130 students choose to attend one of three after school activities: football, tennis or running. There are 58 boys. 49 students choose football, of which 27 are girls. 27 students choose tennis. 24 girls choose running. A student is selected at random. What is the probability this student chose running? Give your answer in its simplest form.

Answer:

15 mL of the solution with 20% water will be needed.

Step-by-step explanation:

Use the inverse relationship

10 mL * (18-15)% = x mL * (20-18)%

x = 10 mL * (3/2) = 15 mL

Answer: 15mL

Step-by-step explanation:

Create a table. Multiply across and add down. The bottom row (Mixture) creates the equation.

                   Qty     ×     %             =      Total          

Solution A     10         15% → 0.15          10(0.15) = 1.5

Solution B      x          20% → 0.20        x(0.20) = 0.20x

Mixture      10 + x   ×    18% → 0.18   =    1.5 + 0.20x

                                  (10 + x)(0.18) = 1.5 + 0.20x

                                    1.8 + 0.18x  = 1.5 + 0.20x

                                    1.8               = 1.5 + 0.02x

                                    0.3              =          0.02x

                                                15  =  x

Answer:

Length = 8x - 3.2

Step-by-step explanation:

Perimeter = 4(Length)   [Since it's a square so all the sides are equal]

Given that Perimeter = 32x - 12.8

32x - 12.8 = 4(Length)

Dividing both sides by 4

=> Length = [tex]\frac{4(8x-3.2)}{4}[/tex]

=> Length = 8x - 3.2

Now, Three equivalent expressions to find the perimeter

=> Perimeter = 32x - 12.8

=> Perimeter = 4(8x - 3.2)   [Perimeter = 4 (Length)]

=> Perimeter = 2(16x - 6.4)

Answer:

[tex]\boxed{8x-3.2}[/tex]

Step-by-step explanation:

The perimeter is 32x - 12.8 of a square.

Use formula for perimeter of a square.

[tex]P=4a[/tex]

[tex]P=perimeter\\a=side \: length[/tex]

[tex]32x - 12.8=4a[/tex]

Solve for side length.

[tex]\frac{32x - 12.8}{4} =a[/tex]

[tex]8x-3.2=a[/tex]

Three equivalent expressions for perimeter:

32x - 12.8

⇒ 8(4x - 1.6)

⇒ 4(8x - 3.2)

⇒ 2(16x - 6.4)

Answer:

B.

Step-by-step explanation:

We know that

Line FG is 7.0 meters

Angle G is 90 degrees

Angle G is 25 degrees

All of the angles of a triangle add up to 180 degrees

We need to find the angle of F

90+25+f=180

115+f=180

f=65 degrees

Now we have narrowed our answers down to A, B, and D

Next we need to find the measure of line GH

For this we will need to use one of the three, Sin, Cos, Tan.

We will be using Tan because we have our variable adjacent to our angle and our number 7 opposite of our angle.

We are looking for the measure of GH

Tan60=7/x

x=3.3

Answer:

140 degrees.

Step-by-step explanation:

As MQ  = NR and MNOP is a trapezoid MNRQ is an isosceles trapezoid.

So m<MNR = m < NMQ.

Answer:

Length is 12 feet, and Width is 10 feet

Step-by-step explanation:

You can use an equation to come up with the answer but you are looking for width × (width + 2) = 120.

Answer:

  the basketball's height is 4 meters at a horizontal distance of R from Kaori

Step-by-step explanation:

The function description tells you that the statement H(R)=4 means the basketball's height is 4 meters at a horizontal distance of R from Kaori.

Answer:

At a horizontal distance of R meters from Kaori, the ball's height was equal to 4 meters.

Step-by-step explanation:

The diagonal of the square is the same as the diameter of the circle.

So, the diameter of the circle is 36.

Circumference formula:

C = 2πr

To find the radius, we just need to divide the diameter by two:

36 / 2 = 18

Now, solve using the given values.

C = 2π(18)

C = 36π

Therefore, the answer is D.

Best of Luck!

Answer:

(x-1.3)^2 + (y+3.5)^2 = 37

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x-1.3)^2 + (y--3.5)^2 = (sqrt(37))^2

(x-1.3)^2 + (y+3.5)^2 = 37

angle HDG = angle HFE

==========================================================

Explanation:

We have the statement [tex]\triangle DHG \cong \triangle FHE[/tex] given to us. Note that "H" is in the middle for both sequences of three letters. For DHG, start at H and move back one space to get to D. Move back another unit to wrap around to G. So the new sequence is HDG which forms the first angle.

