A cereal company is putting 1 11 of 4 44 prizes in each box of cereal. The prizes are evenly distributed so the probability of winning any given prize is always 1 / 4 1/41, slash, 4.

Answer:

(-∞, -4] or [5, ∞)

Step-by-step explanation:

Because the solutions for x can also be equal to -4 and 5, brackets are used.

And because the solutions for x can be any number less than -4 or any number greater than 5, -∞ and ∞ are used respectively.

Since the line is perpendicular, we know that the slope is reciprocal and negative to the other one.

So,

y = -4x + b

We want to find the y-intersect (b) so substitute the intersected points and solve for it.

2 = -4(2) + b

2 = -8 + b

2 + 8 = b

10 = b

So the complete equation would be:

y = -4x + 10

Answer:

9.36 x 10^(-10)

Step-by-step explanation:

Answer:

A: 2/9

Step-by-step explanation:

Answer:

tornado!

Step-by-step explanation:

sometimes tornados can start off slow and sometimes they can go really fast.

Answer:

The correct option is;

a. 20 m/s

Step-by-step explanation:

The given parameters are;

The angle at which the ball is thrown, θ = 30° to the horizontal

The horizontal distance of the top edge of the building where the ball lands from where the ball is thrown, x = 20 m

The height of the top edge of the building above the throwing point = 5 meters

Let "v" represent the speed with which the ball is thrown

We have;

The vertical component of the speed with which the ball is thrown, [tex]v_y[/tex] = v × sin(θ) = v × sin(30°) = v × 0.5 = 0.5·v

[tex]v_y[/tex] = 0.5·v

The horizontal component of the speed with which the ball is thrown, vₓ = v × cos(θ) = v × cos(30°) = v × 0.9 = 0.9·v

vₓ = 0.9·v

The kinematic equation of the motion is y = [tex]v_y[/tex]·t - (1/2)·g·t², where;

y = The vertical height reached = 5 metes

t = The time taken to reach the specified 5 m, height

g = The acceleration due to gravity = 9.8 m/s², we have;

Therefore, we have;

5 = 0.5·v·t - (1/2)·9.8·t²...(1)

Also, from the horizontal motion of the ball, we have the following kinematic equation of motion;

x = vₓ × t

Therefore, by substituting the known values, we have;

20 = 0.9·v × t

∴ v = 20/(0.9·t) = 200/(9·t)...(2)

Substituting the value of t in equation (1) gives;

5 = 0.5·v·t - (1/2)·9.8·t² = 0.5·(200/(9·t))·t - (1/2)·9.8·t²

∴ 5 = 0.5·(200/(9·t))·t - (1/2)·9.8·t² = 100/9 - 4.9·t²

4.9·t² = 100/9 - 5 = 55/9

t = √(55/(9 × 4.9)) ≈ 1.116766

The time taken to reach the specified 5 m height = t ≈ 1.116766 seconds

From equation (2), we have, v = 200/(9·t) = 200/(9 × 1.116766) ≈ 19.8987 m/s

The speed with which the ball is thrown = v ≈ 19.8987 m/s ≈ 20 m/s. to the nearest whole number.

The speed with which the ball is thrown is approximately 20 m/s

Answer:

The answer is:

a) 20 m/s

Hope it helps:D

Step-by-step explanation:

-2x³ + 14x² + 120x

= -2x(x² - 7x - 60)

= -2x(x - 12)(x + 5).

The other 2 dimensions are -2x and (x + 5).

When using a graphing calculator to maximise the volume of the prism, we get x = 7.378. However this value is not reasonable as it makes -2x and (x - 12) negative, which are the sides of the prism.

Answer:

B.) 53/20

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

|-4/5 - 1/10| + |-3/4 + 5/2|

Step 2: Evaluate

Answer:

10 miles

Step-by-step explanation:

1/3 × 30 miles = 10 miles

Answer:

Step-by-step explanation:

30 * 1/3 = 10  :)

Answer:

Step-by-step explanation:

P = perimeter = 114

P =2 * length +2* width

P = 2(2x - 3) + 2(x)

114 =  4x-6  + 2x

114 = 6x -6

19 = x -1

20 = x

check it  

2( 2x -3)+2x =  ?  

4x -6 +2x=?

6x -6 = ?

6(20)-6 =?

120-6 = 114

yep this is correct

Answer:

(0,6)

Step-by-step explanation:

When a system of equations is graphed, the point at which the lines intersect is a solution to the system. Looking at the graph, we can see that the lines intersect at (0,6). Therefore, (0,6) is a solution to the system of equations.

