1. A small college requires its students to take at least one Mathematics course and at least one Science course. A survey of 140 of its students shows that:
60 completed their Mathematics requirement, 45 completed their Science requirement and 20 completed both Mathematics and Science requirements. Use a Venn diagram to find the number of students who had completed:
a. exactly one of the two requirements;
b. at least one of the requirements;
c. neither requirement.

Answer:

x = 20

Step-by-step explanation:

For the lines to be parallel, then (3x + 20) and (3x) are alternate angles and congruent, thus

3x = 2x + 20 ( subtract 2x from both sides )

x = 20

Answer:

Y=[tex]\frac{1}{3}[/tex]X-4

Step-by-step explanation:

Using the slope-intercept equation, a line is given as y=mx+b, where m represents the slope and b represents the y-intercept. From this graph, we can see that the slope is 1/3 and this line meets the y-axis at -4.

Thus, using that information, we substitute this into the equation to get

y= (1/3)x - 4

9514 1404 393

Answer:

  linear

Step-by-step explanation:

The slope of the line between the first pair of points is ...

  m = (y2 -y1)/(x2 -x1)

  m = (3 -2)/(1 -0) = 1/1 = 1

The slope of the line between the second pair of points is ...

  m = (4 -3)/(2 -1) = 1/1 = 1

The slopes are the same, so the points are on the same line. The graph is that of a linear function.

Answer:

0 > -9

Step-by-step explanation:

8 > -1

-8   -8

0 > -9

Answer:

0 solutions

Step-by-step explanation:

when the 2 equations aresolved they get cancelled off each other.

Answer:

Infinite solutions

Step-by-step explanation:

got it right

Answer:

Formula:(from trigonometry)

Tan(A+B)=(tanA+tanB)/(1-tanA*tanB)

Let A=22 degrees,B=23 degrees

Tan(22+23)=(tan22+tan23)/(1-tan22*tan23)

From trigonometry we know tan45=1

Therefore tan(45)=1=(tan22+tan23)/(1-tan22tan23)

=> 1-tan22tan23=tan22+tan23

=> tan22+tan23+tan23tan22 =1

Hence proved

****************DISCLAIMER****************

might not be right, im pretty sure tho

Answer:

the annual interest return rate is .025 i believe.

Step-by-step explanation:

after 6 months the money increased by 5.75 bucks.

the 6 month return rate was .0175, so double that to get the annual rate.

Answer: $1.4

Step-by-step explanation:

Given that:

Discounted price roses = $1

Amount saved = $4

Regular price - discounted price = amount saved

x - 10(1) = 4

x - 10 = 4

x = 4 + 10

x = $14

Regular price of 10 roses = $14

Regular price per rose = $14 / 10 = $1.4

Answer:

It’s either 2 or 3 but I’m say 2.

Answer:

6 units :)

Step-by-step explanation:

The value of x is 5, the correct option is B

A quadrilateral with one side parallel to the other is a Trapezoid.

The midline in a trapezoid is parallel to its bases and the length is equal to half the sum of the bases.

In the figure attached the length of one of the parallel sides and the midline is given, the other base length has to be determined.

The length of AB = 12.6

The length of the midline EF = 8.8

The value of x =?

From the definition,

8.8 = (12.6 + x) /2

8.8 * 2 = 12.6 +x

x = 5

Therefore,the correct option is B.

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Answer:

-12p+p^2+36

Step by step explanation:

(-p+6)^2 is the square of -p+6

we use the formula

(a+b)^2=2ab+a^2+b^2

(-p+6)^2=-12p+p^2+36

the minus of p disappears

I think you meant to say the SQUARE ROOT.

sqrt{-p + 6}

If you meant to SQUARE THE BIMOMIAL, then the set up is:

(-p + 6)^2

(-p + 6)(-p + 6)

p^2 -12p + 36

Answer:

25.5

Step-by-step explanation:

Just did it

Answer:

Yes

Step-by-step explanation:

-4,-9/4, 1/2,s.r. 5, 3.7

Answer:

infinite

Step-by-step explanation:

trust me I would know im a smart man in college

Two or more expressions with an Equal sign is called as Equation.6(3-5w)=5(4-2w)-20w have no solution

Two or more expressions with an Equal sign is called as Equation.

