The histogram below gives the distribution of test scores for a sample of
students in a school in Alaska. Which answer choice gives the number of
students that scored above 50.5?

9514 1404 393

Answer:

  E)  25.5 units²

Step-by-step explanation:

The figure is not carefully drawn, so it is difficult to tell that it is a trapezoid. The "height" of it is BC, the diagonal of a rectangle that is 1 unit by 4 units. The Pythagorean theorem tells you that length is ...

  BC = √(1² +4²) = √17

We notice that the "bases" of the trapezoid (CD and AB) are 1 and 2 times this length. The trapezoid area formula tells us the area is ...

  A = 1/2(b1 +b2)h

  A = 1/2((√17)(1 +2))(√17) = 3/2(17) = 25.5 . . . . square units

_____

Alternate solution

Pick's Theorem is a theorem that can help you find the area of a polygon when its vertices are all on grid points. It tells you the area is ...

  A = i + b/2 -1

where i is the number of grid points interior to the figure, and b is the number of grid points on the boundary. Here, the boundary grid points are those that are labeled plus the one at (-2, 1). Counting the interior grid points gives a total of 24, so the area by Pick's theorem is ...

  A = 24 + 5/2 -1 = 25.5 . . . square units

__

Additional comment

Once you're familiar with Pick's theorem (and/or any of a few other methods of computing area from coordinates), you see that the area of any polygon whose vertices are grid points will be an integer multiple of 1/2. The only such answer choice here is choice E.

Benefit she gets monthly is = 42.25-12.5= 29.75

annual value to Tamsen of this benefit= 12×29.75 = 357$

Answer:

The negative sign is put before numbers to make them negative, or make their signs the opposite of what the are.

You have a 20.

+ 20

You don't need to put the + there if there is nothing before it, but that is a positive 20.

If you put a negative in front of it;

- (+ 20) = - 20

If you have a negative in front of parenthesis;

50 - (2x - 20)

50 - 2x + 20

70 - 2x

Answer:

Function 2 has the steeper slope.

Step-by-step explanation:

Answer:

a. -1

b. -3

Explanation:

To solve negative and positive numbers on the number line, we make a simple analogy. If we wanted to -3+2 for instance:

Imagine a customer placed an order for 3 bags of apples from your store but you are out of stock and only have 2 bags left. You then come to an agreement with the customer to send 2 bags now and send the remaining one later in the week when your stock arrives from your supplier. In this way, you are only able to send two bags which you have,+2, and then be owing the customer one bag left(-1) to deliver out of the three, -3.

To solve -2+1 on the number line, with -2 on the left side of 0(negative) on the number line and +1 on the right side of 0(positive), we use same analogy above.

-2+1= -1

Also using same analogy, -2+(-1)= -3

Note: +1×-1=-1

Answer:7+7=0

Step-by-step explanation: bc im smart

Answer:

x=√30

Step-by-step explanation:

Because the triangle is equilateral and is cut by the bisector, both triangles are 30-60-90 triangles. Therefore, to find side x, you multiply the short side by √3. This means that side x is √10*√3=√30 units.

Answer:

if these are points on a graph, then the point (3,-2) has y-value 2 below the point at (3,0).

Step-by-step explanation:

Answer:

Triangle DEF

Step-by-step explanation:

Hi there!

A translation of a shape occurs when all the coordinates of the original image is shifted up, down, left or right by an equal value.

Triangle ABC is a reflection of the grey triangle across the y-axis. We know this because the y-axis acts like a line of symmetry between the two shapes.

Triangle DEF appears as if it's been shifted. Therefore, triangle DEF is a translation of the grey triangle.

I hope this helps!

Lines parallel to each others only occur when two slopes of equations are same. The definition of parallel lines is:

[tex] \large \boxed{m_1 = m_2}[/tex]

We are given the equation of a line which is x = -2. For x = a, the equation forms a verical line and has an undefined slope. These below are basic that you may need to learn when learning about the line graph:

Back to the question. We want to find the equation of a line that is parallel to the line x = -2 and passes through (5,4) point. Recall the definition of parallel line that both slopes of equations must equal. Since x = a for any a-values would give an undefined slope. That means our parallel would be x = b.

Because the line passes through (5,4) - for any a-values from x = a would give out the set of all real numbers for range. Therefore the equation of a line is x = 5.

Answer

I hope this helps! If you have any doubts or questions, don't hestitate to ask in comment! Good luck on your assignment and have a great day!

Answer:

$728.00

Step-by-step explanation:

10m*14m=140m

140*$5.20=$728.00

Answer:

Mistakes:

Used addition

Didn't flip inequality form

Corrections:

Divide each term

Instead of a positive value it should be negative

flip the direction of the inequality form

Step-by-step explanation:

[tex] - 9x \div - 9 \leqslant 90 \div – 9 [/tex]

cancel the common factor

[tex] \times \leqslant 90 \div - 9[/tex]

Divide 90 by – 9

Answer is:

[tex] \times \leqslant - 10[/tex]

Hope this helps!

Answer:

14 cm

Step-by-step explanation:

Use the formula for the area of a square, a = s², where s is the side length of the square.

