An experiment consists on rolling a fair number cube. There are 6 possible outcomes: 1, 2, 3, 4, 5, and 6. Find the probability P(rolling a 7).

Answer:

look below

Step-by-step explanation:

y = 2 (x + 3)^2 - 2

Geometric figure:  parabola

Alternate forms:

y = 2 (x + 2) (x + 4)

y = 2 (x^2 + 6 x + 8)

-2 x^2 - 12 x + y - 16 = 0

Expanded form:

y = 2 x^2 + 12 x + 16

Roots:

x = -4

x = -2

Properties as a real function:

Domain - R (all real numbers)

Range - {y element R : y>=-2}

Partial derivatives:

d/dx(2 (x + 3)^2 - 2) = 4 (x + 3)

d/dy(2 (x + 3)^2 - 2) = 0

Implicit derivatives:

(dx(y))/(dy) = 1/(12 + 4 x)

(dy(x))/(dx) = 4 (3 + x)

Global minimum:

min{2 (x + 3)^2 - 2} = -2 at x = -3

Answer:

hi

Step-by-step explanation:

Answer:

x^2-7x+8=0

Step-by-step explanation:

(x+1)(x-8)=0

x^2-7x+8=0

Answer:

[tex]\frac{13}{24}[/tex]

Step-by-step explanation:

=> [tex]\frac{3}{8} +\frac{1}{6}[/tex]

LCM = 24

=> [tex]\frac{9+4}{24}[/tex]

=> [tex]\frac{13}{24}[/tex]

Answer:

[tex]\frac{13}{24}[/tex]

Step-by-step explanation:

[tex]\frac{3}{8} +\frac{1}{6}[/tex]

[tex]\frac{3 \times 6}{8\times 6} +\frac{1\times8}{6\times8}[/tex]

[tex]\frac{18}{48} +\frac{8}{48}[/tex]

[tex]\frac{18+8}{48}[/tex]

[tex]\frac{26}{48}[/tex]

[tex]\frac{13}{24}=0.54166...[/tex]

Answer:

D.

[tex] {4}^{x + 7} [/tex]

Step-by-step explanation:

since it is an exponential graph shifted 7units to the left would be

[tex] {4}^{x + 7} [/tex]

Answer:

54 sweets altogether

Step-by-step explanation:

Jim: 27

Dan:

David:

3:2:1

The amount is divided by 6

27/3=9

Dan— 9*2=18

David— 9*1=9

18+9+27=54

Answer:

RQ=35.51 km

PR=34.62 km

Step-by-step explanation:

Bearing of Q from P = 72 degrees

Bearing of R from Q=320 degrees

320=270+50

Therefore, the second angle of Q is 50 degrees.

[tex]\angle P=72^\circ\\\angle Q=68^\circ\\\angle R=180^\circ-(72^\circ+68^\circ)=40^\circ[/tex]

Using Law of Sines

[tex]\dfrac{r}{\sin R} =\dfrac{p}{\sin P} \\\dfrac{24}{\sin 40} =\dfrac{p}{\sin 72} \\p=\sin 72 \times \dfrac{24}{\sin 40}\\\\p=RQ=35.51$ km[/tex]

Using Law of Sines

[tex]\dfrac{q}{\sin Q} =\dfrac{r}{\sin R} \\\dfrac{q}{\sin 68} =\dfrac{24}{\sin 40} \\q=\dfrac{24}{\sin 40}\times \sin 68\\\\q=PR=34.62$ km[/tex]

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:

x^2-6x+9

Step-by-step explanation:

(x-3)^2

(x-3)(x-3)

x^2-3x-3x+9

x^2-6x+9

Answer:

12.5%

Step-by-step explanation:

8 / 64*100 =

(8 * 100) / 64 =

800 / 64 = 12.5

Hope this helped buddy! :D

Answer:

total memory = 8 GB + 64 GB

= 72 GB

extra memory = 64 GB

so percentage increase of memory

= ( 64 GB / 72 GB ) × 100

= 88.89 %

Answer:

Length = 7 cm

Width = 2 cm

Step-by-step explanation:

Perimeter of rectangle = 18 cm

Let length of rectangle = [tex]l[/tex] cm

Let width of rectangle =  [tex]w[/tex] cm

As per given statement, length is 3 cm more than the twice of its width:

Writing equation:

[tex]l = 2\times w +3 ....... (1)[/tex]

Formula for perimeter of a rectangle is given as:

[tex]P = 2 \times (Length + Width)[/tex]

OR

[tex]P = 2 \times (l + w)[/tex]

Putting values of P as given and [tex]l[/tex] by using equation (1):

[tex]18 = 2 \times (2w +3 + w)\\\Rightarrow \dfrac{18}2 = 3w +3 \\\Rightarrow 9 = 3w +3\\\Rightarrow 3w = 9 -3\\\Rightarrow w = \dfrac{6}{3}\\\Rightarrow w = 2\ cm[/tex]

