tex]\frac{x^2-x^1}{y^2-y^1}[/tex]

[tex]\frac{-7-8}{-4-3}=\frac{-15}{-7} =\frac{-15}{7}[/tex]

thats the answer :)

~rere

Answer:

A = 2700   M = 2100 dollars

Step-by-step explanation:

9 + 7 = 16 shares

  2 shares more = 600

       1 share = 300

9 shares * 300 = 2700

7 shares x 300 = 2100

Answer:

f(g(4)) = 13.

Step-by-step explanation:

g(4) = 4^2 = 16

so f(g(4)) = f(16)

=  16 - 3

= 13.

Answer:

178

Step-by-step explanation:

100 plus 78 equal s 179

Answer:

$310.05

Step-by-step explanation:

Method 1: Find the amount of 22% discount and subtract from original price, and find the amount of 6% tax and add to discounted price.

Original price: $375

Discount of 22%

22% of $375 = 0.22 × $375 = $82.50

Price after discount (but before tax): $375 - $82.50 = $292.50

Sales tax of 6%

6% of $292.50 = 0.06 × $292.50 = $17.55

Price after discount and tax: $292.50 + $17.55 = $310.05

Method 2: Add and subtract the discount percent and the tax percent first, then multiply.

Original price: $375

The discount is 22%.

The original price is 100%.

Subtract 22% from 100%: 100% - 22% = 78%

The discounted price is 78% of the original price.

Once you have the discounted price, tax is 6%.

The new discounted price is 100%. Add 6% to get 106%.

The price with tax is 106% of the discounted price.

106% of 78% of $375 = 1.06 × 0.78 × $375 = $310.05

Answer: $310.05

The amount of paper that Lemon needs for the actual poster will be 8 square feet.

It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

The dimension of the poster is 10 cm by 20 cm.

And the scale factor will be 5 cm is equal to 1 ft.

Then the dimension of the poster will be 2 ft by 4 ft.

Then the amount of the paper that Lemon needs for the actual poster will be

Area = 2 × 4

Area = 8 ft²

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Answer:

we can use the pythagorean theorem to each of those right triangles to find the lengths of the pathways

Step-by-step explanation:

for the spinach celery walkway,

d=[tex]\sqrt{6^{2}+8^{2}[/tex] = 10 yd

for each watermelon walkway,

d=[tex]\sqrt{8^{2}+12^{2}[/tex] = 14.42 yd

from the carrots red peppers walkway,

[tex]b^{2}+12^{2} = 15^{2}[/tex]

b=[tex]\sqrt{15^{2}-12^{2}[/tex]= 9yd

for each tomatoes walkway;

d=[tex]\sqrt{6^{2}+9^{2}[/tex] = 10.82 yd

so the total length of the walkway is = 10+14.42+15+10.82 = 50.24 yd

Answer:

4

Step-by-step explanation:

-1 - (-5) = 4

3 - (-1) = 4

7 - 3 = 4

original equation

[tex]v=\frac{d}{t}[/tex]

solve for t

[tex]t=\frac{d}{v}\\\\t=\frac{100}{6.25} \\\\t=16[/tex]

It took Dita 16 seconds to finish the race

Answer:

a

Step-by-step explanation:

aaaaaaa

its a

16 seconds

The number that is equal to [tex]\frac{4}{2}[/tex] is 2

When you ask "What is 4/2 as a whole number?" you are asking to convert the fraction [tex]\frac{4}{2}[/tex] to a whole number.

The fraction [tex]\frac{4}{2}[/tex] has a numerator of [tex]4[/tex] and a denominator of [tex]2[/tex]. To convert [tex]\frac{4}{2}[/tex] to a whole number, you simply divide the numerator by the denominator.

Given that:

[tex]\frac{4/2=2}{2/2=1} =\frac{2}{1}=2[/tex]

Therefore, The number that is equal to [tex]\frac{4}{2}[/tex] is 2

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The graph is showing the equation of circle x²+y²=4

A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.

The given graph in the question represents the equation of the circle cutting the points on the x-axis and y-axis at 4 which is the radius of the circle.

The equation will be as follows:-

x²+y²=4

Hence the graph is showing the equation of circle x²+y²=4

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The amount of the surface area covered with stickers is 0.6 or 60%

The amount of area to cover is given as:

Covered area = 3/5

Express as percentage

Covered area = 3/5 * 100%

Divide 3 by 5

Covered area = 0.6 * 100%

Evaluate the product

Covered area = 60%

Hence, the amount of the surface area covered with stickers is 0.6 or 60%

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Answer:

135.93

Step-by-step explanation:

I took the test

Answer:

I need an image

Step-by-step explanation:

Answer:CPCTC

Step-by-step explanation:

6. AB ≅ CD          Corresponding Parts of Congruent triangles are Congruent(CPCTC)

Hope it helps:)

The equation in slope intercept form is,[tex]31.25 = 1.25 \times 25 +0[/tex]. The given equation is obtained by comparing the standard equation of the straight line.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The given equation is;

1.25 (25) = 31.25

31.25=1.25 (25)

The standard equation of the slope intercept form. is;

[tex]\rm y = mx +x[/tex]

On comparing the given equation with the above equation, we get;

y=31.25

m=1.25

x=25

c=0

The equation in slope intercept form is;

[tex]31.25 = 1.25 \times 25 +0[/tex]

Hence, the above equation is the slope intercept form.

