95 students choose to attend one of three after school activities: footbal,l tennis or running. There are 28 boys. 38 students choose football, of which 26 are girls. 23 students choose tennis. 29 girls choose running. A student is selected at random. What is the probability this student choose running? Give your answer in its simplest form.

Answer:

(-infinity, infinity)

Step-by-step explanation:

The domain of the exponential function f(x) = 3 ^ x - 5 is (-infinity, infinity)

An exponential function is a mathematical function of the following form: f ( x ) = an x. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e, which is equal to approximately 2.71828.

Exponential Function Formula

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

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Answer:

21 glasses of water.

Step-by-step explanation:

You can do a proportion.

[tex]\fraction{1 glass}{1/6 of a bottle)[/tex] or

1 glass/1/6 of a bottle.

x glasses/3.5 bottles.

You can cross multiply.

1/6 times x is 1/6x

1 times 3.5 is 3.5/

1/6x=3.5.

do the reciprocal of 1/6 which is 6.

So, 6 times 3.5 is 21.

Therefore, you have 21 glasses of water.

Answer:

720 cherries

Step-by-step explanation:

Answer:

720

Step-by-step explanation:

Cherries Cherie pie

240 = 3

X = 9

The known number of cherries will be given as x then u cross multiply

3×X=240×9

3X=2,160

Divide both sides by 3

3/3X=2,160/3

X=2,160/3

X=720

This implies that the number of cherries needed to make 9 cherry pie is 720

I hope this help

Answer:

[tex]p=\frac{16}{9}[/tex]

Step-by-step explanation:

[tex]6(3p-2)=20[/tex]

Distribute the brackets.

[tex]6(3p)+6(-2)=20[/tex]

[tex]18p-12=20[/tex]

Add [tex]12[/tex] on both sides.

[tex]18p-12+12=20+12[/tex]

[tex]18p=20+12[/tex]

[tex]18p=32[/tex]

Divide [tex]18[/tex] on both sides.

[tex]\frac{18p}{18}=\frac{32}{18}[/tex]

[tex]p=\frac{16}{9}[/tex]

Answer:

[tex]p = \frac{16}{9} \\ [/tex]

Step-by-step explanation:

[tex]6(3p - 2) = 20 \\ 18p - 12 = 20 \\ 18p = 32 \\ \frac{18p}{18} = \frac{32}{18} \\ p = \frac{16}{9} [/tex]

Answer:

Step-by-step explanation:

Negative one-fourth (x) + three-fourths = 12

-1/4(x)+3/4=12

-x/4 + 3/4 =12

-x+3/4=12

1. Negative 1 (StartFraction x over 4 EndFraction) + three-fourths = 12

-1(x/4)+3/4=12

-x/4+3/4=12

2. (StartFraction negative x over 4 EndFraction + three-fourths = 12

-x/4+3/4=12

3. StartFraction

negative x + 3 over 4 EndFraction = 12

-x+3/4=12

Answer:

B, C, & E

Step-by-step explanation:

-1(x/4) + 3/4

-x + 3 /4 = 12

(-x/4) +3/4 = 12

Hope this helps ^^

Answer:

a rational number

Step-by-step explanation:

a rational number + a rational number will always be a rational number.

Answer: D (4,1)

Step-by-step explanation:

2x + 3(x-3) = 11

2x + 3x - 9 = 11

5x = 11 + 9

x = 20/5 = 4

y = x-3

= 4-3 = 1

Answer: $1.35

Step-by-step explanation:

1.29 * 5% = 1.29 * 0.05 = 0.0645

0.0645 rounds down to 0.06

1.29 + 0.06 = 1.35

Answer: 0 and 12

Step-by-step explanation:

Fractions and mixed numbers aren’t rational numbers and pi isn’t a rational number.

Whole numbers are rational numbers, though so 0 and 12 are your answers.

Answer:

0 and 12

Step-by-step explanation:

you cant have mixed numbers and pie is never ending

Answer:

angle BAC = 50.5°

Step-by-step explanation:

To find the size of angle BAC, we will follow the steps below;

First, we will use Pythagoras theorem to find side AC

from the diagram, AB = 14 cm       BC = 17 cm

Using Pythagoras theorem,

AC² = AB² + BC²

        = 14² + 17²

         =196 +289

           =485

AC² = 485

Take the square root of both-side

AC = √485

AC = 22 .023

AC = 22.023 cm

angle <B = 90°

Using the sine rule,

[tex]\frac{sin A}{a}[/tex]   =  [tex]\frac{sin B}{b}[/tex]

A = ?

a=BC = 17 cm

B = 90°

b = AC = 22.023 cm

we can now [proceed to insert the values into the formula and then solve for A

[tex]\frac{sin A}{a}[/tex]   =  [tex]\frac{sin B}{b}[/tex]

[tex]\frac{sin A}{17}[/tex]  = [tex]\frac{sin 90}{22.023}[/tex]

cross - multiply

22.023× sinA = 17× sin90

Divide both-side of the equation by 22.023

sin A = 17 sin90 / 22.023

sin A = 0.771920

Take the sin⁻¹ of both-side of the equation

sin⁻¹sin A = sin⁻¹0.771920

A = sin⁻¹0.771920

A≈ 50.5°

Therefore, angle BAC = 50.5°

Answer:

342/6 = 57

Step-by-step explanation:

Just basic division

Answer: 640

Step-by-step explanation:

8 x 8 x 9 + 1/3 (8 x 8 x 3)

= 640  in cubic ft

The volume in cubic feet of space the tent occupies will be 640 cubic feet.

