Pedro drives the same route to work on Monday through Friday. His route includes one traffic light. According to the local traffic department, there is a 55% chance that the light will be red when he arrives at the intersection on a randomly selected workday. Suppose we choose 10 of Pedro's workdays at random and let Y = the number of times that the light is red.

Answer:

z=-3

Step-by-step explanation:

Step 1: Subtract 9z from both sides.

Step 2: Subtract 3 from both sides.

Answer:  Holly would take 60 minutes to clean alone.

Step-by-step explanation:

Let t = Time taken by Holly to clean alone.

Given: Time taken by Mia to clean alone = 30 minutes

Time taken by Mia and holly to clean their room = 20 minutes

Then,

[tex]\dfrac1t+\dfrac{1}{30}=\dfrac{1}{20}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{20}-\dfrac{1}{30}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{3-2}{60}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{60}\\\\\Rightarrow\ t= 60[/tex]

Hence, Holly would take 60 minutes to clean alone.

Answer:

[tex]r=9.0\:\mathrm{cm}[/tex]

Step-by-step explanation:

The volume of a sphere is given as [tex]\frac{4}{3}r^3\pi[/tex]. Therefore we have the following equation:

[tex]\frac{4}{3}r^3\pi=3026,\\r^3=\frac{3}{4}\cdot\frac{3026}{\pi},\\r^3=722.40428,\\r=\sqrt[3]{722.40428},\\r\approx \fbox{$9.0\:\mathrm{cm}$}[/tex].

Rounding this to the nearest tenth of a centimeter, the radius of the sphere is approximately 14.0 cm.

Volume refers to the amount of space occupied by an object or substance. In mathematics, it is usually measured in cubic units (e.g. cubic meters, cubic centimeters).

The volume of an object can be calculated using its dimensions and specific formulas that depend on the shape of the object.

For example, the volume of a cube is calculated by multiplying its length, width, and height, while the volume of a sphere is calculated using the formula [tex](4/3)\pi r^3[/tex], where r is the radius of the sphere.

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere and π (pi) is a mathematical constant approximately equal to 3.14159.

We can rearrange this formula to solve for r:

r = [tex](3V/4\pi)^{(1/3)[/tex]

Substituting the given volume V = 3026 [tex]cm^3[/tex], we get:

r = [tex](3(3026)/(4\pi))^{(1/3)[/tex] ≈ 14.0 cm

Thus, the radius of the sphere is approximately 14.0 cm, rounded to the nearest tenth of a centimetre.

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THe 3rd equation is true

Property of Addition and division.

Answer: h = 14.5 ft

Step-by-step explanation: Since it is given angles and side and it wants a side, let's use Law of Sines, which is formulated as

                                           [tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

i.e., the ratio of a side and the sin of its opposite angle is constant.

So, for this triangle, height is

[tex]\frac{sin46}{h} =\frac{sin44}{14}[/tex]

[tex]h=\frac{14sin46}{sin44}[/tex]

[tex]h=\frac{10.07}{0.69}[/tex]

h = 14.51

Height of the main sail rounded to the nearest tenth is 14.5 ft.

Answer:

321%

Step-by-step explanation:

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Answer:

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Answer:

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Answer:

Any real number strictly larger than 9 and strictly less than 21.

Step-by-step explanation:

By triangle inequality, the sum of the lengths of any two sides are greater than the length of the third side.

We therefore could set up three inequalities.

x+6>15, x+15>6, 15+6>x

Solving these, we get x>9, x>-9, x<21 i.e. 9 < x < 21.

Answer:

C

Step-by-step explanation:

Answer:

No, 3 is not a factor of 34

Answer:

no

Step-by-step explanation:

34: 1,2,17,34

Answer:

[tex]V(x) = -\frac{340}{3}x +2220[/tex]

[tex]V(8) = 1313.3[/tex]

Step-by-step explanation:

Given

Let x represent years and V represents the value.

So, we have:

[tex](x_1,v_1) = (0,2220)[/tex]

[tex](x_2,v_2) = (6,1540)[/tex]

Solving (a): The linear function

First, we calculate the slope (m)

[tex]m = \frac{v_2 - v_1}{x_2 - x_1}[/tex]

This gives:

[tex]m = \frac{1540-2220}{6-0}[/tex]

[tex]m = \frac{-680}{6}[/tex]

[tex]m = -\frac{340}{3}[/tex]

The linear function is calculated using:

[tex]v - v_2 = m(x - x_2)[/tex]

Where:

[tex](x_2,v_2) = (6,1540)[/tex]

[tex]m = -\frac{340}{3}[/tex]

So, we have:

[tex]v - 1540 = -\frac{340}{3}(x - 6)[/tex]

Open bracket

[tex]v - 1540 = -\frac{340}{3}x +\frac{340}{3}* 6[/tex]

[tex]v - 1540 = -\frac{340}{3}x +680[/tex]

Make v the subject

[tex]v = -\frac{340}{3}x +680+1540[/tex]

[tex]v = -\frac{340}{3}x +2220[/tex]

So, the function is:

[tex]V(x) = -\frac{340}{3}x +2220[/tex]

Solving (b): When x = 8

Substitute 8 for x in [tex]V(x) = -\frac{340}{3}x +2220[/tex]

