250 students in a high school senior class are surveyed about what majors they intend to declare in college. Of the 250 students, 100 plan to major in mathematics, 80 plan to major in computer science and 20 plan to pursue a double major in mathematics and computer science.

Let M be the even that a randomly selected student plans to major in mathematics and C be the event that a randomly selected student plans to major in computer science.

What is P(M), the probability that a student plans to major in mathematics?
What is P(C), the probability that a student plans to major in computer science?
What is P(M and C), the probability that a student decided to major in mathematics and computer science?
What is P(M or C), the probability that a student has chosen to major in mathematics or computer science?

Answer:

Step-by-step explanation:

(2x² - 3x  + 1 )(x - 3) = (2x² - 3x + 1)*x + (2x² - 3x + 1)*(-3)

                               = 2x²*x - 3x*x  + 1*x + 2x²*(-3) - 3x*(-3) + 1*(-3)

                               = 2x³ - 3x² + x -  6x² + 9x - 3

                               = 2x³ - 3x² - 6x² + x + 9x - 3 {Combine like terms}

                              = 2x³ - 9x² + 10x - 3

Answer:

 -17 and 2

Step-by-step explanation:

Factors of -34 are

-1, 1,-2,2, -17, 17,-34,34

   -17+2=15

so   (-17 ,2)

Answer:

0.3

Step-by-step explanation:

the small quare is 90 so do 21/60/9=

Answer:

I think c and d

Step-by-step explanation:

srry if im wrong

Answer:

it should be (-6,-2) if I remember how to do this correctly

Answer:

The percent of increase is 20

Step-by-step explanation:

(18:15-1)*100=

120-100=20

Answer:

(6,1) I’m pretty sure because it is the midpoint between the focus and directrix.

Step-by-step explanation:

Answer:

$2.25

Step-by-step explanation:

1. 20-6.50= 13.50

2. 13.50/6(pieces of candy) = $2.25

Answer:

107

Step-by-step explanation:

A circle is 360 degrees, so subtract 53,110, and 90 (right angle) from that.

Answer:

x = 107°

Step-by-step explanation:

a circle has 360°

to find 'x':

360-(53+90+110)

360 - 253 = 107

Answer:

[tex]\sqrt{80}[/tex]

Step-by-step explanation:

Pythagorean theorem (Gougu theorem) states that the hypotenuse squared is equal to the sum of the squares of two other sides. (a^2 = b^2 + c^2). Hence x^2 = 4^2 + 8^2 = 80.

As x squared is 80, x is the square root of 80.

You can factorise this into 4[tex]\sqrt{5}[/tex]

Answer:

2

Step-by-step explanation:

you take you longest side half it and it equals the other two sides

Answer:

7.26 to the nearest hundredth.

Step-by-step explanation:

The ratio opp/hyp is the sine of the angle.

So if we let the opposite side = x then

3.5/ 8.2 = x /17

x = (3.5 * 17) / 8.2

= 7.256

Answer:

XZ = 42

Step-by-step explanation:

By the property of similar triangles,

"If two triangles are similar, their corresponding sides will be proportional."

By applying the property of similarity in ΔABC and ΔXYZ,

[tex]\frac{AB}{XY}= \frac{BC}{YZ}= \frac{AC}{XZ}[/tex]

[tex]\frac{4}{24}=\frac{8}{48}= \frac{7}{XZ}[/tex]

[tex]\frac{1}{6}= \frac{7}{XZ}[/tex]

XZ = 42

Therefore, length of unknown side XZ = 42 units.

Answer:

y < 6

Step-by-step explanation:

Answer:

C) 4/(x+y)²

Step-by-step explanation:

start by expanding so it is written as 2÷(x+y)/(x+y)÷2.

Then rearrange so that it is 2×2/(x+y)×(x+y) or 4/(x+y)²

Answer:

1.5 pounds of beans are in each nag

Answer:

The completed proof is presented as follows;

The two column proof is presented as follows;

Statements    [tex]{}[/tex]                                               Reason

1. [tex]\overline {HI}[/tex] ║ [tex]\overline {KL}[/tex], J is the midpoint of [tex]\overline {HL}[/tex] [tex]{}[/tex]         1. Given

2. ∠IHJ ≅ ∠JLK[tex]{}[/tex]                                            2. Alternate angles are congruent

3. ∠IJH ≅ ∠KJL   [tex]{}[/tex]                                         3. Vertically opposite angles

4.  [tex]\overline {HJ}[/tex] ≅ [tex]\overline {JL}[/tex]   [tex]{}[/tex]                                              4. Definition of midpoint