The steps are as follow:

Length = 8 ft.

Width = 8 ft.

height = 9 ft.

Length = width = 8 ft.

height = 3 ft.

volume of cuboid = length x width x height

volume of cuboid = 8 x 8 x 9

volume of cuboid = 576 cubic ft

volume of square pyramid = (length x length x height) / 3

volume of square pyramid = (8 x 8 x 3) / 3

volume of square pyramid = 64 cubic ft.

volume of cuboid + volume of square pyramid = 576 + 64

Total volume of space = 640 cubic feet

So the volume in cubic feet of space the tent occupies will be 640 cubic feet

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Answer:

75 is the required answer.

Step-by-step explanation:

Length of missing side = S

(45xS)/2 = 1350

S = 60

Hypotenuse = √(45^2 + 60^2) = 75

Best Regards!

Answer:

D. 44.79

Step-by-step explanation:

[tex]\frac{43}{96}[/tex] who worked 8 or more years said that e-mail was their favorite communication method.

[tex]\frac{43}{96}[/tex] ≈ [tex]\frac{44.79}{100}[/tex]

So around 44.79% who have worked 8 years or more said that email were their preferred communication method. Our answer is D. 44.79.

Answer:

44.79%

Step-by-step explanation:

Answer:

FG = 28

Step-by-step explanation:

You are given the ratio 1:2. That means that the photocopied monorail is twice as big as the original. All you need to do is multiply 14 by 2 to get your answer.

Answer:

FG=28

Step-by-step explanation:

cuz the ratio is 1:2 so 14*2=28

Answer:

what i know for sure is 10/19 is rational

Answer:

=> All of the options are correct.

Step-by-step explanation:

a rational number is a number that can be shown as the quotient of two integers a and b(the denominator b must not be equal to zero).

10/19 => a = 10, b = 19 (correct)

85/74 => a = 85, b = 74 (correct)

-48 => a = -48, b = 1 (correct)

-57 =>a = -57, b = 1 (correct)

=> All of the options are correct.

Hope this helps!

Answer:

did u ever get hte answers for this ?

Answer:

m∠D = 32°

Step-by-step explanation:

From the figure attached,

In ΔABE,

By the property of a triangle,

m∠AEB + m∠ABE + m∠AEB = 180°

14° + 45° + m∠AEB = 180°

m∠AEB = 180° - 59°

m∠AEB = 121°

Since, m∠AEB = m∠CED = 121° [Vertical angles]

Similarly, in triangle CDE,

m∠ECD + m∠CED + m∠EDC = 180°

27 + 121 + m∠CDE = 180

m∠CDE = 180 - 148

m∠D = 32°

Answer: The expression is (c-7) / 3

Step-by-step explanation:

Let's say Adam has c pieces of candy

He took seven pieces for himself which means we can write this as c-7

He then divided this amount between his 3 children (c-7)/3

Answer:

The answet is C.

Step-by-step explanation:

First, you have to find the angle of ACB using Sine Rule, sinθ = opposite/hypotenuse :

[tex] \sin(θ ) = \frac{oppo.}{hypo.} [/tex]

[tex]let \: oppo. = 4 \\ let \: hypo. = 5[/tex]

[tex] \sin(θ) = \frac{4}{5} [/tex]

[tex]θ = {\sin( \frac{4}{5} ) }^{ - 1} [/tex]

[tex]θ = 53.1 \: (1d.p)[/tex]

Given that line AB is parallel to line CD so ∠C = 90°. Next, you have to find the angle of ACD :

[tex]ACD = 90 - 53.1 = 36.9[/tex]

Lastly, you can find the length of CD using Cosine rule, cosθ = adjacent/hypotenuse :

[tex] \cos(θ) = \frac{adj.}{hypo.} [/tex]

[tex]let \: θ = 36.9 \\ let \: adj. = 5 \\ let \: hypo. = CD[/tex]

[tex] \cos(36.9 ) = \frac{5}{CD} [/tex]

[tex]CD \cos(36.9) = 5[/tex]

[tex]CD = \frac{5}{ \cos(36.9) } [/tex]

[tex]CD = 6.25 units\: (3s.f)[/tex]

Answer:

  x = 8

Step-by-step explanation:

A graphing calculator can show you the answer easily. It works well to define a function whose x-intercept is the solution. We can do that by subtracting 300 from the given equation so we have ...

  F(2, x, 4, 11) -300 = 0

The solution is x = 8.