[tex]V(8) = -\frac{340}{3}*8 +2220[/tex]

[tex]V(8) = -\frac{340*8}{3} +2220[/tex]

[tex]V(8) = -\frac{2720}{3} +2220[/tex]

Take LCM

[tex]V(8) = \frac{-2720+2220*3}{3}[/tex]

[tex]V(8) = \frac{-2720+6660}{3}[/tex]

[tex]V(8) = \frac{3940}{3}[/tex]

[tex]V(8) = 1313.3[/tex]

Hence, its value after 8 years is 1313.3

Answer: y = -1/2x - 1

Answer:

[tex]y - 8 = \frac{5}{3}(x - 1)[/tex]

Step-by-step explanation:

1) Use the slope formula, [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex], and the given points to find the slope. [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line must intersect, and [tex]x_2[/tex] and [tex]y_2[/tex] represent the x and y values of another point the line must also intersect:

[tex]\frac{(3)-(8)}{(-2)-(1)}[/tex]

= [tex]\frac{-5}{-3}[/tex]

= [tex]\frac{5}{3}[/tex]

2) Using the point-slope formula, [tex]y-y_1 = m (x - x_1)[/tex], use the slope you just calculated and substitute it for m. Choose any of the two points given (I chose (1,8)) and substitute its x and y values for [tex]x_1[/tex] and [tex]y_1[/tex]. Don't worry, the equation of the line is the same no matter which point you choose (unless the question specifies which one you need to choose):

[tex]y - 8 = \frac{5}{3}(x - 1)[/tex]

The value of x from the figure is 4

From the figure given we are told that ABC ~ DEC. Hence to get the value of x we will use the relationship shown;

Cross multiply

25(2x) = 20(3x - 2)

50x = 60x - 40

50x - 60x =-40

-10x = -40

x = 4

Hence the value of x from the figure is 4

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Answer:

its A :)

Step-by-step explanation:

35, 42, 105 respectively

Answer:

32, 42, 105

Step-by-step explanation:

(32)^2 = 32×32

= 1225

(42)^2 = 42×42

= 1764

(105)^2 = 105×105

=11025

Answer:

m∠C = 66°

Step-by-step explanation:

Given

m∠ A = 33°

m∠ B = 81°

To determine

m∠C = ?

We know that sum of angles of a triangle is 180°.

so using the equation

m∠ A + m∠ B +  m∠C = 180°

substituting m∠ A = 33°, and m∠ B = 81° in the equatio

33° + 81°+m∠C= 180°

114° + m∠C = 180°

m∠C = 180° - 114°

m∠C = 66°

Therefore,

Answer:

x= tm+5/4-t

Step-by-step explanation:

4x-5=t(x+5)

4x-5-=tx+tm   distributive

4x-5-tx=tm    substract tx from both sides

4x-tx=tm+5   add 5 to both sides

x * 4+ x(-t) =tm+5  factor x out 4x-tx

x(4-t)=tm+5   factor x out x*4 + x(-t)

x(4-t)/4-t= tm/4-t+ 5/4-t   divide each term in 4-t

x= tm/4-t + 5/4-t combine the numerators over the common denominator

x=tm+5/4-t

Answer:

− 3.5 ( x + y )

Hope this helps

Step-by-step explanation:

Answer:

− 3.5 ( x + y )

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Step-by-step explanation:

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Answer:

2 is the correct answer you know it also

Answer:

Y=−3x2+6x+9

Step-by-step explanation:

Answer

5.33 units

Step-by-step explanation:

uh kakis

Use the Pythagorean theorem

a^2 + b^2 = c^2

a^2 + 15^2 = 25^2

a^2 + 225 = 625

a^2 = 400

a = 20

Answer: 20 cm

Hope this helps!!

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Answer:

...

against the wind, an airplane travels 3640 km in 7 hours.

with the wind, the same plane travels 6000 km in 6hrs.

...

let speed of plane in still air be x mph

speed of wind be y mph.

..

t=d/r

..

against wind speed = x-y mph

with wond speed = x=y mph

...

3640/(x-y)=7

3640 = 7x-7y

/7

520=x-y.....................1

...

6000/x+y = 6

6000 = 6x+6y

/6

1000=x+y.....................2

...

Add (1) & (2)

2x=1520

/2

x=760 mph speed of plane in still air

...

plug value of x in 2

1000=760+y

100-760=y

240 = y

240 mph speed of wind

Answer:

-5 1/2

The first one is right.

Step-by-step explanation:

k12 right ?

The solution of the given expression if p = 1, r= -7, and s = -2 will be; -5 and 1/2

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

WE have been given an expression as

-3p-2r / 6+4s

We have to substitute the value p = 1, r= -7, and s = -2 to find the solution.

Plug the values;

-3p-2r / 6+4s

-3 (1) -2 (-7) / 6+4(-2)

-3 + 14 / 6 - 8

11 / -2

Hence, the solution of the given expression if p = 1, r= -7, and s = -2 will be; -5 and 1/2

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Answer:

0.8

Step-by-step explanation:

that's the decimal.

Answer:

0.8

Step-by-step explanation:

Answer:

the answer is $3

Step-by-step explanation:

I just looked it up lol