Putting value of [tex]w[/tex] in equation (1):

[tex]l = 2\times 2 +3 \\\Rightarrow l = 4+3\\\Rightarrow l = 7\ cm[/tex]

So, the dimensions are:

Length = 7 cm

Width = 2 cm

Answer:

35 cm

Step-by-step explanation:

As shown in the image attached, the A large rectangle is made by joining three identical small rectangles,

The width of one small rectangle is x cm and the length of one small rectangle is 2x cm. Therefore the perimeter of the small rectangle is given as:

2(length + width) = Perimeter

2(2x + x) = 21

2(3x) = 21

6x = 21

x = 21/6 = 3.5 cm

x = 3.5 cm

From the image attached, the width of the large rectangle is 2x (x + x) and the length is 3x (2x + x). Therefore, the perimeter of the large rectangle is:

2(length + width) = Perimeter

2(3x + 2x) = Perimeter

Perimeter = 2(5x)

Perimeter = 10x

Perimeter = 10(3.5)

Perimeter = 35 cm

Answer:

Zeroes: (-1.45, 0) and (3.45, 0)

Step-by-step explanation:

I plugged the equation into a graphing calc and located the x-values when graphing.

Answer:

6 : 1

Step-by-step explanation:

Given the ratio

12 : 2 ( divide both parts by 2 )

= 6 : 1 ← in the form n : 1

Answer:

-10

Step-by-step explanation:

Variable k is denoted as vertical movement. In this case, the -10 is k. Therefore, the graph is moving 10 units down from the parent graph.

Answer:

4.92*10^5

Step-by-step explanation

The annual flow of the Mississippi River would fit in the Atlantic Ocean approximately 4.92 x 10⁵ times.

The space occupied by an object in three-dimensional space is called the volume of an object. In simple words, space is taken by an object.

To find out how many times the annual flow of the Mississippi River would fit in the Atlantic Ocean, we need to divide the volume of the Atlantic Ocean by the annual flow of the Mississippi River:

number of times = (volume of Atlantic Ocean) / (annual flow of Mississippi River)

= (3.1 x 10¹⁷ cubic meters) / (6.3 x 10¹¹ cubic meters)

= 4.92 x 10⁵

Rounding to two decimal places, the final answer is approximately 4.92 x 10⁵. Therefore, the annual flow of the Mississippi River would fit in the Atlantic Ocean approximately 492,000 times.

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Answer:

Step-by-step explanation:

correct one is b

Answer:

d

Step-by-step explanation:

To construct an angle bisector with a compass  D. Place the compass needle on the vertex of the angle, and draw an arc across both legs of the angle.

An angle bisector is a line segment that divides angle into two equal parts.

According to the given statements to construct an angle bisector using a compass span any width of radius in a compass pace in onto the vertex of the angle cut the two arc on the two lines then without changing the radius draw two arcs where the previous arcs have intersected the two lines.

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Answer:

[tex] \sin( \frac{31\pi}{3} ) [/tex]

= 0.537

Answer:

√3/2

Step-by-step explanation:

sin((31π/3)= sin( 10π + π/3)= sin(π/3) =√3/2

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:

1060

Step-by-step explanation:

Given:

No. of boys = 870

No. of girls = 800

Probability that a boy chosen studies Spanish = [tex]\dfrac{2}{3}[/tex]

Probability that a girl chosen studies Spanish = [tex]\dfrac{3}{5}[/tex]

the number of boys in the school who study Spanish :

[tex]\dfrac{2}{3}\times 870=290\times 2=580[/tex]

the number of girls in the school who study Spanish :

[tex]\dfrac{3}{5}\times 800 \\=3\times 160\\\\=480[/tex]

Therefore, total number of students who study Spanish would be :

480+580=1060

Answer:

[tex]\frac{8}{27}[/tex] is the probability that a player draws out two tiles of the same color assuming they are drawing one tile from each bag.

Step-by-step explanation:

In each bag there are red, green, and blue tiles, meaning that no matter which color is pulled out first there is always some probability that the second tile will be the same color. So, we can set up three possible outcomes:

Red: The player pulls out a red tile first. This has a [tex]\frac{1}{9}[/tex] probability of happening. Then in order to succeed for the problem, the next tile also needs to be red which has a [tex]\frac{6}{12}[/tex] probability attached to it. [tex]\frac{1}{9}[/tex] × [tex]\frac{6}{12}[/tex]=[tex]\frac{1}{18}[/tex] probability of happening.

Green: There is a [tex]\frac{5}{9}[/tex] probability of the player pulling out a green tile first. In this case we want to calculate the probability of the second tile being green, which would be [tex]\frac{4}{12}[/tex]. [tex]\frac{5}{9}[/tex]×[tex]\frac{4}{12}[/tex]=[tex]\frac{5}{27}[/tex].

