63 students choose to attend one of three after school activities: football, tennis or running. There are 38 boys. 20 students choose football, of which 19 are girls. 19 students choose tennis. 5 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:

x=6

Step-by-step explanation:

first write out the equation that is given:

18+6x=2x+42

next subtract 2x from both sides:

18+6x-2x=2x-2x+42, which becomes 18+4x=42

then subtract 18 from both sides:

18-18+4x=42-18, which becomes 4x=24

finally divide both sides by 4:

4x/4=24/4, which becomes x=6

Therefore, x=6 is your answer

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]18+6x=2x+42\\ \\\text{subtract 18 from both parts of the equation }\\\\18+6x-18=6x=2x+42-18=2x+24 \\ \\\text{subtract 2x from both parts of the equation }\\ \\6x-2x=4x=24\\ \\\text{divide by 4 both parts of the equation }\\ \\x=\dfrac{24}{4}=6\\ \\\text{So the solution is ... }\\ \\\large \boxed{\ \ x=6 \ \ }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

First find height using Pythagorean theorem.

[tex]h^2+4^2=13^2\implies h=\sqrt{153}\approx12.37[/tex].

Then use cone surface area formula and compute the result:

[tex]A=\pi r(r+\sqrt{h^2+r^2})\approx\boxed{68\pi}\mathrm{units^2}[/tex].

Hope this helps.

Answer:

1. 31.67 degrees

2. 38 degrees

3.

PNQ  = 117 degrees

LKQ =  102 degrees

4. XYV = 120 degrees

Step-by-step explanation:

1. Using sum of angles of a triangle = 180

angle ACB = 180 - 55.14 - 93.19 = 31.67

2.

FDE = 180-GDE = 180 - 135.11 = 44.89   [angles on a line are supplementary]

FED = HEJ = 97.11         [vertical angles]

DFE = 180-FDE-FED = 180 - 44.89 - 97.11 = 38 degrees

3.

MLN = 180 - 82 = 98   [angles on a line are supplementary]

PNQ = 360 - 67 - 78 - 98 = 117  [sum of exterior angles of a polygon = 360]

LKQ = 180 - 78 = 102  [angles on a line are supplementary]

4.

WXY+YXZ = 180 [angles on a line are supplementary]

=>

3x + x = 180

=>

x = 180/4 = 45

Now solve for XYV

XYV = 360 - 135 - 60 - 45 = 120  [sum of interior angles of quadrilateral = 360]

Note: In the future, please limit the number of problems per question to three.

Answer:

B

Step-by-step explanation:

You have to use cos because you are using the adjacent and hypotenuse

So

cos38=x/14

multiply each side by 14

14cos38

Answer:

a   1 : 5

Step-by-step explanation:

Blue mables: 3

green and red marbles: 8 + 7 = 15

then, the radio blue:(green+red) is:

3 : 15

simplified unit rate is:

3/3 = 1

15/3 = 5

then:

3:15

is equal to:

1:5

Answer:

a   1 : 5

Answer:

A. (-8, 20)

Step-by-step explanation:

The formula for dilations is

[tex]\left(x_{1}\cdot t_{1},\ y_{1}\cdot t_{1}\right)[/tex] Where t is the scale factor

The first step is to plug in the numbers appropriately

[tex](-2*4,5*4)[/tex]

Then, multiply -2 by 4 and 5 by 4 to get

[tex](-8, 20)[/tex]

So your answer is (-8, 20)

Hope this helps

Have a great day! :)

Answer:

the Probability of Fair coin = 0.2664=26.64 % and

Probability of Bent coin = 0.7336= 73.36 %

Step by step Explanation:

The fair coin has a 60% probability of coming up heads, same thing with the bent coin , when the coin was thrown up ten times,it comes up heads 8 times,

Here we were told to find the probability fair coin vs. probability bent coin

A)THE FAIR COIN::

The probability of getting Head Coin = 1/2

Probability of getting tail Coin = 1/2

Then the Probability of head 8 times out of 10 can be calculated using combination