Plug in 196 as the area, then solve for s.

a = s²

196 = s²

14 = s

So, the length of the pathway is 14 cm

Answer:

143.7cm^2

Step-by-step explanation:

Given data

Volume= 576cm^3

Radius= 8cm

The expression for the volume of cylinder is

V= πr^2h

substitute

576= 3.142*8^2*h

576= 3.142*64*h

576= 201.088h

h= 576/201.088

h=2.86cm

The formula for finding the lateral area of a right circular cylinder is:

A=2πrh

substitute

A= 2*3.142*8*2.86

A= 143.7cm^2

Hence the area is 143.7cm^2

Answer:

7

Step-by-step explanation:

I just guessed 7 and believe me its right

Answer:

642 miles

Step-by-step explanation:

Distance of Midville from their home = 214 miles

Walesburg is 3 times as far.

How far is Walesburg from their home?

Distance of Walesburg from their home = 3 × Distance of Midville from their home

= 3 × 214 miles

= 642 miles

Distance of Walesburg from their home = 642 miles

Answer:

perp. just switch from -2/5 to positive 5/2

Step-by-step explanation:

Answer:

m2 =5/2

Step-by-step explanation:

m1=-1/m2

m2=-1/m1

y=-2/5x-10

m1=-2/5

m2= -1/-2/5

m2=5/2

y=5/2x-10 ⊥ y=-2/5x-10

Answer:

24radios

Step-by-step explanation:

Given that the dollar cost of producing x ratios is c(x)=800+40x-0.2x^2. Find

Average cost is expressed as dC(x)/dx

dC(x)/dx = 40-0.4x

C'(x) = 40 - 0.4x

If x = 40

C'(40) = 40 - 0.4(40)

C'(40) = 40 - 16

C'(40) = 24

Hence the average cost per radio of producing the first 40 radios is 24radios

Use calculator for the solving:

12 / 24 - 3/216 +5600 -5554 = ?

Answer: 46.4861111111

Hopefully it's correct :)

Answer:

x=-8

Steps:

Simplify-

−3(−7−x)= x+2/2

Simplify-

−3(−7−x)= 1+ x/2

Multiply both sides by 2-

−6(−7−x)=2+x

Expand-

42+6x=2+x

Subtract 2 from both sides-

42+6x−2=x

Simplify-

6x+40=x

Subtract 6x from both sides-

40=x−6x

Simplify-

40=−5x

Divide-

-40/5=x

Simplify-

-8=x

Switch sides-

x=-8

I believe this is correct, if not let me know and I will fix it.

Answer:

[tex]\huge\boxed{Answer\hookleftarrow}[/tex]

Given,

[tex]3x - 2y = 5[/tex]

[tex]xy = - 2[/tex]

Now,

[tex](3x - 2y) {}^{2} = (5) {}^{2} \\ [/tex]

Use the algebraic identity ⇻ (a - b)² = a² - 2ab + b²

[tex](3x - 2y) {}^{2} = (5) {}^{2} \\ 3x {}^{2} - 2 \times 3x \times 2y + 2y {}^{2} = 5 {}^{2} \\ 9 {x}^{2} - 12xy + 4y {}^{2} = 25 \\9x {}^{2} + 4y {}^{2} = 25 + 12xy \\ 9x {}^{2} + 4 {y}^{2} - 1 = 24 + 12xy[/tex]

✐ So, the value of 9x² + 4y² - 1 is 24 + 12xy

Now,

xy = - 2

So, 12xy = 12 × - 2 = - 24

•°• 24 + 12xy

= 24 + (-24)

= 24 - 24

= 0

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

# ꧁❣ RainbowSalt2²2² ࿐

Answer:

[tex]( -2 ,\:-6) [/tex]

Step-by-step explanation:

Given points are: [tex] S=(-7,-8)=(x_1, \:y_1) \:\&\:T= (3,-4)=(x_2, \:y_2) [/tex]

Midpoint of segment ST

[tex]M=( \frac{x_1+x_2}{2} ,\:\frac{y_1+y_2}{2}) [/tex]

[tex]M=( \frac{-7+3}{2} ,\:\frac{-8+(-4)}{2}) [/tex]

[tex]M=( \frac{-7+3}{2} ,\:\frac{-8-4}{2}) [/tex]

[tex]M=( \frac{-4}{2} ,\:\frac{-12}{2}) [/tex]

[tex]M=( -2 ,\:-6) [/tex]

Answer:

1200 Containers

Step-by-step explanation:

According To The Question, We Have

By All this Data We Found That, Basically A Big Size Cuboid is Formed Here.

Now, For The Total Numbers Of Containers = 10×15×8 = 1200 Containers

Answer:

b=57° (vertically opposite angles)

Step-by-step explanation:

57°+a+b+c=360° (angles around a point)

57°+57°+a+c=360°

114°+a+c=360°

a+c=360°-114°=246°

a=c (vertically opposite angles)

therefore 2a=246°

a=123°

b=123°

Answer:

w> -24

Step-by-step explanation:

w +6 > -18

Subtract 6

w+6-6 > -18-6

w> -24

Answer:

16.7 miles

Step-by-step explanation:

6.7+10=16.7

The two of them ran 16.7 miles.

Answer:

[tex]12\frac{1}{5}[/tex] in

Step-by-step explanation:

That's the correct answer :)