__

We can solve this algebraically:

  F(2, x, 4, 11) -300 = 0

  2^x +4·11 -300 = 0 . . . . use the function definition

  2^x -256 = 0 . . . . . . simplify

  2^x = 2^8 . . . . . add 256

  x = 8 . . . . . . . . . match exponents of the same base

Answer:

There are no solutions.

Step-by-step explanation:

1y+6=26+1y

Add -1y and -6 on both sides.

1y-1y=26-6

Factor out y.

y(1-1)=20

y(0)=20

0=20

There are no solutions for y.

Answer:

feet/inches

Step-by-step explanation:

most gardening hoses are like 20 feet and 8 inches or whatever. So the best unit would be feet/inches

feet/inches is the best measure the length of a garden hose

A unit is any standard used for making comparisons in measurements. Unit conversions allow for measurements of a property that have been recorded using different units—for instance, centimeters to inches.

Most gardening hoses are like 20 feet and 8 inches or whatever. So the best unit would be feet/inches

Hence, feet/inches is the best measure the length of a garden hose.

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Answer:

14)

21√2

15)

Leg: 7√3

Hypotenuse: 14

Step-by-step explanation:

The hypotenuse is √2 as long as each leg. That means the leg is 42/√2. Simplified to make 21√2.

The hypotenuse is always twice as long as the shortest leg on a 30-60-90 triangle. The longer leg is √3 as long as the shortest side.

Answer:

84

Step-by-step explanation:

k(x+6)= 4x²+20

k(10)= k(4+6)= 4*4²+20= 64+20= 84

Answer:

1, 2, 4

Step-by-step explanation:

The triangles are similar by AAA or SSS (yes)

The sides are proportional (yes)

The length of AB is 21, not 15 (no)

The length of BC is 9 (yes)

The dilation is an enlargement, not reduction (no)

Answer:

1, 2, and 4

Step-by-step explanation:

I got it right on edge. good luck.

Answer:

Total area = 237.09 cm²

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Field book of an agricultural land is given in the figure. It is divided into 4 plots. Plot I is a right triangle, plot II is an equilateral triangle, plot III is a rectangle and plot IV is a trapezium, Find the area of each plot and the total area of the field. ( use √3 =1.73)

From the figure attached,

Area of the right triangle I = [tex]\frac{1}{2}(\text{Base})\times (\text{Height})[/tex]

Area of ΔADC = [tex]\frac{1}{2}(\text{CD})(\text{AD})[/tex]

                        = [tex]\frac{1}{2}(\sqrt{(AC)^2-(AD)^2})(\text{AD})[/tex]

                        = [tex]\frac{1}{2}(\sqrt{(13)^2-(19-7)^2} )(19-7)[/tex]

                        = [tex]\frac{1}{2}(\sqrt{169-144})(12)[/tex]

                        = [tex]\frac{1}{2}(5)(12)[/tex]

                        = 30 cm²

Area of equilateral triangle II = [tex]\frac{\sqrt{3} }{4}(\text{Side})^2[/tex]

Area of equilateral triangle II = [tex]\frac{\sqrt{3}}{4}(13)^2[/tex]

                                                = [tex]\frac{(1.73)(169)}{4}[/tex]

                                                = 73.0925

                                                ≈ 73.09 cm²

Area of rectangle III = Length × width

                                 = CF × CD

                                 = 7 × 5

                                 = 35 cm²

Area of trapezium EFGH = [tex]\frac{1}{2}(\text{EF}+\text{GH})(\text{FJ})[/tex]

Since, GH = GJ + JK + KH

17 = [tex]\sqrt{9^{2}-x^{2}}+5+\sqrt{(15)^2-x^{2}}[/tex]

12 = [tex]\sqrt{81-x^2}+\sqrt{225-x^2}[/tex]

144 = (81 - x²) + (225 - x²) + 2[tex]\sqrt{(81-x^2)(225-x^2)}[/tex]

144 - 306 = -2x² + [tex]2\sqrt{(81-x^2)(225-x^2)}[/tex]

-81 = -x² + [tex]\sqrt{(81-x^2)(225-x^2)}[/tex]

(x² - 81)² = (81 - x²)(225 - x²)

x⁴ + 6561 - 162x² = 18225 - 306x² + x⁴

144x² - 11664 = 0

x² = 81

x = 9 cm

Now area of plot IV = [tex]\frac{1}{2}(5+17)(9)[/tex]

                                = 99 cm²

Total Area of the land = 30 + 73.09 + 35 + 99

                                    = 237.09 cm²

Answer: The answer is B. (4,-1)

Step-by-step explanation: This is the correct answer because this is where the two lines intersect. You can also find this algebraically by finding the equation of each line. You then solve them as a system, cancelling one variable at a time.

Answer:

First to find AB we use cosine

cos ∅ = Adjacent / hypotenuse

AB is the adjacent

BC is the hypotenuse

cos ∅ = AB/AC

cos 70 = AB / 8

AB = 8 cos 70°

AB = 2.736

AB = 2.7cm to one decimal place

Hope this helps

Answer:

D

Step-by-step explanation:

The angle between the vertical and horizontal line is 90°, thus

75° + x = 90° ( subtract 75 from both sides )

x = 15° → D