= ¹⁰C₈ × (1/2)⁸ ×(1/2)²

= 45/1024

= 0.0439

Therefore, the Probability of head 8 times out of 10= 0.0439

B)BENT COIN

the probability of getting Head Coin = 0.6

= 6/10

= 3/5

NOTE: 60%=0.6

The probability of getting tail Coin = 1 - 3/5

= 2/5

Then, the probability of getting head 8 times out of 10 can be calculated using combination;

= ¹⁰C₈ × (3/5)⁸ × (2/5)²

= 45 × 6561 ×( 4 / 5¹⁰)

= 0.1209

Therefore, the probability of getting head 8 times out of 10 = 0.1209

We can now calculate the Probability of Fair coin

(Probability of head 8 times out of 10 in fair coin )/(Probability of head 8 times out of 10 in fair coin )+(the probability of getting head 8 times out of 10 in bent coin)

= (0.0439 )/(0.0439 + 0.1209)

= 0.2664

Probability of bent coin can as well be calculated as 0.1209 /(0.0439 + 0.1209)

= 0.7336

Therefore, the Probability of Fair coin = 0.2664=26.64 % and

Probability of Bent coin = 0.7336= 73.36 %

Answer:

88

Step-by-step explanation:

mother's age = 12+24

= 36

father's age = 12+40

=52

add the parent age= 36+52

= 88

Answer:  A) 3.2 ft

Step-by-step explanation:

f(4) = -0.3(4)² + 2(4)

     = -4.8 + 8

     =  3.2

Answer:

3.2 feet

Step-by-step explanation:

Answer:

C: [tex]\lim_{x \to 0} y \to -\infty[/tex]

Step-by-step explanation:

The y-axis is the asymptote, and G(x) approaches it as x is getting smaller and smaller.

Actually, even more accurate would be to write

[tex]\lim_{x \downarrow 0} y \to -\infty[/tex]

The down arrow shows that x has to approach 0 from the positive side.

Answer:

x=4

Step-by-step explanation:

sqrt(x+5) = sqrt(x)+1

Square each side

(sqrt(x+5))^2 = (sqrt(x)+1)^2

x+5 = (sqrt(x)+1)^2

Foil

x+5 = (sqrt(x)) ^2 + sqrt(x) + sqrt(x) + 1

x+5 = x + 2 sqrt(x) + 1

Subtract x from each side

5 = 2 sqrt(x) + 1

Subtract 1 from each sdie

4 = 2 sqrt(x)

Square each side

4^2 = (2 sqrt(x))^2

16 = 4 x

Divide by 4

16/4 = 4x/4

4 =x

Check to see if it is extraneous

sqrt(4+5) = sqrt(4)+1

sqrt(9) = sqrt(4) +1

3 = 2+1

3=3

It is a valid solution

Answer:

[tex]\boxed{x=4}[/tex]

Step-by-step explanation:

[tex]\sqrt{x+5} = \sqrt{x}+1[/tex]

Take the square on both sides.

[tex]x+5=( \sqrt{x}+1)^2[/tex]

Expand brackets.

[tex]x+5=( \sqrt{x}+1) ( \sqrt{x}+1)[/tex]

[tex]x+5= \sqrt{x} ( \sqrt{x}+1) +1 ( \sqrt{x}+1)[/tex]

[tex]x+5= x+ \sqrt{x}+ \sqrt{x}+1[/tex]

[tex]x+5= x+ 2 \sqrt{x}+1[/tex]

Subtract 2√x, x, and 5 on both sides.

[tex]x- 2 \sqrt{x} -x= 1-5[/tex]

[tex]-2 \sqrt{x} = -4[/tex]

Cancel negative signs.

[tex]2\sqrt{x} = 4[/tex]

Divide both sides by 2.

[tex]\sqrt{x} =2[/tex]

Square both sides.

[tex]x=2^2[/tex]

[tex]x=4[/tex]

Check if the solution in the equation works.

[tex]\sqrt{x+5} = \sqrt{x}+1[/tex]

Let [tex]x=4[/tex]

[tex]\sqrt{4+5} = \sqrt{4}+1[/tex]

[tex]\sqrt{9} = 2+1[/tex]

[tex]3=3[/tex]

The value of x as 4 works in the equation.

