A student and a professor each choose a number between 1 and 8 (1 and 8 are both possible choices). what is the probability that the two choose the same number

Answer:

(2x+3)(x+2)

Step-by-step explanation:

i hope this helps

we know that

The simple interest formula is equal to

[tex]I=Prt[/tex]

where

I represents simple interest

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=5\ years\\ P=?\\ I=\$40\\r=0.10[/tex]

[tex]I=Prt[/tex]

Solve for P

[tex]P=I/(rt)[/tex]

substitute the values

[tex]P=40/(0.10*5)=\$80[/tex]

therefore

the answer is

[tex]\$80[/tex]

15 /3 = 5. so each 1/5 is $5

5*5 = 25

 so the game costs $25

The average rate of change from x = –4 to x = 1 is 3.

To find the average rate of change from x = –4 to x = 1, we need to calculate the change in y-values and divide it by the change in x-values. Given that the slope of the line is 3, we can use the formula for average rate of change: (change in y) / (change in x). In this case, the change in x is 1 - (-4) = 5, and the change in y is 3 * 5 = 15. Therefore, the average rate of change is 15 / 5 = 3.

Answer: 1.)

A. 30in^2

B. 18cm^2

C. 130yd^2

2.) The formula for the area of a triangle is half the base times the height. So 1/2 x 40 x 32 = 640cm^2

3.) 17 yards. The fence that enclose Sondra's backyard is a right triangle whose sides measuring 8 yards, 15 yards and 17 yards respectively.

4.) From the Pythagorean Theorem we know:

hypotenuse^2 = side^2 + side^2

hypotenuse^2 = 36 + 36

hypotenuse = square root (72)

hypotenuse = 8.48528... feet

5.) a. 5

b. √128

c. √221

Area of triangle are  [tex]30inches^{2}[/tex] in part(a),

[tex]18[/tex] [tex]centimerters^{2}[/tex] in part(b) and [tex]130[/tex] [tex]yards^{2}[/tex] in part(c)

What is Triangle?

In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

What is area?

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

According to questions, we have the following

In part (a.), h = [tex]6[/tex] inches; b = [tex]10[/tex] inches

In part (b.), h =[tex]9[/tex] centimeters; b =[tex]4[/tex] centimeters

In part (c.) h = [tex]13[/tex] yards; b = [tex]20[/tex] yards

We have to find the area of each triangle with the given heights and bases.

Now, Area of triangle in part a

[tex]=\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]

[tex]=\frac{1}{2}[/tex]×[tex]6[/tex]×[tex]10[/tex]

[tex]=30inches^{2}[/tex]

Area of triangle in part b

[tex]=\frac{1}{2}[/tex]×[tex]9[/tex]×[tex]4[/tex]

[tex]=18[/tex] [tex]centimerters^{2}[/tex]

Area of triangle in part c

[tex]=\frac{1}{2}[/tex]×[tex]13[/tex]×[tex]20[/tex]

[tex]=130[/tex] [tex]yards^{2}[/tex]

Hence, we can conclude that area of triangle are  [tex]30inches^{2}[/tex] in part(a),

[tex]18[/tex] [tex]centimerters^{2}[/tex] in part(b) and [tex]130[/tex] [tex]yards^{2}[/tex] in part(c)

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The solution to the system of equations is x = 6 and y = 84.

The given equations are:

-13x = 90 - 2y

-6x = 48 - 2y

To find the values of x and y, we can solve the system of equations. We can start by multiplying the second equation by -2 to eliminate the y variable. This gives us:

12x = -96 + 4y

Now we have two equations:

-13x = 90 - 2y

12x = -96 + 4y

We can add the two equations together:

-13x + 12x = 90 - 2y + (-96 + 4y)

-x = -6

Then, we can divide both sides of the equation by -1 to solve for x:

x = 6

Substituting the value of x back into one of the original equations, we can solve for y. Let's use the first equation:

-13(6) = 90 - 2y

-78 = 90 - 2y

-2y = -168

y = 84

Therefore, the solution to the system of equations is x = 6 and y = 84.

