Students taking an online english test are randomly assigned 3 questions out of a set of 9 different questions. How many different sets of questions (i.e. tests) are possible for the students?

Answer:

3x+2+6x+5x

Step-by-step explanation:

perimeter of triangle = side 1 + side 2 + side 3

expression of the perimeter of triangle 3x+2+6x+5x

perimeter of traingle = 14x + 6

The expression 14x + 2 represents the perimeter of the triangle in terms of "x."

To find an expression that represents the perimeter of a triangle.

The perimeter is the sum of all three sides of the triangle. We have three sides with different lengths given by the expressions 3x + 2, 6x, and 5x. To find the expression representing the perimeter, we just need to add these three sides together.

Let's represent the sides as follows:

- The first side of the triangle is denoted as "a," which has a length of 3x + 2.

- The second side is denoted as "b," with a length of 6x.

- The third side is denoted as "c," having a length of 5x.

Now, let's find the expression for the perimeter, which we'll call "P." To do that, we add the three sides together:

P = a + b + c

Substitute the given expressions for the sides into the equation:

P = (3x + 2) + (6x) + (5x)

Now, let's simplify the expression by combining like terms (terms with the same variable "x"):

P = 3x + 2 + 6x + 5x

To further simplify, add the coefficients of the "x" terms:

P = (3 + 6 + 5)x + 2

Now, add the coefficients: 3 + 6 + 5 = 14, so the expression for the perimeter becomes:

P = 14x + 2

The expression 14x + 2 represents the perimeter of the triangle in terms of "x."

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Answer:

30.28 yd²

Step-by-step explanation:

Area enclosed = area of trapezoid + area of semicircle

= ½(a + b)*h + ½(πr²)

Where,

a = 5 yd

b = 2 + 5 = 7 yd

h = 4 yd

r = ½(4) = 2 yd

Plug in the known values

Area enclosed = ½(5 + 7)*4 + ½(π*2²)

Area enclosed = ½(12)*4 + ½(π*4)

= 6*4 + π*2

= 24 + 2π

= 30.2831853

≈ 30.28 yd² (2 decimal places)

Answer:

x=14

Step-by-step explanation:

x - 42 = 98 – 9x

x+9x=98+42

10x=140

x=14

Answer:

[tex]x - 42 = 98 - 9x \\ x + 9x = 98 + 42 \\ 10x = 140 \\ x = 14 \\ thank \: you[/tex]

Answer:

Step-by-step explanation:

Common difference is 3.

Let x be a term in the sequence. The next term in the sequence is x+3.

x(x+3) = 598

x² + 3x - 598 = 0

x = [-3 ± √(3²-4⋅1(-598))]/[2⋅1] = [-3 ± 49]/2 = 23, -26

-26 is an extraneous solution, so x = 23.

The two terms are 23 and 26.

Answer:

25 students take both subjects.

Step-by-step explanation:

Solve for 60% of 300 students:

60/100 = x/300

Cross multiply:

60 × 300 = 100 × x

18000 = 100x

Divide both sides by 100:

180 = x

Solve for 20% of 300 students:

20/100 = x/300

20 × 300 = 100 × x

6000 = 100x

60 = x

Solve for the percentage of students in chemistry:

x/100 = 35/300

x × 300 = 100 × 35

300x = 3500

x = 11.66666...7

x = about 11.7%

Find the difference in percentages:

100 - 60 - 20 - 11.7

8.3

8.3% take both subjects

Solve for 8.3% of students:

8.3/100 = x/300

8.3 × 300 = 100 × x

2490 = 100x

24.9

About 25 students

Check your work by adding all the students together (to get to 300):

25 + 60 + 180 + 35

300 students total

This is correct!

Answer:

Equation of Ellipse is [tex]\frac{x^{2} }{32} +\frac{y^{2} }{36} =1[/tex]

Step-by-step explanation:

Let's find the value for [tex]a^{2}[/tex] and [tex]b^{2}[/tex] to write the equation for vertical ellipse.

Here 'a'  is the distance from center to one of the vertices.

"b" is the distance from center to one of the Co-vertices. We need to find this using formula [tex]a^{2} -b^{2} =c^{2}[/tex]

'c' is the distance between center to one of the Foci.

In this problem center is origin.

So, a =6(because distance between(0,0) and (0,6) is 6)

c= 2 (because distance between (0,0) and (0,2) is 2)

Plug in the known values into the formula [tex]a^{2} -b^{2} =c^{2}[/tex]

36-[tex]b^{2}[/tex]= 4

Subtract both sides 36

[tex]-b^{2}[/tex] = -32

Divide both sides by -1

[tex]b^{2}[/tex] =32

So, equation would be

[tex]\frac{x^{2} }{32} +\frac{y^{2} }{36} =1[/tex]

Answer:

233.05

Step-by-step explanation:

take the diameter and divide it by 2, that will give you the radius. Take the radius and multiply it by 2 then by pi. That will give you the circumference. So for the this question it would be:

71 divided by 2 = 35.5cm

35.5 x 2 x pi = 233.05

Answer:

B

Step-by-step explanation:

We do 20 percent of 2500 which comes to 1500 and then you do plus 325 which gives you 2625

Answer:

m<√-3 OR m<√3i

Step-by-step explanation:

f(x)=x²+2m(x+1)-3

with x<0

b²-4ac<0

(2m)²-4(1×-3)<0

4m²+12<0

4m²<-12

m²<-12/4

m²<-3

m<√-3 OR m<√3i

Answer:

D. 195 cm^2

Step-by-step explanation:

The given is a trapezoid and to calculate the are of it we use the following formula :

(a+b)/2*h (a: base, b: base, h: height)

(9+21) / 2 * 13 = 195

Answer:

22.4 cm

100% 2021 on edge!

Step-by-step explanation:

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See this attachment

Answer:

A = 18 units²

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h ( b₁ + b₂ )

where h is the perpendicular height and b₁, b₂ the parallel bases

By counting squares

h = 3, b₁ = 3, b₂ = 9 , then

A = [tex]\frac{1}{2}[/tex] × 3 × (3 + 9) = 1.5 × 12 = 18 units²

4x2-3x+1

represents the polynomial below written in standard form

Answer:

the question?

Step-by-step explanation:

Hi, you've asked an incomplete question. Attached is the full question.

Answer:

1. c and b

2. No. The definitions have opposite results.

Step-by-step explanation:

1. Two different ways Analia could define this quantity is:

2. Indeed, whatever the definition selected, they both have opposite results.

Answer:

1.C and B

2. Yes. According to both definitions, School B has the lower SAT range relative to the resources invested per student.

Step-by-step explanation:

Got it wrong  on khan and used a hint these are the answers

Angle 4 and Angle 2 are vertical angles, meaning that they are congruent. Therefore, the measure of angle 2 is 127 degrees.

Angle 4 and Angle 3 are a linear pair, meaning that they are supplementary and add up to 180 degrees. Therefore, the measure of angle 3 is 53 degrees.

Angle 3 and Angle 1 are vertical angles, meaning that they are congruent. Therefore, the measure of angle 1 is 53 degrees.

Hope this helps!