Blue: There is a [tex]\frac{3}{9}[/tex] probability of the first tile being blue in which case we are hoping for the second tile to be blue as well. The probability of the second tile being blue is [tex]\frac{2}{12}[/tex] on its own, and them both being blue is  [tex]\frac{3}{9}[/tex]×[tex]\frac{2}{12}[/tex]=[tex]\frac{1}{18}[/tex]

Adding [tex]\frac{1}{18}[/tex]+[tex]\frac{1}{18}[/tex]+[tex]\frac{5}{27}[/tex] we get the answer [tex]\frac{8}{27}[/tex].

Answer:

Step-by-step explanation:

This is an exponential function. In order to find the answer to the question, we need to first determine what the equation is that models this information. The standard form for an exponential function is

[tex]y=a(b)^x[/tex] where a is the initial value and b is the growth/decay rate. If the starting population is 5000, then

a = 5000

If the population is growing, that means that it retains 100% of the initial population and is added to by another 3.5%. So in a sense the population grows 100% + 3.5% = 103.5% or, in decimal form, 1.035. So

b = 1.035

Our function is

[tex]y=5000(1.035)^x[/tex] where y is the ending population and x is the number of years it takes to get to that ending population. We want to know how long, x, it will be til the population reaches 7300, y.

[tex]7300=5000(1.035)^x[/tex] and we need to solve for x. The only way to do that is by using logs. I'll use natural logs for this.

Begin by dividing both sides by 5000 to get

[tex]1.46=1.035^x[/tex] and take the natural log of both sides:

[tex]ln(1.46)=ln(1.035)^x[/tex]

The power rule for natural logs is that we can now bring the exponent down in front of the ln to get:

[tex]ln(1.46)=xln(1.035)[/tex] To solve for x, we now divide both sides by ln(1.035):

[tex]\frac{ln(1.46)}{ln(1.035)}=x[/tex]

Do that division on your calculator and get that

x = 11.0 years.

That means that 11 years after the population was 5000 it will be expected to reach 7300 (as long as the growth rate remains 3.5%)

Step-by-step explanation:

We have,

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function :

[tex]h=-16t^2 + 36t + 10[/tex] ......(1)

Part (a) :

The maximum height reached by the ball is given by :

[tex]\dfrac{dh}{dt}=0\\\\\dfrac{d(-16t^2 + 36t + 10)}{dt}=0\\\\-32t+36=0\\\\t=\dfrac{36}{32}\\\\t=1.125\ s[/tex]

Part (b) :

The maximum height of the ball is calculated by putting t = 1.125 in equation (1) such that :

[tex]h=-16(1.125)^2 + 36(1.125)+ 10\\\\h=30.25\ m[/tex]

Answer:

-x^2+3x+3;  5

Step-by-step explanation:

polynomial is -x^2+3x+3

when x=2 then -2^2+3*2+3=-4+6+3=5

The solution is Option B.

The value of the equation is A = -x² + 3x + 3 , and when x = 2 , A = 5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = x + 3x² + 2x - 3 - 4x² + 6   be equation (1)

On simplifying the equation , we get

A = 3x² - 4x² + x + 2x - 3 + 6

A = -x² + 3x + 3

Now , when x = 2

Substitute the value of x = 2 in the equation , we get

A = - ( 2 )² + 3 ( 2 ) + 3

A = -4 + 6 + 3

A = 9 - 4

A = 5

Therefore , the value of A is 5

Hence , the equation is A = -x² + 3x + 3

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I'm thinking line 2 and 3 are Parallel

Answer:

C. Lines 2 and 4 are perpendicular

Step-by-step explanation:

If you just graph them all, none of them are parallel. But lines 2 and 4 are perpendicular and so are the lines 1 and 3.

Out of the options, C. Lines 2 and 4 are perpendicular, is the only correct answer in the choices given.

The last 2 shapes.

When you rotate both of them 360 degrees only at 180 and back at 360 it looks same.

Answer:

y=34, x=17 root 3

Step-by-step explanation:

30 60 90 triangle.

Shortest side is x, hypotenuse is 2x, bottom length is x root 3

Answer:

Using the Leg Opposite to 30° Theorem we derive that y = 34 and from the Pythagorean Theorem, x = 17√3.

Answer:

Do it your self

Step-by-step explanation:

Answer:

Option B is the right option

solution,

A(4,5)------->(X1,x2)

B(2,1)-------->(y1,y2)

Now,

[tex]ab = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ \: \: \: = \sqrt{ {(2 - 4)}^{2} + {(1 - 5)}^{2} } \\ \: \: = \sqrt{ {( - 2)}^{2} + {( - 4)}^{2} } \\ \: \: = \sqrt{4 + 16} \\ \: \: \ = \sqrt{20} [/tex]

hope this helps....

Good luck on your assignment..