Answer:

subtraction; division

Step-by-step explanation:

the first step is to subtract 7/2 from both sides.

the second step is to divide by -2

Answer:

✔ Subtraction

✔ Division

Step-by-step explanation:

It's right in Edgen

Answer:

No there is not  enough evidence to support the claim that the mean expenditure for auto insurance is less than the 2002 amount at the α = 0.05 level of significance

Step-by-step explanation:

Sample Mean = μ1 = $806

Sample Mean = μ2 = $ 781

Standard Deviation= S= σ =39.13

n= 32

Confidence Interval = 95 %

α= 0.05

z∝=± 1.96

We state the null and alternative hypotheses as

H0: μ1 = $806  and Ha: μ1 ≠ $806  two sided tail test

z= μ1 -μ2/σ/√n

z= 806-781/ 39.13/√32

z= 806-781/ 39.13/5.6568

z=806-781/ 6.92

z= 25/6.92

z= 3.613

Z> z∝

3.613 > ± 1.96

No there is not  enough evidence to support the claim that the mean expenditure for auto insurance is less than the 2002 amount at the α = 0.05 level of significance

Answer:

  true

Step-by-step explanation:

  3 -2x is a polynomial of degree 1, consisting of two terms. Such a polynomial can be referred to as a "binomial."

Your observation is True.

Answer:

Option C

Step-by-step explanation:

A line has a 2-Fold rotational symmetry because if we rotate the line about 180, The resulting thing will be the same line.

Answer:

[tex]\boxed{\mathrm{C}}[/tex]

Step-by-step explanation:

A line has two-fold rotational symmetry.

The line rotated two times from a central point remains the same.

Or the line rotated 180 degrees from a central point remains the same.

Answer:

88.7

Step-by-step explanation:

P(Z < z) = 0.25

z = -0.674

z = (x − μ) / σ

-0.674 = (x − 99.6) / 16.2

x = 88.7

Answer:

1/625

Step-by-step explanation:

When you multiply, you add the exponents. You now have [tex]6^{-4}[/tex]. This is equivalent to [tex]\frac{1}{5^{4} }[/tex] which equals 1/625.

Answer:

1/625

Step-by-step explanation:

5^ -1 * 5^-3

The bases are the same, so we can add the exponents

5^ (-1+-3)

5^-4

We know that a^-b = 1/ a^b

1/5^4

1/625

Answer: 148.5

Step-by-step explanation:

To find the area of this shape, comprised of a rectangle and a triangle, we can find the area of each shape and add them together.

The area of a triangle is 12⋅b⋅h. We are given the triangle's height, 13. The base of the triangle will be the same as the width of the rectangle, which we also know: 11. Now we can calculate the area of the triangle:

A = 1/2⋅b⋅h

A = 12⋅11⋅13

A = 71.5

Now we can find the area of the rectangle, which is l⋅w. The width of the rectangle is 11, which is the same as the base of the triangle; the length is 7:

A =l⋅w

A = 7⋅11

A = 77

Finally, we can add together the area of the triangle and the rectangle to find the total area:

A = 71.5 + 77 = 148.5

The total area of the front of a house will be 148.5.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A rectangle has a width = 11

The triangle's height = 13

The rectangle's height = 7

Now,

Since, The base of the triangle will be the same as the width of the rectangle.

Hence, The area of rectangle = 7 x 11

                                              = 77

And, The area of triangle = 1/2 x 11 x 13

                                      = 71.5

Thus, The total area of the front of a house = 77 + 71.5

                                                                  = 148.5

Therefore, The total area of the front of a house will be 148.5.

Learn more about the rectangle visit:

https://brainly.com/question/398984

#SPJ2

Answer:

4

Step-by-step explanation:

Answer:

[tex]\boxed{D = 15.8\ units}[/tex]

Step-by-step explanation:

The coordinates are (0,9) and (-8,-4)

Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

D = [tex]\sqrt{(-8-0)^2+(-4-9)^2}[/tex]

D = [tex]\sqrt{(-8)^2+(-13)^2}[/tex]

D = [tex]\sqrt{81+169}[/tex]

D = [tex]\sqrt{250}[/tex]

D = 15.8 units

Answer:

15.3

Step-by-step explanation:

The coordinates are (0,9) and (-8,-4)

Distance of two points formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Plug in the values.