Answer:

<1 = 53

<2 =127

<3 = 53

Step-by-step explanation:

Angles 2 and 4 are vertical angles and vertical angles are equal

<2 = <4 = 127

<1 + <2 =180 since they form a straight line

<1 + 127 = 180

< 1 = 53

<1 and <3 are vertical angles so they are equal

<1 = <3 = 53

Answer:

Step-by-step explanation:

C -> Percentage of people who take cold drinks

H -> Percentage of people who take hot drinks

J - > Percentage of people who take Juice

i) At least one of drinks = 17 + 3 +15 +18 +7 + 15 + 5 = 75%

ii)  Exactly two types of drinks = Percentage of people who take cold  and hot drinks + Percentage of people who take cold and Juice + Percentage of people who take hot drinks and Juices

= 15 + 13 + 7

= 35%

iii) Exactly one type of drink =  Percentage of people who take only cold drinks + Percentage of people who take only hot drinks + Percentage of people who take only juices

= 17 + 3 + 15

= 35%

iv) None of the drinks = Total percentage - at least one of the drinks

                                    = 100 - 75

                                    = 25%

Answer:

° 3/2 × 4/15

Step-by-step explanation:

for checking a division problem use the product and one of the fractions to multiply. if the answer matches the other fraction then your division is correct.

Answer:

x<_-3 or 2_<x<7 or A

Step-by-step explanation:

Hope it helps

Answer: 6 blocks

Step-by-step explanation:

Given

Volume of the rectangular prism is [tex]V=\dfrac{3}{4}\ yd^3[/tex]

Length of the cubic block is [tex]a=\dfrac{1}{2}\ yd[/tex]

Volume of each cubic block is

[tex]\Rightarrow V_o=\left (\dfrac{1}{2}\right)^3\\\\\Rightarrow V_o=\dfrac{1}{8}\ yd^3[/tex]

Suppose, n blocks are required to measure the volume of Prism

[tex]\Rightarrow V=nV_o\\\\\Rightarrow \dfrac{3}{4}=n\cdot \dfrac{1}{8}\\\\\Rightarrow n=\dfrac{3\times 8}{4}\\\\\Rightarrow n=6\ \text{blocks}[/tex]

Thus, 6 blocks are required to measure the volume of prism.

Yes that person is correct

The image of the bar chart is missing and so i have attached it.

Answer:

Bus = 75

Cycle = 20

Walk = 45

Step-by-step explanation:

We are told that 50 students said they travel to school by car.

However, in the bar chart, we see that we have a portion for boys and girls

Under car, when we count along the y-axis, we will see that, there are 6 units for boys and 4 units for girls.

Thus, to find the value of a unit since number of people that took cars is 50, we have;

(6x + 4x)/2 = 50

Where x is the value of one unit. Thus;

10x/2 = 50

5x = 50

x = 50/5

x = 10

Thus, a unit is 10

Under bus;

Boys have 7 units while girls have 8 units.

Thus;

Frequency by bus = ((7 × 10) + (8 × 10))/2 = 150/2 = 75

Under cycle;

Boys have 1 unit while girls have 3 units.

Thus;

Frequency by cycle = ((1 × 10) + (3 × 10))/2 = 20

Under walk;

Boys have 5 units while girls have 4 units.

Thus;

Frequency by cycle = ((5 × 10) + (4 × 10))/2 = 45

The statement that is true about the variables analyzed is that there is a negative correlation between the number of miles driven and the gallons of gasoline left in the tank.

This refers to the relation or connection between two or more variables. In this case:

This has the sign -, which shows the correlation is negative. This implies that as the number of miles increase the amount of gasoline decreases.

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Step-by-step explanation:

C. angle bisector

hope this helps you

have a nice day:)

A line PQ is the median of triangle PRS.

A median of a triangle is a line segment that join a vertex to the mid-point of the side that is opposite to the vertex.

According to the given question.

We have a triangle PRS in which a line segment PQ dividing the side RS in two equal parts means point Q is acting as a mid point for RS.

Since, RS is the side which is opposite to the vertex P, and PQ is dividing RS in two equal parts therefore, PQ is the median of the triangle PRS.

Thus, option D is correct.

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Answer:

A' : {2, 4, 5, 6, 8, 9, 10, 11, 13, 15, 16, 18}

Answer:

she should add 2 cups of water.

Step-by-step explanation:

2 : 1 = 4 : 2

cosine 122.2 = -0.532876276......