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Answer:

= 25√3/3

Step-by-step explanation:

x/25 = tan 30o

x = 25/√3

= 25√3/3

Answer:

B

Step-by-step explanation:

4x4= 8

10x10= 20

8+20= 28

5x2= 10

9x2= 18

10+18= 28

Answer:

[tex]4x + 10y = 28 \\ 5x + 9y = 28 \\ 10y = 28 - 4x \\ y = \frac{28 - 4x}{10} \\ y = 2.8 - 0.4x \\ 5x + 9(2.8 - 0.4x) = 28 \\ 25.2 - 3.6x + 5x = 28 \\ 1.4x = 2.8 \\ x = 2 \\ [/tex]

[tex]y = 2.8 - 0.4 \times 2 \\ y = 2[/tex]

B

Answer:

(x-2)^2-2

Step-by-step explanation:

x^2-4x+2

take the x out

x(x-4) + 2

(x-2)^2-2

because (x-2)^2 is

x^2-4x+4

its like completing the square

Answer:

(x-2)² -2

Step-by-step explanation:

Consider that (a+b)² = a²+2ab+b²

To find the form (x-A)²+B compare  x²-4x+2 with a²+2ab+b²

x² - 4x +2

a² + 2 a b+ b², so a= x and b = (-2)

x²+ 2· x ·(-2)+ (-2)² -  2  = (x-2)² -2 is in the form (x-A)²+B

Check our answer:

(x-2)² -2= (x²-2·2x+4)-2 = x²-4x +2 ✅

The amount that was invested in the first fund is $8300.

The amount that was invested in the second fund is 3700.

0.09a + 0.03b = $858 equation 1

0.1a + 0.01b = $867  equation 2

Where:

Multiply equation 2 by 0.9:

0.09a + 0.009b = 780.30 equation 3

Subtract equation 1 from equation 3

0.021b = 77.70

Divide both sides by 0.021

b = $3700

Substitute for b in equation 1: 0.09a + 0.03(3700) = $858

0.09a + 111 = 858

a = (858 - 111) / 0.09

a = $8300

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Answer & Step-by-step explanation:

USDA's Dietary Guidelines for Americans provide percent ranges for each macronutrient. For adults, the organization recommends consuming 10%–35% of calories from protein, 45%–65% from carbohydrates, and 20%–35% of calories from fat. They also suggest consuming less than 10% of total calories from saturated fat.

Answer:

8 feet

Step-by-step explanation:

3 + 5 = 8

..................................................

Answer:

angle A = 112 degrees

Step-by-step explanation:

Angle ADC is bisected (given)  ...so angle 1 = angle 2  

    then angle D = 68 degrees

now you have to remember that adjacent corners (angles on the same LEG) of a trapezoid sum to 180 (they are 'supplementary' )

  angle A = 180 - 68 = 112 degrees

Answer:

[tex]y=\frac{3}{4} x-3[/tex]

Step-by-step explanation:

Given information: x-int: 4 and y-int:-3

x-int point : (4,0).

y-int point : (0,-3).
Plug this information to point-slope form to solve for m and then convert that to slope-intercept form.

[tex]y-y_0=m(x-x_0)\\0-(-3)=m(4-0)\\3=4m\\m=\frac{3}{4} \\[/tex]

[tex]y-y_0=m(x-x_0)\\y-(-3)=\frac{3}{4} (x-0)\\y+3=\frac{3}{4}x\\y=\frac{3}{4}x-3[/tex]

Answer: The answer is d

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

For absolute values   | x |    just drop the sign of the number and make it positive

  example :     | -3|  = 3

so for this Q

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

Answer:

2^3 a^5 b^4

4b^2 c^3

2^(3-2) a^5 b^(4-2)

c^3

2a^5 b^2

2a^5 b^2 c^3

Using supplementary angles, it is found that the measures of the angles are given as follows:

Supplementary angles are two angles whose sum is of 180º.

An interior angle is supplementary with it's exterior angle, hence:

m<a + 150º = 180º -> m<a = 30º.

The sum of the three interior angles of a triangle is of 180º, hence:

30º + m<b + 60º = 180º

90º + m<b = 180º

m<b = 90º.

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Check the picture below.

[tex]sin(\theta )=\cfrac{\stackrel{opposite}{30\cdot sin(24^o)}}{\underset{hypotenuse}{50}}\implies sin^{-1}[sin(\theta )]=sin^{-1}\left[ \cfrac{30\cdot sin(24^o)}{50} \right] \\\\\\ \theta =sin^{-1}\left[ \cfrac{30\cdot sin(24^o)}{50} \right]\implies \theta \approx 14.1^o[/tex]

The value of angle does this replacement ramp make with the horizontal is,

⇒ θ = 14.1°

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

A 30-foot ramp is used to move product to a loading dock.

The ramp makes a 24° angle with the horizontal.

And, The ramp is to be replaced with a ramp that is 50 feet long.

Hence, By given figure;

We have;

⇒ sin θ = 30 × sin 24° / 50

⇒ θ = sin ⁻¹ (30 × sin 24° / 50)

⇒ θ = 14.1°

Thus, The value of angle does this replacement ramp make with the horizontal is,

⇒ θ = 14.1°

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