5. ΔHIJ ≅ ΔLKJ  [tex]{}[/tex]                                         5. By ASA rule of congruency

Step-by-step explanation:

Alternate angles formed by the crossing of the two parallel lines [tex]\overline {HI}[/tex] and [tex]\overline {KL}[/tex], by the transversal [tex]\overline {HL}[/tex] are equal

Vertically opposite angles formed by the crossing of two straight lines [tex]\overline {IK}[/tex] and [tex]\overline {HL}[/tex] are always equal

A midpoint divides a line into two equal halves

Angle-Side-Angle, ASA rule of congruency states that two triangles ΔHIJ and ΔLKJ, that have two congruent angles, ∠IHJ in ΔHIJ ≅ ∠JLK[tex]{}[/tex] in ΔLKJ and ∠IJH in ΔHIJ ≅ ∠KJL in ΔLKJ, and that the included sides between the two congruent angles is also congruent [tex]\overline {HJ}[/tex] ≅ [tex]\overline {JL}[/tex], then the two triangles are congruent, ΔHIJ ≅ ΔLKJ.

Answer:

3x - 6

Step-by-step explanation:

Uwu if you want me to explain it more let me know

You didnt give a picture of the question showing the shorts

Answer:   $24.34

Step-by-step explanation:

28/X=115/100

Part/Whole= %/100

28=1.15*x

x=28/1.15

x=24.34

Answer:

0.7

Step-by-step explanation: I hope this helps!

Answer:

x < -56/3

Step-by-step explanation:

i hope this helps :)

Answer:

x < − [tex]\frac{56}{3}[/tex]

Step-by-step explanation:

-3x-11>45

-3x>56

Both side divide by -3

x>[tex]\frac{56}{-3}[/tex]

x < − [tex]\frac{56}{3}[/tex]

Answer:

Step-by-step explanation:

Clusters:

There is a cluster with a regression line of -0.4

Outliers:

(8,8) because it is not near the cluster that was said earlier.

Answer:

The maximum number of tickets Susana can buy is 8.

Step-by-step explanation:

From the information provided, you can say that the total amount spent at the carnival would be equal to the price per ticket for the number of tickets purchased which can be expressed as:

c=3x, where:

c is the total amount spent

x is the number of tickets purchased

Now, you can replace c with 24 that is the amount Susana's parents gave her to spend at the carnival and then, solve for x:

24=3x

x=24/3

x=8

According to this, the answer is that the maximum number of tickets Susana can buy is 8.

Answer:

175

[tex] {cm}^{3} [/tex]

Step-by-step explanation:

25×7=175

Answer:

175cm3

Step-by-step explanation:

How to find the volume

In math, volume is the amount of space in a certain 3D object. For instance, a fish tank has 3 feet in length, 1 foot in width, and two feet in height. To find the volume, you multiply length times width times height, which is 3x1x2, which equals six. So the volume of the fish tank is 6 cubic feet.

Multiply 25cm2 and 7cm

Therefore, the answer is 175cm3

Answer:

Expand:5x+3y

Simplify:6x^2+11xy-10y^2

Step-by-step explanation:

2x(3x-2y)+5y(3x-2y)

6x^2-4xy+15xy-10y^2

6x^2+11xy-10y^2

Answer:

( C ) 428.1 ft²

Step-by-step explanation:

Alright, we know the surface area of a shape is the area the entire outside covers. So, we just need to find the areas of each side and add them together.

Let's start with the two rectangular sides. The dimensions of both of these are 10×12. The area of rectangles can be calculated by multiplying the length and width, so let's do that. Then, we will multiply this answer by two, so we have the areas of both rectangles.

10 · 12 = 120

120 · 2 = 240

The area of the two rectangular sides is 240 ft². We have 3 sides left to solve for.

Next, we will find the area of the triangular sides. Again, we will multiply the answer by two so we have the area of both. The area of the triangle can be found by multiplying [tex]\frac{1}{2}[/tex] the width by the height.

4.5 · 8.9 = 40.05

Multiply this by two for the area of both sides.

40.05 · 2 = 80.1

The area of the triangle sides is 80.1 ft².

The last side is also a rectangle, with the dimensions 9×12.

9 · 12 = 108

The bottom side has an area of 108 ft².

Now, we can add the areas together.

240 + 80.1 + 108 = 428.1

The surface area of the shape is 428.1 ft². The answer is C.

I hope this helps ^^

Good luck :)