[tex]D=\sqrt{(-8-0)^2+(-4-9)^2}[/tex]

[tex]D=\sqrt{(-8)^2+(-13)^2}[/tex]

[tex]D=\sqrt{64+169}[/tex]

[tex]D=\sqrt{250}[/tex]

[tex]D= 15.264338...[/tex]

[tex]D \approx 15.3[/tex]

Answer:

3 hours

Step-by-step explanation:

1/5 of an hour would be equivalent to 12 minutes (60 minutes in an hour divided by 5)

Multiply 12 minutes by 15 to see how long it will take to water the entire lawn in minutes ----> 12x15=180

Divide 180 by 60 to see how many hours it takes ---> 180/60=3

Answer:

3 hours.

Step-by-step explanation:

1/15 of the lawn is watered in 1/5 hours

So  the whole lawn is watered in  15 * 1/5

= 3 hours.

Answer:

$20, 533.33

Step-by-step explanation:

From the question, we are given the following values

Principal = $20000

Rate = 8% = 0.08

Time( in years) = 120days = 4 months = 4/12 years = 1/3 years

Interest = Principal × Rate × Time

Interest = 20,000 × 0.08× (1/4)

Interest = $533.33

Hence, the proceeds to Aster Corporation are

$20000 + $533.33

= $20,533.33

Answer:36

Step-by-step explanation: first I did

9÷5=1.80 per box.

so then I did 1.80 x 20 which = 36

Answer:

20 boxes cost $36

Step-by-step explanation:

Using proportions,

5 boxes cost 9$

20 boxes cost X$

Cross multiply

X = 9/5 * 20 = 36$

Answer:

True

Step-by-step explanation:

Answer:

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

Answer 4

Hope this helps :)

To remove a possible source of bias

Step-by-step explanation:

If the test subjects know they are part of an experiement, this could cause them to think that it worked and it could either lead to untruthful answers or the test subjects tricking themselves to think that the vaccine worked

Answer:

Correct answer is option D. 96.4 yd.

Step-by-step explanation:

Please refer to the attached figure for labeling of the given diagram.

ABC is a triangle with the following labeling:

A is the hole, B is the Tee and C is the point where the ball is.

Sides are labeled as:

[tex]a =255\ yd\\c = 305\ yd\\\angle B =17^\circ[/tex]

To find:

Side [tex]b = ?[/tex]

Solution:

Here, we have one angle and two sides . Third side of the triangle is to be found opposite to the given angle.

We can use cosine formula here to find the value of the unknown side.

[tex]cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}[/tex]

Putting all the values:

[tex]cos 17 = \dfrac{255^{2}+305^{2}-b^{2}}{2\times 255\times 305}\\\Rightarrow 0.956 = \dfrac{65025+93025-b^{2}}{155550}\\\Rightarrow 148753.2= 158050-b^{2}\\\Rightarrow b^{2}= 158050-148753.2\\\Rightarrow b^{2}= 9296.795\\\Rightarrow b= 96.42\ yd[/tex]

So, the distance between the Ball and hole is 96.42 yd

Correct answer is option D. 96.4 yd.

Answer:

D.) 96.4 yd

Step-by-step explanation:

I got it correct on founders edtell

Answer:

96

Step-by-step explanation:

We simply need to plug in a = 4 so 6a² = 6 * 4² = 6 * 16 = 96.

Answer:

x = 121°

Step-by-step explanation:

The angle supplementary to 115° is 180 - 115 = 65° and the angle that forms a full circle with 304° is 360 - 304 = 56°. Since the measure of an exterior angle is equal to the sum of its remote interior angles, we know that x = 65 + 56 = 121°.

Step-by-step explanation:

since PQRT is a rhombus,

URQ=TPU

y=180-90-24=66

x=180-32-90-24=34