Answer:

12

Step-by-step explanation:

Answer: The object and its image have opposite orientations

Step-by-step explanation:

A reflection is a type of rigid transformation in which the preimage is flipped across a line of reflection to produce the image, such that the figure and its image have opposite orientations.

Since, it preserves distance.

Therefore, the points of the image have the same distance from the line as the points of pre-image on the opposite side of the line.

Hence, the right option is "the object and its image have opposite orientations".

A critical value is the point on the scale of the test statistic (z test in this case) outside which we reject the null hypothesis, and is taken from the level of significance of the test. The critical values can be obtained from the standard distribution tables for z and for this case, it is equivalent to:

critical value zα/2 at 98% confidence level = 2.326

Answer: 2.326

Answer:

2.33

Step-by-step explanation:

1 1/3 + 1 1/6

 add the 1 +1 = 2

add 1/3 + 1/6 ( find common denominator, which in this case is 6)

 so 1/3 becomes 2/6

2/6 + 1/6 = 3/6 which reduces to 1/2

 they ate  2 1/2 pints total

Step-by-step explanation:

[tex]x + 2y \leq 4[/tex]

To graph this inequality we replace <= symbol with = sign

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

subtract x on both sides

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

divide both sides by 2

[tex]y= \frac{-1}{2} x +2[/tex]

Graph the equation using a table

LEts assume some number for x  and find out y

x                           [tex]y= \frac{-1}{2} x +2[/tex]

-2                           3

0                             2

2                             1

Now graph the equation using points (-2,3)  (0,2)(2,1)

use solid line for graphing

Now use test point (0,0) for shading

[tex]x + 2y \leq 4[/tex]

[tex]0 + 2(0) \leq 4[/tex]

[tex]0 \leq 4[/tex]     true

So  we shade the region that contains (0,0)

the graph is attached below

Answer:

Vertex=(-4,3)

Focus=(-4, 2)

Directrix: y=4

Step-by-step explanation:

Given the equation

[tex]x^2+8x+4y+4=0[/tex]

we have to find the vertex, focus, and directrix of parabola.

[tex]x^2+8x+4y+4=0[/tex]

[tex]y=\frac{-x^2}{4}-2x-1[/tex]

[tex]h=\frac{-b}{2a}=\frac{2}{2(\frac{-1}{4})}=-4[/tex]

Now, k can be calculated by putting x=4 and y=k in given equation

[tex]k=-1-\frac{16}{4}-2(-4)=-1-4+8=3[/tex]

The vertex is (h,k) i.e (-4,3)

[tex]y=\frac{-x^2}{4}-2x-1[/tex]

[tex]y=\frac{1}{4}(-x^2-8x-4)[/tex]

[tex]=\frac{1}{4}(-x^2-8x-16+16-4)[/tex]

[tex]y=\frac{1}{4}(-(x+4)^4+12)[/tex]

[tex]y=\frac{-1}{4}(x+4)^2+3[/tex]

which is required vertex form [tex]4p(y-k)=(x-h)^2[/tex]

gives p=-1

Focus=(-4, 3+(-1))=(-4,2)

Now directrix can be calculated as

y=3-p=3-(-1)=4

2/3x = 4/15 =

 x = 4/15 / 2/3 =   4/15 x 3/2 = 12/30 = 2/5

x = 2/5

all i know is x=25 its hard for me to explain.

Without more information or a diagram, it's hard to give a specific answer. However, on a cube net, the face opposite 'D' is likely the one not directly connected to 'D' on the plane of the net.

Unfortunately, without a diagram or more context, it's difficult to provide a definitive answer to the question. However, typically on a cube net, sides that are opposite each other when the net is folded into a cube are adjacent (next to each other) on the net. For example, if 'D' were on a flat square in the center of the net, the squares directly connected to it (on the top, bottom, left, and right) on the plane of the net would end up being the sides adjacent to 'D' when the cube is formed. The square not connected directly to 'D' on the plane would be opposite 'D' once the cube is formed.

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