The given equation is 6 times of three minus five w equal to five times of four minus two w minus twenty w.

6(3-5w)=5(4-2w)-20w

Apply distributive law on LHS side

6(3)-6(5w)=5(4)-5(2w)-20w

18-30w=20-10w-20w

Let us take all the variable w terms to one side

18-20=30w-10w-20w

-2=0

Hence based on the given equation , it has no solution.

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Hey,

Length to width ratio ;

[tex] \frac{10}{6} = \frac{10 \div 2}{6 \div 2} = \frac{5}{3} [/tex]

`Sorry if it's wrong

Good luck :)

Answer:

Step-by-step explanation:

if he has 500 and wants to have 200 left subtract 500-200=300

then if he spends 24 each week divide 300/24=12.5

the maximum number is 12 because cant have a remainder

at the end of the summer he would have 212 left.. 12x24=288..500-288=212

Answer:

12 weeks .

Step-by-step explanation:

24 x 12 = 288 . 24 x 13 = 312 .

500 - 288 = 212 . 500 - 312 =188 .

its 12 because if you do 13 its to below the price so you'll have some change left .

Answer: -3486784401

Step-by-step explanation:

This is a geometric progression and the formula to use to find the nth term will be: = ar^(n-1)

where,

a = 3

r = -9/3 = -3

n = 20

Therefore, ar^(n-1)

= 3 × -3^19

= 3 × -1162261467

= -3486784401

Answer:

y=-x+3.

Step-by-step explanation:

The graph goes down one and right one before making another point. This means that the slope is -1/1. Simplify and you get -1. So far we have y=-1x. -1x is the same as -1. Now we have y=-x. The graph intersects the y-axis at the point (0,3). This makes our y-intercept 3. Our final equation is y=-x+3.

Answer:

Exact Form:

557/24

Decimal Form:

23.208¯3

Mixed Number Form:

23   5/24

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

Answer:

3/2x

Step-by-step explanation:

x feet and half x = x+1/2x or 3/2x

Hope this helps plz hit the crown :D

Answer: 225

Step-by-step explanation:

Answer:

C= -50x+475

Step-by-step explanation:

Step one:

given data

distance travelled = 475miles

velocity = 50miles per hour

let the distance you cover per hour be x

hence per hour, your distance decreases by 50x hours

Required:

The expression for the distance remaining

Step two:

let the distance remaining be C

hence the expression

C= -50x+475

Answer:

The answer is in the picture.

Question:

The height of Peter’s baseball is given by the graph below (See attachment)

Answer:

Step-by-step explanation:

The (a) & (b) will be answered by making reference to the attachment.

Solving (a): Time to reach maximum height

The height is plotted at the vertical axis while the time taken is at the horizontal axis.

From the attachment; the following details can be observed

Using function notations, this can be represented as:

[tex]f(1.5) = 90[/tex]

And the interpretation is that:

Peter's baseball reached the maximum height at 1.5 seconds

Solving (b): Time to hit the ground

The interpretation of this question is to solve for the x intercept of the graph.

From the attachment; the following details can be observed

Using function notations, this can be represented as:

[tex]f(4) = 0[/tex]

And the interpretation is that:

Peter's baseball hit the ground at 4 seconds

The polygon has 6 sides.

'A polygon, in geometry is any closed curve consisting of a set of line segments (sides) connected such that no two segments cross.'

According to the given problem,

Sum of measures of angle = 720

We know,

Sum of interior angles of polygon = 180( n - 2 )

Where, n = number of sides.

⇒ 180( n - 2 ) = 720

⇒ n - 2 = 720/180

⇒ n - 2 = 4

⇒ n = 6

Hence, we can conclude that the polygon has 6 sides.

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Answer:

D

Step-by-step explanation: