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1 year ago

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The science teacher has to write report cards for all her students. It takes 1/8 of an hour to complete one report card. How man

y report cards can the teacher complete in 14 hours?

1 answer:

Vinvika [58]1 year ago

4 0

Answer:

112

Step-by-step explanation:

If she takes 1/8 of an hour to complete one then she can finish 8 in 1 hour.

8 x 14 = 112

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If y varies directly as x, and y is 20 when x is 4, what is the constant of variation for this relation?

yuradex [85]

Y
y=ax
where a is a constant of proportionality;
y=20, x=4
20=4a
a=20/4
a=5
y=5x
The constant of variation is 5

3 0

3 years ago

Refer to the diagram shown.

Serggg [28]

Answer:

60º

Step-by-step explanation:

3 0

3 years ago

If the distance between the points (2, -2) and (1, x) is 5 one of the values of x is

son4ous [18]

Answer:

2.899

Step-by-step explanation:

The formula for calculating the distance between two points P(x1, y1) and (x2, y2) is expressed as:

D = √(x2-x1)²+(y2-y1)²

Given the points (2,-2) and (1,x) and the distance between the point as 5, we are to get x. To get x we will substitute the points and the distance given into the formula.

Given x1 = 2, y1 = -2, x2 = 1, y2 = x and D = 5

On substitution:

5 = √(1-2)²+(x-(-2))²

5 = √1²+(x+2)²

5 = √1+(x+2)²

Square both sides of the equation

5² = (√1+(x+2)²)²

25 = 1+(x+2)²

(x+2)² = 25-1

(x+2)² = 24

Square both sides

√(x+2)² = √24

x+2 = √24

x = √24- 2

x = 4.899-2

x = 2.899

Hence the other value is 2.899

7 0

3 years ago

A pencil consists of a cone stacked on top of a cylinder. The diameter of the cylindrical base of the pencil is 10 mm and the he

Anna11 [10]

Answer:

$790\pi\,\,mm^2$

Step-by-step explanation:

Given: The diameter of the cylindrical base of the pencil is 10 mm and the height of the cylinder is 70 mm, while the height of the cone is 12 mm

To find: surface area of the pencil

Solution:

Radius of the cone = Radius of the cylinder (r) = diameter/2 = $\frac{10}{2}=5\,\,mm$

Height of the cylinder (H) = 70 mm

Height of the cone (h) = 12 mm

Slant height of the cone (l) = $\sqrt{r^2+h^2}=\sqrt{5^2+(12)^2}=\sqrt{25+144}=\sqrt{169}=13\,\,mm$

Curved surface area of cone = $\pi rl=\pi (5)(13)=65\,\pi \,\,mm^2$

Surface are of cylinder = curved surface area of cylinder + base area of cylinder

$=2\pi rH+\pi r^2\\=\pi r(2H+r)\\=\pi(5)\left [ 2(70)+5 \right ]\\=5 \pi\left ( 140+5 \right )\\=725\pi\,\,mm^2$

So,

surface area of the pencil = Curved surface area of cone + Surface are of cylinder = $65\pi+725\pi=790\pi\,\,mm^2$

5 0

3 years ago

Fraction 33/100 as decimal

Rashid [163]

33/100 = 0.333333333

The 3 goes on and on.

7 0

2 years ago

Read 2 more answers