Answer:

Disagree ΔABC ≅ ΔDEC by ASA butt by SAS

Step-by-step explanation:

point C is the midpoint of (A/E), C is also the midpoint of (B/D )

BC = CD   and AC = CE

∠BCA = ∠ECD

ΔABC ≅ ΔDEC by SAS not by ASA

Answer:

55 mph

Step-by-step explanation:

Given that:

Total miles of journey = 350 miles

Miles already driven = 75 miles

To cover the rest of the journey in 5 hours, the average speed of travel. Will be:

Recall:

Speed = (Distance left to cover ÷ budgeted travel time)

Distance left to cover : (total miles - distance already driven)

Average speed required = (350 - 75) / 5

= 275 / 5

= 55 mph

Answer:

There is nothing but your question and you should try on your own

Step-by-step explanation:

Answer:

N/A

Step-by-step explanation:

There is not context with this problem, therefore it cannot be solved.

you need both sides of the equation to be equal to each other.

ex: 1 = 1

x = x

10 - x = -x + 10

this may not be what you're looking for and if it isn't just let me know

Answer:

1

Step-by-step explanation:

Answer:

One

Step-by-step explanation:

[tex] \frac{1}{2} (x +12) = 4x - 1 \\ \\ \frac{1}{2} x + \frac{1}{2} \times 12 = 4x - 1 \\ \\ \frac{1}{2} x + 6 = 4x - 1 \\ \\ 6 + 1 = 4x - \frac{1}{2} x \\ \\ 7 = \frac{8x - x}{2} \\ \\ 7 = \frac{7}{2} x \\ \\ 7 \times 2 = 7x \\ \\ x = \frac{7 \times 2}{7} \\ \\ x = 2[/tex]

So, there exist only one solution for the given equation.

Answer:

It is

Scale Factor = Ratio of Side Lengths

= 12/8 = 9/6 = 1.5.

Step-by-step explanation:

Hope this helped have an amazing day!

The two rectangles are similar and the scale factor is 3/2.

Given data:

The first rectangle is represented as ABCD

The second rectangle is represented as PQRS

Now, the dimensions of ABCD is 8 cm x 6 cm

The dimensions of PQRS is 12 cm x 9 cm

So, the scale factor is represented as k and the value of k is :

k = length of PQRS / length of ABCD

So, k = 12 / 8

k = 3/2

Hence , the similar rectangles have a scale factor of 3/2

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Answer:

0

Step-by-step explanation:

Anything multiplied by 0 is 0

Answer:

The solution to the system of equations be:

[tex]x=3,\:y=-1[/tex]

Hece, option B is correct.

Step-by-step explanation:

Given the system of equations

[tex]\begin{bmatrix}x-3y=6\\ 2x+2y=4\end{bmatrix}[/tex]

Multiply x − 3y = 6 by 2:      2x-6y=12

[tex]\begin{bmatrix}2x-6y=12\\ 2x+2y=4\end{bmatrix}[/tex]

so

[tex]2x+2y=4[/tex]

[tex]-[/tex]

[tex]\underline{2x-6y=12}[/tex]

[tex]8y=-8[/tex]

so the system of equations becomes

[tex]\begin{bmatrix}2x-6y=12\\ 8y=-8\end{bmatrix}[/tex]

Solve 8y = -8 for y

[tex]8y=-8[/tex]

Divide both sides by 8

[tex]\frac{8y}{8}=\frac{-8}{8}[/tex]

[tex]y=-1[/tex]

[tex]\mathrm{For\:}2x-6y=12\mathrm{\:plug\:in\:}y=-1[/tex]

[tex]2x-6\left(-1\right)=12[/tex]

[tex]2x+6=12[/tex]

subtract 6 from both sides

[tex]2x+6-6=12-6[/tex]

[tex]2x=6[/tex]

Divide both sides by 2

[tex]\frac{2x}{2}=\frac{6}{2}[/tex]

[tex]x=3[/tex]

Therefore, the solution to the system of equations be:

[tex]x=3,\:y=-1[/tex]

Hence, option B is correct.

⚽ From Equation (i) we get :

⚽ Now, Substitute the equation (iii) in equation (ii) we get :

→ 2(6 + 3y) + 2y = 4

→ 12 + 6y + 2y = 4

→ 8y = 4 - 12

→ 8y = -8

→ y = -8 ÷ 8

→ y = -1

⚽ Now Substituting value of y = -1 in equation (iii) we get :

→ x = 6 + 3y

→ x = 6 + 3(-1)

→ x = 6 + (-3)

→ x = 6 - 3

→ x = 3

Answer:

209 m²

Step-by-step explanation:

The class room has a measurement of 11 m long, 8 m wide and 5.5 m high. Hence the walls of the classroom would be 4, with the following measurements.

