Colin predicted whether he got answers right or wrong in his 50 question exam.
He identified the 18 questions he thought he got wrong.
It turns out that Colin got 3 questions right that he thought he got wrong.
Colin also got a total score of 27 out of 50 in the test.
What is the percentage accuracy he had with predicting his scores?

Answer:

  17

Step-by-step explanation:

The geometry program that drew the circle through the three given points wrote this equation for the circle:

  (x -6)^2 +(y -11)^2 = 130

Compared to the standard form equation, ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . . circle with center (h, k) and radius r

we can see that the center is (h, k) = (6, 11).

The sum h+k is 6+11 = 17.

__

Additional comment

The center is at the point of intersection of the perpendicular bisectors of chords of the circle.

Here it is convenient to choose one of them as the horizontal segment with endpoints (3, 0) and (9, 0). The vertical line that bisects this segment is x=(3+9)/2 = 6. So, x=6 is the x-coordinate of the circle center.

We can use endpoints (-1, 2) and (3, 0) as another chord. Its midpoint is (-1+3, 2+0)/2 = (1, 1). The slope of this chord is (y2-y1)/(x2-x1) = (0-2)/(3-(-1)) = -1/2. So, the slope of the perpendicular bisector is -1/(-1/2) = 2, and the equation of that line is

  y -1 = 2(x -1)

For x=6, the point of intersection of the chord bisectors is ...

  y -1 = 2(6 -1) = 10

  y = 11

The coordinates of the circle center are (6, 11), so h+k = 6+11 = 17.

Answer:

Length = 8+7 = 15

Width = 8

Step-by-step explanation:

                       New

Length = x+7 , x+4

Width = x ,x+2

(x+7) x = (x+4)( x+2)

expand and simplify x =8

The length of the shorter side length of original rectangle is 8 inches and of original rectangle longer side length is 15 inches.

Let l is the length and b is the breadth of the rectangle.

then the area of the rectangle is ab.

Given One side of a rectangle is 7 inches longer than another side.

then shorter side length is x and the large side length is 7+x.

then the area of the original rectangle is x(x+7)

Now calculate the sides of the new rectangle.

longer side of this rectangle decreases by 3 then new side is 7+x -3= 4+x

The shorter side increases by 2 inches then x+2.

So new rectangle area is (x+4)(x+2)

Both rectangle area is equal then

(x+4)(x+2) = x(x+7)

x² +2x+4x+8 = x²+7x

x²+6x+8 = x²+7x

x²-x²+7x-6x = 8

x = 8

Since a shorter side length is 8 inches and a longer side length is 8+7 =15 inches.

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Answer:

v > - 78

Step-by-step explanation:

Version 1.

   v

-----------  < 92

-6 + 79

    v

------------  <  92

    73

    v

------------  <  92(73)

    73(73)

v < 6716

-------------------------------------

Version 2

    v

------------ + 79 <  92

    -6       -79      -79

        v

(-) ------------  <  13(6)

        6(6)

-v < 78

÷-1   ÷-1

v > -78

I hope this helps!

Answer: 45

Step-by-step explanation: 2 1/4 = 2hr and 15 min

1/3 of 2hr and 15 min = 45

Amount of time spent by Nathan's family watching the video is 3/4 hour or 45 minutes.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Given that,

Nathan’s family spent 2 and 1/4 hours visiting national monument near their home.

They watched a video in the visitor center for 1/3 of that time.

Total time spent by Nathan's family in the monument = 2 + 1/4 hours

                                                                                         = 9/4 hours

Fraction of time spend in watching the video = 1/3

Time spend in watching the video = 1/3 × 9/4

                                                         = 3/4 hour

                                                         = 45 minutes

Hence the time spent is 3/4 hour.

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Answer:

Radius of sphere =1unit

SurfaceareaVolume=4πr234πr3=34π(1)3×4π(1)21=31

∴V:S=1:3 cm

Step-by-step explanation:

Hope this helps. If any questions, please ask in comments.