Follow the same pattern but for FHE now. Start at H, move backward one spot to F, then move back again to wrap around to E. We have HFE

This shows angle HDG pairs up with angle HFE. The corresponding angles are congruent due to CPCTC

CPCTC = corresponding parts of congruent triangles are congruent

Notice how angles HDG and HFE are alternate interior angles, which lead to showing DG is parallel to EF.

Answer:

c = 6√2

Step-by-step explanation:

The following data were obtained from the question:

Angle θ = 30°

Opposite = 3√2

Hypothenus = c

The value of 'c' can be obtained by using the sine ratio as shown below:

Sine θ = Opposite /Hypothenus

Sine 30° = 3√2/c

Cross multiply

c × sine 30° = 3√2

Divide both side by sine 30°

c = 3√2 / sine 30°

But: sine 30° = 1/2

c = 3√2 / sine 30°

c = 3√2 ÷ 1/2

c = 3√2 × 2

c = 6√2 yard

Therefore, the value of 'c' is 6√2 yard.

Answer:

105 m

Step-by-step explanation:

Given that Jules has a mirror that has a shape of a triangle, the length of the border Jules would add = the perimeter of the triangular mirror.

The perimeter of the triangular mirror is simply the sum of all the 3 sides of the triangle.

Since, each side is of equal length (35 cm), therefore, perimeter of the mirror = 35 + 35 + 35 = 105 m

Perimeter of mirror = length of border to add = 105 m

The border is 105 m long.

Answer:

? = 26 in

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

?² = 24² + 10² = 576 + 100 = 676 ( take the square root of both sides )

? = [tex]\sqrt{676}[/tex] = 26

Answer:

26 inch

Step-by-step explanation:

unknown side can be found using Pythagorean theorem

a*a+b*b=c*c

24*24+10*10=c*c

576+100=c*c

√676=c

c=26inche

Answer:

2.5 second

Step-by-step explanation:

The equation is missing in the question.

The equation is,  [tex]h=-8t^2+40t[/tex]  , where 'h' is the height and 't' is time measured in second.

Now we know to reach its maximum height, h in t seconds, the derivative of h with respect to time t is given by :

[tex]\frac{dh}{dt} =0[/tex]

Now the differentiating the equation with respect to time t, we get

[tex]\frac{dh}{dt}=\frac{d}{dt}(-8t^2+40t)[/tex]

[tex]\frac{dh}{dt}=-16t+40[/tex]

For maximum height,  [tex]\frac{dh}{dt} =0[/tex]

So, [tex]-16t+40=0[/tex]

 [tex]\Rightarrow 16t=40[/tex]

[tex]\Rightarrow t=\frac{40}{16}[/tex]

[tex]\Rightarrrow t = 2.5[/tex]

Therefore, the ball takes 2.5 seconds time to reach the maximum height.

Answer:

Step-by-step explanation:

f(x) = 3x + 2

To find f(5) substitute 5 into f(x)

That's

f(5) = 3(5) + 2

= 15 + 2

= 17

Hope this helps you

Answer:

17

Step-by-step explanation:

You just plug 5 into the equation

f(5)= 3(5)+2

=15+2

=17

Hope this helped! :)

Answer:

  b = 17

  ∠QPS = 124°

  ∠SPT = 17°

  ∠TPR = 39°

Step-by-step explanation:

This fact can be used to write an equation:

  (8b -12)° +b° +(2b+5)° = 180°

  11b -7 = 180

  11b = 187

  b = 17

  8b -12 = 8(17) -12 = 124

  2b +5 = 2(17) +5 = 39

The value of b is 17.

The angle measures are ...

  ∠QPS = 124°

  ∠SPT = 17°

  ∠TPR = 39°

Hey there! I'm happy to help!

We have 6 rock, 4 country, and 4 rap CDs. If we add these all together ,we have 14 total CDs.

Since there are 4 country CDs, we have a 4/14 chance of picking one, which simplifies to 2/7 chance.

Have a wonderful day!

Answer:

a

Step-by-step explanation:

there are 4 quarts in a gallon.

4 times $0.79 =$3.16

Answer:

10

Step-by-step explanation:

nCr = 5!/(3! × (5 - 3)!)

= 10

123/ 124/ 125/ 134/ 135/ 145/ 234/ 235/ 245/ 345

The formula for combinations is generally n! / (r! (n -- r)!), where n is the total number of possibilities to start and r is the number of selections made. In our example, we have 52 cards; therefore, n = 52.

Answer: get 2 more frames

Step-by-step explanation:

Answer:

1/19

Step-by-step explanation:

Let's say there are x yellow cubes.

That means there are 3x blue cubes.

Therefore, there must be 15x green cubes.

In total: we have 19x cubes.

Therefore the probability of a cube being yellow is x / 19x

which simplifies to 1/19

Answer:

1/19

Step-by-step explanation:

Solution:-

- First we will define the distribution of colors in the bag.

- We will use variable:

                     x: the number of yellow cubes in bag

- The following color distribution can be made by using the data given in the question:

                   Color                     Number of cubes

                   Yellow                               x

                   Blue                                  3*x = 3x

                   Green                               3x*5 = 15x

          ======================================

                  Total                                 19x

          ======================================

- Sarah is to draw a cube from the bag. We are to determine the probability that the randomly picked cube would be yellow. We will denote our event as randomly picking a yellow cube from the bag with a defined finite distribution.

         p ( Picks Yellow cube ) = [ Number of yellow cubes ] / [ Total cubes ]

         p ( Picks Yellow cube ) = [ x ] / [ 19x ]

         p ( Picks Yellow cube ) = 1 / 19   .... Answer

Answer:

Hey there!

3x+y=7

2x+y=6

3x+y=7

-2x-y=-6

Add these two equations vertically so the y terms cancel out (this is known as the elimination method)

x=1

3x+y=7

3(1)+y=7

3+y=7

y=4

(x=1, y=4)

Hope this helps :)

Answer:

192km^2

Step-by-step explanation:

Well there are 5 surfaces

1) The back one

10km*6km=60km^2

2) the square

(6km)^2=36km^2

3) the two triangles

2(6km*8km/2)=48km^2

4) the front one

6km*8km=48km^2

add all up and get

192km^2

Answer: 192 square kilometers

Step-by-step explanation:

Two triangular Sides A=bh/2 8×6/2=24

So add two of them. : 48

Back side 10 × 6 = 60

Top 6×6=36

Front 6×8=48

Total: 48+60+36+48=192

Answer:

Step-by-step explanation:

it is ASA

by definition if two pairs of corresponding angles and the side between them are known to be congruent, the triangles are congruent. This shortcut is known as angle-side-angle (ASA)

Answer:

Joel’s is the 28

Step-by-step explanation:

For the one is me cause Zyou KNOW ULTRA,,,!,,,,,,292

Answer:

The table D represents the function that will have the greatest y-values for very large values of x.

Step-by-step explanation:

The table A represents a linear function, for which each one unit increment in the "x" variable produces a three unit increment in the "y" variable. This means that the growth rate of this function is 3.

The table B also represents a linear function, for which each one unit increment in the x variable produces a 100 unit increment in the y variable. This means that the growth rate of this function is 100.

The table C also represents a linear function, for which each one unit increment in the x variable produces a 10 unit increment in the y variable. This means that the growth rate of this function is 10.

The table D on the other hand does not represent a linear function, since the growth rate is variable and increases for greater values of x. This means that as x grows larger, the growth rate of the function also grows larger, resulting in a much greater y value for very large x values if we compare it to a linear function, like the other options.

Answer:

D

Step-by-step explanation:

BIGBRAIN

Answer:

They are on their simplified form.

Step-by-step explanation:

Since these numbers are prime numbers we can't simplify them. But we can change them to decimal.

1/2=0.5

1/3=0.3 (in which 3 repeats itself)

Hope this helps ;) ❤❤❤

This question is incomplete

Complete Question

Mr. Conner is placing stone tiles to make a patio. Each tile is 1 square foot. The drawing shows the dimensions of his patio. A quadrilateral is broken into a triangle and rectangle. The triangle has a base of 20 feet and a height of 6 feet. The rectangle has a base of 20 feet and a height of 12 feet. How many total stone tiles will Mr. Connor need for the patio?

Answer:

300 tiles

Step-by-step explanation:

From the above question, we know that the patio is a combination of a triangle and a rectangle.

Step 1

Find the area of the shape

a) Area of the Triangle = 1/2 × Base × Height

Base = 20 feet

Height = 6 feet

Area = 1/2 × 20 × 6

Area = 60 square feet

b) Area of the rectangle

= Length × Breadth.

The rectangle has a

Base = Breadth = 20 feet

Height = Length = 12 feet

Area = 20 × 12 = 240 square feet.

Total Area of the patio

= Area of Triangle + Area of square

= 60 square feet + 240 square feet

= 300 square feet

Step 2

We are told that each stone tile = 1 square foot.

Hence, if the total area of the patio = 300 square feet, the number of stone tiles that would be used is

1 square foot = 1 stone tile

300 square feet = 300 stone tiles.

Therefore,the total stone tiles that Mr. Connor will need for the patio is 300 stone tiles.

Answer:

The answer is 300

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

the position is labeled -6 since it goes down

Answer:

  -6

Step-by-step explanation:

Ground level is taken to be zero on this scale, so 6 feet below ground level will be designated as -6.