Wall 1: 11 m by 5.5 m, Wall 2: 8 m by 5.5 m, Wall 3: 11 m by 5.5 m and Wall 4: 8 m by 5.5 m

The area of wall 1 = 11 m * 5.5 m = 60.5 m²

The area of wall 2 = 8 m * 5.5 m = 44 m²

The area of wall 3 = 11 m * 5.5 m = 60.5 m²

The area of wall 4 = 11 m * 5.5 m = 44 m²

The sum of areas of the fall wall = area of wall 1 + area of wall 2 + area of wall 3 + area of wall 4

The sum of areas of the fall wall = 60.5 + 44 + 60.5 + 44 = 209 m²

Answer:

Decimal form: 0.4286

Step-by-step explanation:

The value of 3/7 in decimal form up to nearest thousands will be 0.4285.

A fraction 3/7 is given in the question.

We have to find it's decimal form and round-off it to nearest thousands.

What will be the value of 1/2 in decimal form rounded to units place ?

The value will be 0.5

To find the decimal form let's divide 3 by 7.

3 ÷ 7 = 0.428572

We have to round it to nearest thousands i.e., up to 4 places Right to decimal point.

The rounded value will be 0.4285.

thus , the decimal form of 3/7 will be 0.4285 rounded off to nearest thousands.

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Answer:

c

Step-by-step explanation:

The value of sin x in the given right triangle is 0.894.

The sine of an angle is a trigonometric function that is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

Given is right triangle ABC, we need to find the value of sin x,

So, we see that the figure is divided into three similar triangles,

Namely,

Δ CDB ~ Δ BDA ~ Δ CBA,

Therefore, according to the definition of similarity,

We have,

CD / CB = BD / BA = 16/17.89

Therefore, BD / BA = 0.894

Also,

sin x = BD / BA

Therefore,

sin x = 0.894

Hence the value of sin x in the given right triangle is 0.894.

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Step-by-step explanation:

Angle 3 + Angle 5 = 180° (C-angles)

Therefore 7y + 15 + 110 - 2y = 180, 5y = 55, y = 11.

Angle 4 = Angle 5 (Z-angles)

Hence Angle 4 = 110 - 2y = 110 - 2(11) = 88°.

Step-by-step explanation:

1/7 + ? = 1/3

? = 1/3 - 1/7 = 7/21 - 3/21 = 4/21.

The missing fraction is 4/21.

[tex] \sf \left|\begin{array}{c c} sin20\degree & -cos20\degree \\ sin70\degree & cos70\degree \end{array}\right|=?[/tex]

They are asking us to find the determinant

[tex]\boxed{\sf \left|\begin{array}{c c} a & b \\ c & d \end{array}\right| =ad-bc}[/tex]

[tex]\left|\begin{array}{c c} sin20\degree & -cos20\degree \\ sin70\degree & cos70\degree \end{array}\right| \: = sin20 \degree cos70 \degree - ( - cos20 \degree sin70 \degree) \: \\ \\ = sin20 \degree cos70 \degree + cos20 \degree sin70 \degree [/tex]

[tex]\boxed{\sf sin(A+B)=sinAcosB+cosAsinB}[/tex]

it becomes

[tex] \longrightarrow \: sin(20 + 70) \\ \\ \longrightarrow \: sin(90 \degree) = 1[/tex]

[tex] \boxed{\sf \left|\begin{array}{c c} sin20\degree & -cos20\degree \\ sin70\degree & cos70\degree \end{array}\right|=1}[/tex]

☄It is a rectangular representation or array of numbers,symbols and many more functions

☄It is represented in rows and columns

Answer:

14

Step-by-step explanation:

Answer:

y=2x-6. ---------(1)

4x-2y=14. --------(2)

substituting equation 2 in 1

4x-2(2x-6)=14

4x-4x+12=14

so it has no solution

Step-by-step explanation:

As you can see in the image below, the answer is no solution.

Answer:

that hard

Step-by-step explanation:

Answer: Choice C.  g(x) = (3x)^2

To confirm this, plug in x = 1 and you'll find that:

g(x) = (3x)^2

g(1) = (3*1)^2

g(1) = (3)^2

g(1) = 3*3

g(1) = 9

Showing that (1,9) is on the red g(x) curve.