Answer:

Step-by-step explanation:

a)

The total amount coffee beans

b)

The total amount of market price

Answer:

a)   750a + 1200r = 1000000

b)   1065a + 876r = 1000000

Step-by-step explanation:

Define the variables:

Part (a)

Given:

If the plantation yields 1,000,000 kg of coffee:

⇒ 750a + 1200r = 1000000

Part (b)

Given:

If the price of Arabica beans is $1.42 per kg, and Arabica yields about 750 kg per hectare, then the price per hectare of Arabica coffee beans is:

⇒ $1.42 × 750 = $1065 per hectare

If the price of Robusta beans is $0.73 per kg, and Robusta yields about 1200 kg per hectare, then the price per hectare of Robusta coffee beans is:

⇒ $0.73 × 1200 = $876 per hectare

Therefore, if the plantation produces coffee worth $1,000,000:

⇒ 1065a + 876r = 1000000

Answer:

6x³ - 15x² - 1

3x divided by 3x is 1

So, here we are to simplify the polynomial :

[tex] \\ \longrightarrow \sf \qquad6x^3 - 15x^2 - \frac{3x}{ 3x}\\ \\[/tex]

We can simplify it as,

[tex]\\ \longrightarrow \sf \qquad6x^3 - 15x^2 - 1 \\ \\[/tex]

Some points to know :

Answer:

Philadelphia

Step-by-step explanation:

Philadelphia

San Diego

Houston

Phoenix

Explanation:

The top bar as a darker shade represents the population in 1990, and the lighter shade down below is the population for the year 2000.

The city of Dallas has its population increase because the lighter shaded bar is longer. This rules out choice A. Choices B and C are ruled out for similar reasoning (Phoenix and San Diego also show population growth).

Only Philadelphia experiences population decline during this time period.

The surface area of the pencil is the amount of space it covers

The surface area of the pencil is 61 square centimeters

The given parameters are:

H = 20 cm

L = 0.5 cm

The surface area (SA) is then calculated as:

SA = 6LH + 3[tex]\sqrt 3[/tex]L^2

This gives

SA = 6 * 0.5 * 20 + 3[tex]\sqrt 3[/tex] * 0.5^2

Evaluate the sum

SA = 61

Hence, the surface area of the pencil is 61 square centimeters

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Answer:

140 child tickets were sold

Step-by-step explanation:

a = number of adult tickets

c = number of child tickets

a+c = 350

6.50 c + 8.50a = 2695

Multiply the first equation by -8.50 together

-8.50c  -8.50c =-2975

Add this to the second equation to eliminate a

-8.50c  -8.50c =-2975

6.50 c + 8.50a = 2695

---------------------------------

-2c   + 0a = -280

Divide by -2

-2c/-2 = -280/-2

c = 140

Answer:

Step-by-step explanation:

Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

So:

[tex]9^2+13^2=c^2[/tex]

[tex]250 = c^2[/tex]

[tex]\sqrt{250} = \sqrt{c^2}[/tex]

[tex]c = 15.8113883[/tex]

OR (rounded)

[tex]c = 15.8[/tex]

Answer:

10 years

Step-by-step explanation:

Simple interest formula:

AV=PV(1+it)

13200=8000(1+.065t)

1.65=1+.065x

.65=.065x

10=x

Answer:

  13 units

Step-by-step explanation:

Points A(-1, -6) and B(-1, 7) both lie on the vertical line x=-1. That means the distance between them is the difference of their y-coordinates:

__

  By -Ay = 7 -(-6) = 13

Segment AB is 13 units long.

Answer:

y = -2x - 5

Step-by-step explanation:

2y = x - 3

y = 1/2x - 3/2

gradient = 1/2

perpendicular gradient = negative reciprocal = -2

y = -2x + c

(-3) = -2(-1) + c

-3 = 2 + c

-5 = c

Answer:

y = -x/2 - 7/2

Step-by-step explanation:

Equation of the line (current) in y = mx + c

The slope of a perpendicular line has to be -ve to the current line.

⇒ m' = -1/2

To find the y-intercept, take the x-coordinate to be 0 and substitute in the equation :

y - y₁ = m (x - x₁)

y + 3 = -1/2 (0 + 1) [Also using the point (-1, -3) to make sure line crosses it]

y + 3 = -1/2

y = -7/2

Therefore, the new equation is :

Answer:

Step-by-step explanation:

49

Answer:

Step-by-step explanation:

(i)

PQRS is a parallelogram (given)

      ∴ QT = TS (Diagonals of a parallelogram bisects each other)

also,   QT = RM (given)

      ∴TS = RM

PQRS is a parallelogram,

     ∴RT = PT (Diagonals of a parallelogram bisects each other)

also, SM = PT (given)

    ∴RT = SM

TS = RM

RT = SM

∴ RTSM is a parallelogram (both pairs of opposite sides are equal in length)

(ii)

QP // RS (Opposite sides of a parallelogram are parallel)

∴ ∡RQP = ∡NRS (Corresponding ∡s)

RTSM is a parallelogram(Proved above)

∴MS // RT (Opposite sides of a parallelogram are parallel)

∴NS//RP

∴∡RNS = ∡ QRP (Corresponding ∡s)

in ΔPQR and Δ NSR,

QP = RS (Opposite sides of a parallelogram are equal)

∡RQP = ∡NRS (Proved above)

∡RNS = ∡ QRP(Proved above)

∴ ΔPQR≡ΔSRN (AAS)

Corresponding sides of ≡ Δs are equal, ∴QR = RN

Answer:

infinite many solutions

Step-by-step explanation:

As L.H.S = R.H.S, there are infinite many solutions

[tex]\\ \rm\Rrightarrow 5(2b+1)=10b+5[/tex]

[tex]\\ \rm\Rrightarrow 10b+5=10b+5[/tex]

[tex]\\ \rm\Rrightarrow 0=0[/tex]

Answer:

Step-by-step explanation:

Use a simple interest formula.

Simple interest formula:

→ 2000*4.6%4

You have to convert 4.6% into a decimal form.

→ 4.6%=0.046

→ I=2000*0.046*4

Solve.

Multiply the numbers from left to right.

→ 2000*0.046*4=368

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

16 rows, 8 seedlings left.

Step-by-step explanation:

Divide 200 by 12, since 200 seedlings are going to be split in 12 groups in order to fill the rows.

200 ÷ 12 = 16 with a remainder of 8.

The remainder is basically what is left.

Since 12 seedlings are planted in each row, 8 seedlings is not enough to completely fill the row. So, the answer is 16 rows with 8 seedlings left.

Hope this helped !

Tony deposited three checks as given in deposite ticket. The amount of the third check that Tony deposited is given by: Option B: $105.20

Resultant deposited amount = Deposited amount - The amount deducted.

We subtract the amount deducted from the amount deposited to get the resultant deposite amount that will go in bank.

Well, it might be that we deduced more than what we deposite, in that case net deposite will come as negative, indicating that there is deduction instead of deposite.

The missing image of the deposite ticket is attached below.

From that image, we can see that:

Thus, the net deposited amount is:

Net deposite = deposited amounts - deduced amounts

686.04 = 491.6 + 157.68 + x - 68.44 (all in dollars)

[tex]686.04 = x+ 491.6 + 157.68 - 68.44\\686.04 = x + 580.84\\\\\text{Subtracting 580.04 from both the sides} \\\\686.04 - 580.84 = x\\x = 105.20 \: \rm dollars[/tex]

Net deposite = 105.20 (in dollars).

Thus, the amount of the third check that Tony deposited is given by: Option B: $105.20

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Answer:

7.8

Step-by-step explanation:

3.2 + 4.6 = 7.8 because 6+2 equals 8 and 4+3 equals 7 so 7.8

yes it is true and second is false

Answer:

D, assuming that the function continues past the line shown

Step-by-step explanation:

There is no reason that the X is ending on either side. There should be arrows on both ends of the graphed function though.

Answer:

$1,537.14

I had this question once and this was the answrr

Answer:

3 hrs. 30 mins.

Step-by-step explanation:

7:00 - 3:30

Answer:

I'm talking about the boxes:

1st-false, there are 7/19, which is not more

2nd-true, there are 12/19 which is the most

3rd-true, 12/20 of the women like dancing

4th-false, 7/20 like dancing

5th-true, 13/20 don't like dancing

The hot air balloon's(above the eagle) elevation, relative to sea level is 98 meters

Elevation is the height to which something is elevated or to which it rises.

Therefore,

The eagle circle 48 meters above the mouse that scurried in the valley. The valley is 16 meters below sea level.

At the same time a hot ballon floated 66 meters above the eagle.

Therefore, the hot air balloon's elevation, relative to sea level is as follows;

elevation = 66 + 48 - 16 = 98 meters

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Answer:

Formula of Mean= Efx/n

Formula of Median=n+1/2

I think it will help you

Answer:

There are 3 ways to find the slope of a line.

I'll use a simple method.

First, let's look at a random point on this line(and make sure it's close to the start of the line).

I'll choose (1,4).

Then, see how much it rises and how far it runs to another fixed point.

Though, in this case we can see that the rise is going down and the run is moving towards the right. So, the slope will be negative since the rise is negative.

You always want to confirm if it'll be a negative or positive slope and which direction the slope is guiding you to.

Now, if we go down 8 and over 3, we'll reach a fixed point of (4, -4).

Therefore, we can infer that the slope of this line will be 8/3.

Answer:

8/3

Step-by-step explanation:

rise over run, only clearly intercepts a point twice.

its b i know

Step-by-step explanation: